{ "about": { "fixture": "Oracle fits for the 33 synthetic curves and the worked MTT example, the rules that decide what is shown, Z' and F-tests by hand (brief sections 4.3 and 5.4)", "ruling": "CSO ruling, 6 October 2026 (items 6 to 9): Wald, profile, the not-determinable rules, 1/Y^2 weighting and Z'; with the CSO's confirmation of the same day (items 1, 2, 4, 5 and 8): no finite minimum, C32 and C33, direct minimisation under weighting, the bend-point constant and the weighted flat line", "generatedBy": "pipeline/assay-analyser/reference.R", "scriptSha256": "912ea05cabc1bd2ddccee30bc815ee09defd3b505ab717c10c4cbfdbc39420f7", "recordedOn": "2026-10-06", "r": "R version 4.3.3 (2024-02-29)", "packages": [ { "name": "drc", "version": "4.0-0", "licence": "GPL-2" }, { "name": "MASS", "version": "7.3-60.0.1", "licence": "GPL-2 | GPL-3" }, { "name": "jsonlite", "version": "1.8.8", "licence": "MIT + file LICENSE" } ], "platform": "x86_64-pc-linux-gnu", "inputs": { "syntheticCurves": { "file": "pipeline/assay-analyser/fixtures/synthetic-curves.json", "sha256": "6b564a434829d9250f230bbc5fe6dd552e69819422af490b2693931d57e0928a" }, "mttExample": { "file": "pipeline/assay-analyser/fixtures/mtt-example.json", "sha256": "50029b58c869ecb47767215f6b6ba9b54ef33575a77dcd1044cf2c6b3c2a8214" }, "zPrimeControls": { "file": "pipeline/assay-analyser/fixtures/zprime-controls.json", "sha256": "dd3f2b587d4585ac1a15ab09c3f39de68087920a4297491245c0a8a0fa6bb356" } }, "oracleLicence": "drc and MASS are GPL; build-time oracles only, never shipped; this script is MIT and calls them by their public API", "rule": "No value in this file comes from the Drybench engine under test.", "review": { "status": "awaiting the Q-19 reviewer's signature on this regenerated file (the CEO names the reviewer)", "reviewer": null, "signedOn": null }, "model": "y = Bottom + (Top - Bottom) / (1 + 10^((logIC50 - x) * Hill)), x = log10(concentration in M)", "drcMapping": "drc LL.4 f(x) = c + (d - c) / (1 + exp(b (log(x) - log(e)))): e = IC50 = 10^logIC50, b = -Hill, c = Bottom, d = Top. LL2.4 is the same curve with e = log(IC50) (natural log).", "confidenceLevel": 0.95, "oracles": { "estimates": "expected.estimates = bestFit: the lowest objective found (nls from the generating parameters and from drc's estimates; drc LL.4 where its unweighted minimum is lower)", "wald": "expected.waldLogIC50 = the nls fit's Wald interval on logIC50, logIC50 +/- t(0.975, n - p) x SE with SE from (J^T J)^-1 s^2, wherever nls converged; badge 'Wald interval on log10 IC50'. drc LL2.4's interval (drcLL24.waldLogIC50) is a cross-check only; drc LL.4's linear-scale interval on IC50 is never used and is not recorded", "profile": "expected.profileLogIC50 = directProfileLogIC50: logIC50 held at each value and the other free parameters refitted; a bound is where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found by root finding; unbounded when not reached within 10 log10 units. MASS confint() (nls.profileCrossCheck) interpolates along a spline: cross-check only", "weighting": "1/Y^2 weighting by the fitted curve (C24, C25): minimise sum(((y - f) / f)^2) directly, the residual (y - f) / f with its full Jacobian, and take the Wald and profile intervals on that objective (CSO confirmation, item 4; GraphPad 'Math theory of weighting', Prism 11 guide, read by the CSO 6 October 2026); refuse if any fitted value is zero or below. nls with the one-sided formula ~ (y - f) / f; drc cannot weight by the fitted curve, so it gives start values only. nls.irlsCrossCheck shows that iteratively reweighted least squares settles elsewhere; agreement with Prism is not checked.", "noFiniteMinimum": "Where least squares has no finite minimum (minimumCheck: polishing keeps lowering the objective toward a limit no finite 4PL reaches), expected.engineMustReport is 'no finite minimum' and the engine shows and exports no estimates, intervals or parameters; on every other fitted curve it is 'a minimum' (CSO confirmation, item 1)" }, "tolerances": { "ruling": "CSO ruling, 6 October 2026", "logIC50": { "absolute": 0.00043, "unit": "log10 units (0.1 percent in concentration)" }, "hill": { "relative": 0.001 }, "topAndBottom": { "absolute": "0.001 x |Top - Bottom|, from the oracle's estimates" }, "waldBoundsLogIC50": { "absolute": 0.0022, "unit": "log10 units (0.5 percent in concentration)" }, "profileBoundsLogIC50": { "absolute": 0.0043, "unit": "log10 units (1 percent in concentration)", "appliesTo": "every finite bound of every fitted curve, withheld values included; the two curves with no finite minimum (expected.minimumAttained false: C30 and MTT Compound C) have no profile to compare" }, "unboundedFlags": "exact, using the oracle's search limit of 10 log10 units each side of the estimate", "objective": { "relative": 1e-06, "note": "the engine's (weighted) residual sum of squares within 1e-6 relative of expected.objective; if the engine's is lower, rerun the oracle" }, "fixedParameters": "exact", "rules": "withheldBy, shown and every count in ruleChecks exact", "notRuled": "The ruling sets no tolerance for F, p, absolute IC50 or Z'; they are arithmetic on the oracle's numbers (suggestion: 1e-6 relative)", "never": "No percentage tolerance on a logarithm" }, "rules": { "source": "CSO ruling, 6 October 2026 (item 8); rules (iv) and (v) from Sebaugh 2011 (PMID 22328315, abstract read by the CSO 6 October 2026): 'at least two assay concentrations beyond the lower and upper bend points'; k = 4.6805 (Sebaugh and McCray 2003, paper not yet read), the root of (k - 1) ln k = k + 1 by the CSO's arithmetic (CSO confirmation, item 5)", "bendConstant": { "k": 4.6805, "rootOfEquation": 4.68049857988291, "equation": "(k - 1) ln k = k + 1", "spanFromEachPlateau": 0.176040841475222, "note": "the bend points lie 1 / (1 + k) = 17.6 percent of the span from each plateau" }, "counting": "counts are of distinct concentrations with at least one kept well", "order": "applied in order; the first of (i) to (v) that fires withholds the value and gives the reason; (vi) keeps the value and adds a flag", "i": "refuse: fewer than four concentrations, or any concentration of zero or below used as a point (not fitted)", "ii": "no response: flat-line F-test p >= 0.05. The flat line is fitted by the full model's objective: y = mean(y) unweighted, y = sum(y^2) / sum(y) under 1/Y^2 weighting (CSO confirmation, item 8; the mean under weighting is kept as crossCheckMean); F = ((objective_flat - objective_4PL) / (p - 1)) / (objective_4PL / (n - p)), p free 4PL parameters, n kept wells; p is approximate for a nonlinear model (the methods page says so). Withholds both IC50s.", "iii": "relative IC50 not bracketed: fewer than two concentrations on either side of the fitted IC50", "iv": "relative IC50, plateau unbracketed: fewer than two concentrations at or beyond a free plateau's bend point, logIC50 -/+ log10(4.6805) / |Hill| (Top's on the low-concentration side of a falling curve); a plateau the user fixed is exempt", "v": "absolute IC50 (percent-of-control responses only): fewer than two concentrations where the fitted curve is below 50, or fewer than two where it is above 50", "vi": "poorly determined (relative IC50, value kept with the flag): profile interval wider than two log10 units, or unbounded", "noFiniteMinimum": "on a fit with no finite minimum, rules (ii) to (v) are evaluated at the best point (expected.rulesAtBestPoint); if none fires, both IC50s are still withheld (withheldBy 'noFiniteMinimum'): 'IC50 between {c1} and {c2}' for a step-shaped fit, otherwise 'no finite best fit' (CSO confirmation, item 1)", "reasonTexts": "expected.*.reason is the oracle's wording, except what the CSO wrote: 'IC50 beyond the highest concentration' and 'below 50 percent only at 100 M' (ruling, item 8; U+00B5 MICRO SIGN), and 'IC50 between {c1} and {c2}' and 'no finite best fit' (confirmation, item 1). Tests assert withheldBy and shown exactly; the wording belongs to the CPO." }, "fitSettings": { "drc": "drmc(relTol = 1e-12, maxIt = 5000): drc's optim (BFGS) with a tighter relative tolerance than the default 1e-7; unweighted only", "nls": "Gauss-Newton, nls.control(maxiter = 1000, tol = 1e-8, minFactor = 1e-10), from the generating parameters, then from drc's estimates; tol 1e-6 as a fallback (convergenceTolerance records which)", "exclusions": "wells marked excluded in the input are dropped before fitting", "warnings": "warnings records what R raised per curve; 'NaNs produced' comes from inside drm()'s optimiser for LL.4 and the returned fits are unaffected", "zPrime": "sample standard deviations (n - 1), n recorded; refused when either control has fewer than two wells" } }, "curves": [ { "id": "C01", "description": "Hill -1, triplicates", "truth": { "top": 100, "bottom": 0, "logIC50": -6, "hill": -1, "ic50_M": 1e-06, "drcLL4": { "b": 1, "c": 0, "d": 100, "e": 1e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 30, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 0.957505986505246, "c": 0.517521650762668, "d": 101.682423814337, "e": 9.16014829363499e-07 }, "standardErrors": { "b": 0.0472108355386179, "c": 1.22226064978537, "d": 1.08567709222656, "e": 5.22479453567647e-08 }, "wald": { "b": { "lower": 0.86046272423269, "upper": 1.0545492487778 }, "c": { "lower": -1.99487109656593, "upper": 3.02991439809127 }, "d": { "lower": 99.4507825904053, "upper": 103.914065038269 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "rss": 163.430466743594, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 101.682423814337, "bottom": 0.517521650762668, "logIC50": -6.03809749548214, "hill": -0.957505986505246 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -13.903234296531, "lnIC50StandardError": 0.0570387098199638, "waldLogIC50": { "lower": -6.08901668232261, "upper": -5.98717918886026 }, "logIC50": -6.03809793559143, "dfResidual": 26 }, "nls": { "estimates": { "top": 101.682449644629, "bottom": 0.517511521009015, "logIC50": -6.03809792103845, "hill": -0.95750468303754 }, "standardErrors": { "top": 1.10894678967083, "bottom": 1.24429878883374, "logIC50": 0.0246484595256659, "hill": 0.0497180714162137 }, "wald": { "top": { "lower": 99.4029768725725, "upper": 103.961922416686 }, "bottom": { "lower": -2.04018126990642, "upper": 3.07520431192445 }, "logIC50": { "lower": -6.08876355521065, "upper": -5.98743228686625 }, "hill": { "lower": -1.05970164246612, "upper": -0.855307723608964 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "objective": 163.430466735365, "rss": 163.430466735365, "minimumFitted": 1.63620851822991, "startedFrom": "truth", "convergenceTolerance": 1e-06, "earlierAttempts": ["start truth, tol 1e-08: step factor 5.82077e-11 reduced below 'minFactor' of 1e-10"], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.08890970377993, "upper": -5.98691092468106, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 1.95735842893694e-05, "logIC50Difference": -4.25556307526165e-07, "objectiveDrcMinusNls": 8.22876700112829e-09 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 101.682449644629, "bottom": 0.517511521009015, "logIC50": -6.03809792103845, "hill": -0.95750468303754 }, "objective": 163.430466735365, "df": 26, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 163.430466735365, "polishedObjective": 163.430466735278, "relativeImprovement": 5.33894626224299e-13, "minimumAttained": true, "polishedEstimates": { "top": 101.682451914367, "bottom": 0.517507654334032, "logIC50": -6.03809790237679, "hill": -0.957504512370201 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 163.430466735365, "threshold": 189.989182739906, "lower": -6.08890965912743, "upper": -5.98691119271738, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.996586197941967, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -6.01836793090697, "absoluteIC50_M": 9.58588178963819e-07, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 9.58588763573409e-07, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 53.3869666666667, "objectiveFlat": 47873.4454889667, "objectiveFull": 163.430466735365, "weighted": false, "n": 30, "parametersFull": 4, "df1": 3, "df2": 26, "F": 2530.04721285461, "p": 3.57314954880928e-32, "alpha": 0.05, "noResponse": false, "working": "F = ((47873.4455 - 163.430467) / 3) / (163.430467 / 26) = 2530.04721; p = P(F(3, 26) > F) = 3.57315e-32 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 3.57314954880928e-32, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.700040701056866, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.73813862209532, "bendPoint_M": 1.82751679946674e-07, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.33805721998158, "bendPoint_M": 4.59137515703996e-06, "concentrationsAtOrBeyond": 3, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 5, "concentrationsPredictedAbove50": 5, "fires": false }, "vi": { "profileWidthLog10": 0.101998466410051, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 101.682449644629, "bottom": 0.517511521009015, "logIC50": -6.03809792103845, "hill": -0.95750468303754 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 163.430466735365, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.08876355521065, "upper": -5.98743228686625, "standardError": 0.0246484595256659, "dfResidual": 26, "tQuantile": 2.05552943864287, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.08890965912743, "upper": -5.98691119271738, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 2530.04721285461, "p": 3.57314954880928e-32, "df1": 3, "df2": 26, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -6.03809792103845, "ic50_M": 9.16013931779685e-07, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -6.01836793090697, "absoluteIC50_M": 9.58588178963819e-07 } }, "warnings": [] }, { "id": "C02", "description": "Hill -1, one replicate per concentration", "truth": { "top": 100, "bottom": 0, "logIC50": -6.5, "hill": -1, "ic50_M": 3.16227766016838e-07, "drcLL4": { "b": 1, "c": 0, "d": 100, "e": 3.16227766016838e-07 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 10, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 1.12931792163037, "c": 1.78741509334286, "d": 99.3548331146169, "e": 2.78370855398451e-07 }, "standardErrors": { "b": 0.123175126551658, "c": 1.68832010934402, "d": 2.50903054217914, "e": 2.69513669356215e-08 }, "wald": { "b": { "lower": 0.827919244704835, "upper": 1.4307165985559 }, "c": { "lower": -2.34375539073739, "upper": 5.91858557742312 }, "d": { "lower": 93.2154565460741, "upper": 105.49420968316 } }, "dfResidual": 6, "tQuantile": 2.44691185114497, "rss": 44.8596202897834, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 99.3548331146169, "bottom": 1.78741509334286, "logIC50": -6.5553762360234, "hill": -1.12931792163037 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -15.0943086005114, "lnIC50StandardError": 0.0968201402743785, "waldLogIC50": { "lower": -6.65826379047869, "upper": -6.45248607621507 }, "logIC50": -6.55537493334688, "dfResidual": 6 }, "nls": { "estimates": { "top": 99.3550360028384, "bottom": 1.7870728842687, "logIC50": -6.55537501268994, "hill": -1.1293016658616 }, "standardErrors": { "top": 2.42492994073367, "bottom": 1.64514968708588, "logIC50": 0.0422575946331889, "hill": 0.112691324390952 }, "wald": { "top": { "lower": 93.4214461926609, "upper": 105.288625813016 }, "bottom": { "lower": -2.23846338196917, "upper": 5.81260915050657 }, "logIC50": { "lower": -6.65877562179877, "upper": -6.45197440358112 }, "hill": { "lower": -1.40504740303504, "upper": -0.853555928688156 } }, "dfResidual": 6, "tQuantile": 2.44691185114497, "objective": 44.8596199785342, "rss": 44.8596199785342, "minimumFitted": 1.91382447439558, "startedFrom": "truth", "convergenceTolerance": 1e-06, "earlierAttempts": ["start truth, tol 1e-08: number of iterations exceeded maximum of 1000"], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.66295608611036, "upper": -6.45415475091092, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 0.000191454730036646, "logIC50Difference": 1.22333345498049e-06, "objectiveDrcMinusNls": 3.11249280571246e-07 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 99.3550360028384, "bottom": 1.7870728842687, "logIC50": -6.55537501268994, "hill": -1.1293016658616 }, "objective": 44.8596199785342, "df": 6, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 44.8596199785342, "polishedObjective": 44.8596199785243, "relativeImprovement": 2.18898435004653e-13, "minimumAttained": true, "polishedEstimates": { "top": 99.3550342099374, "bottom": 1.7870741880519, "logIC50": -6.55537500875052, "hill": -1.12930180432631 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 44.8596199785342, "threshold": 89.6248673335813, "lower": -6.66293924942799, "upper": -6.45415595320434, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.997110824535915, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -6.54637124153464, "absoluteIC50_M": 2.84203065773115e-07, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 2.84202932138696e-07, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 42.2589, "objectiveFlat": 15526.7897489, "objectiveFull": 44.8596199785342, "weighted": false, "n": 10, "parametersFull": 4, "df1": 3, "df2": 6, "F": 690.239022815162, "p": 5.26985609242824e-08, "alpha": 0.05, "noResponse": false, "working": "F = ((15526.7897 - 44.85962) / 3) / (44.85962 / 6) = 690.239023; p = P(F(3, 6) > F) = 5.26986e-08 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 5.26985609242824e-08, "fires": false }, "iii": { "concentrationsBelowIC50": 4, "concentrationsAboveIC50": 6, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.593545790147607, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -7.14892080283755, "bendPoint_M": 7.09707177090981e-08, "concentrationsAtOrBeyond": 3, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.96182922254234, "bendPoint_M": 1.09186960752202e-06, "concentrationsAtOrBeyond": 5, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 6, "concentrationsPredictedAbove50": 4, "fires": false }, "vi": { "profileWidthLog10": 0.208783296223651, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 99.3550360028384, "bottom": 1.7870728842687, "logIC50": -6.55537501268994, "hill": -1.1293016658616 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 44.8596199785342, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.65877562179877, "upper": -6.45197440358112, "standardError": 0.0422575946331889, "dfResidual": 6, "tQuantile": 2.44691185114497, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.66293924942799, "upper": -6.45415595320434, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 690.239022815162, "p": 5.26985609242824e-08, "df1": 3, "df2": 6, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -6.55537501268994, "ic50_M": 2.78371639522759e-07, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -6.54637124153464, "absoluteIC50_M": 2.84203065773115e-07 } }, "warnings": ["NaNs produced"] }, { "id": "C03", "description": "Hill -1, duplicates, low noise", "truth": { "top": 100, "bottom": 0, "logIC50": -7, "hill": -1, "ic50_M": 1e-07, "drcLL4": { "b": 1, "c": 0, "d": 100, "e": 1e-07 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 20, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 1.01397454894968, "c": -0.727080680977157, "d": 99.3898370693305, "e": 1.02476156762797e-07 }, "standardErrors": { "b": 0.0223385214472058, "c": 0.515469452515934, "d": 0.440825899700505, "e": 2.36110529201723e-09 }, "wald": { "b": { "lower": 0.966618998956977, "upper": 1.06133009894238 }, "c": { "lower": -1.81982710495236, "upper": 0.36566574299805 }, "d": { "lower": 98.4553279085214, "upper": 100.32434623014 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "rss": 12.1440902273772, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 99.3898370693305, "bottom": -0.727080680977157, "logIC50": -6.98937717061708, "hill": -1.01397454894968 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -16.0936369144543, "lnIC50StandardError": 0.0230407662812158, "waldLogIC50": { "lower": -7.01059049070881, "upper": -6.9681649206951 }, "logIC50": -6.98937770570196, "dfResidual": 16 }, "nls": { "estimates": { "top": 99.389867216593, "bottom": -0.727102326653816, "logIC50": -6.98937743561014, "hill": -1.01397254004121 }, "standardErrors": { "top": 0.439734637953634, "bottom": 0.515822094567061, "logIC50": 0.0100136660205851, "hill": 0.0222776769399014 }, "wald": { "top": { "lower": 98.457671427344, "upper": 100.322063005842 }, "bottom": { "lower": -1.82059631838194, "upper": 0.366391665074304 }, "logIC50": { "lower": -7.01060545927181, "upper": -6.96814941194847 }, "hill": { "lower": -1.06119910544044, "upper": -0.96674597464197 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "objective": 12.1440902205206, "rss": 12.1440902205206, "minimumFitted": 0.226086591206421, "startedFrom": "truth", "convergenceTolerance": 1e-06, "earlierAttempts": ["start truth, tol 1e-08: number of iterations exceeded maximum of 1000"], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -7.01055869599494, "upper": -6.96811907051148, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 2.977066675689e-05, "logIC50Difference": -2.64993062160102e-07, "objectiveDrcMinusNls": 6.85659884425149e-09 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 99.389867216593, "bottom": -0.727102326653816, "logIC50": -6.98937743561014, "hill": -1.01397254004121 }, "objective": 12.1440902205206, "df": 16, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 12.1440902205206, "polishedObjective": 12.1440902205197, "relativeImprovement": 6.80171108186735e-14, "minimumAttained": true, "polishedEstimates": { "top": 99.3898669105434, "bottom": -0.727101953397565, "logIC50": -6.98937743614586, "hill": -1.01397256320578 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 12.1440902205206, "threshold": 15.5550604057495, "lower": -7.01055870505942, "upper": -6.96811911435352, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.99962116294637, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -7.00081975370473, "absoluteIC50_M": 9.98114227646764e-08, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 9.98114707953665e-08, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 52.6154, "objectiveFlat": 32056.2365908, "objectiveFull": 12.1440902205206, "weighted": false, "n": 20, "parametersFull": 4, "df1": 3, "df2": 16, "F": 14072.8390160487, "p": 1.41610026602025e-27, "alpha": 0.05, "noResponse": false, "working": "F = ((32056.2366 - 12.1440902) / 3) / (12.1440902 / 16) = 14072.839; p = P(F(3, 16) > F) = 1.4161e-27 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 1.41610026602025e-27, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.661055623411254, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -7.6504330590214, "bendPoint_M": 2.23648989866949e-08, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -6.32832181219889, "bendPoint_M": 4.69546046057035e-07, "concentrationsAtOrBeyond": 3, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 5, "concentrationsPredictedAbove50": 5, "fires": false }, "vi": { "profileWidthLog10": 0.0424395907058992, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 99.389867216593, "bottom": -0.727102326653816, "logIC50": -6.98937743561014, "hill": -1.01397254004121 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 12.1440902205206, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -7.01060545927181, "upper": -6.96814941194847, "standardError": 0.0100136660205851, "dfResidual": 16, "tQuantile": 2.11990529922125, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -7.01055870505942, "upper": -6.96811911435352, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 14072.8390160487, "p": 1.41610026602025e-27, "df1": 3, "df2": 16, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -6.98937743561014, "ic50_M": 1.02476094235034e-07, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -7.00081975370473, "absoluteIC50_M": 9.98114227646764e-08 } }, "warnings": [] }, { "id": "C04", "description": "Hill -0.5 (shallow), half-log series of 12", "truth": { "top": 100, "bottom": 0, "logIC50": -6, "hill": -0.5, "ic50_M": 1e-06, "drcLL4": { "b": 0.5, "c": 0, "d": 100, "e": 1e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 24, "distinctConcentrations": 12, "drcLL4": { "estimates": { "b": 0.507644069181381, "c": 0.835354784817674, "d": 100.844759008922, "e": 8.52745346925541e-07 }, "standardErrors": { "b": 0.033523197256228, "c": 1.58255919888083, "d": 2.2369173200717, "e": 1.02171569567018e-07 }, "wald": { "b": { "lower": 0.437715905069406, "upper": 0.577572233293356 }, "c": { "lower": -2.46580585718208, "upper": 4.13651542681743 }, "d": { "lower": 96.1786312446969, "upper": 105.510886773148 } }, "dfResidual": 20, "tQuantile": 2.08596344726586, "rss": 89.7094729278925, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 100.844759008922, "bottom": 0.835354784817674, "logIC50": -6.06918064167732, "hill": -0.507644069181381 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -13.9748145134742, "lnIC50StandardError": 0.119816519077378, "waldLogIC50": { "lower": -6.17772929909481, "upper": -5.96064035855185 }, "logIC50": -6.06918482882333, "dfResidual": 20 }, "nls": { "estimates": { "top": 100.844891942102, "bottom": 0.835389626302108, "logIC50": -6.06918576848469, "hill": -0.507643068356951 }, "standardErrors": { "top": 2.23321301636408, "bottom": 1.59272701911057, "logIC50": 0.0518617376600823, "hill": 0.0336548710133567 }, "wald": { "top": { "lower": 96.1864912200086, "upper": 105.503292664196 }, "bottom": { "lower": -2.48698071703526, "upper": 4.15775996963947 }, "logIC50": { "lower": -6.17736745755532, "upper": -5.96100407941407 }, "hill": { "lower": -0.577845899113261, "upper": -0.437440237600642 } }, "dfResidual": 20, "tQuantile": 2.08596344726586, "objective": 89.7094728833845, "rss": 89.7094728833845, "minimumFitted": 3.52778182181929, "startedFrom": "truth", "convergenceTolerance": 1e-06, "earlierAttempts": ["start truth, tol 1e-08: step factor 5.82077e-11 reduced below 'minFactor' of 1e-10"], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.18275307813954, "upper": -5.9634644720379, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 4.17086070100073e-05, "logIC50Difference": -5.12680737063675e-06, "objectiveDrcMinusNls": 4.45080132749354e-08 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 100.844891942102, "bottom": 0.835389626302108, "logIC50": -6.06918576848469, "hill": -0.507643068356951 }, "objective": 89.7094728833845, "df": 20, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 89.7094728833845, "polishedObjective": 89.7094728833804, "relativeImprovement": 4.59388260230417e-14, "minimumAttained": true, "polishedEstimates": { "top": 100.84489300455, "bottom": 0.835388272079446, "logIC50": -6.06918576189899, "hill": -0.507643046743604 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 89.7094728833845, "threshold": 109.226860936931, "lower": -6.18274260419145, "upper": -5.96346253494483, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.996721949475715, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -6.04043579071128, "absoluteIC50_M": 9.110961454603e-07, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 9.11100817721197e-07, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 45.8322916666667, "objectiveFlat": 27366.7145209583, "objectiveFull": 89.7094728833845, "weighted": false, "n": 24, "parametersFull": 4, "df1": 3, "df2": 20, "F": 2027.06241019704, "p": 5.29329726263076e-25, "alpha": 0.05, "noResponse": false, "working": "F = ((27366.7145 - 89.7094729) / 3) / (89.7094729 / 20) = 2027.06241; p = P(F(3, 20) > F) = 5.2933e-25 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 12, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 5.29329726263076e-25, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 7, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 1.32040067393871, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -7.3895864424234, "bendPoint_M": 4.07768391050577e-08, "concentrationsAtOrBeyond": 3, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -4.74878509454599, "bendPoint_M": 1.78326097461847e-05, "concentrationsAtOrBeyond": 4, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 7, "concentrationsPredictedAbove50": 5, "fires": false }, "vi": { "profileWidthLog10": 0.219280069246622, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 100.844891942102, "bottom": 0.835389626302108, "logIC50": -6.06918576848469, "hill": -0.507643068356951 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 89.7094728833845, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.17736745755532, "upper": -5.96100407941407, "standardError": 0.0518617376600823, "dfResidual": 20, "tQuantile": 2.08596344726586, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.18274260419145, "upper": -5.96346253494483, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 2027.06241019704, "p": 5.29329726263076e-25, "df1": 3, "df2": 20, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -6.06918576848469, "ic50_M": 8.52735280402692e-07, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -6.04043579071128, "absoluteIC50_M": 9.110961454603e-07 } }, "warnings": ["NaNs produced"] }, { "id": "C05", "description": "Hill -0.5, Bottom 10", "truth": { "top": 100, "bottom": 10, "logIC50": -5.5, "hill": -0.5, "ic50_M": 3.16227766016838e-06, "drcLL4": { "b": 0.5, "c": 10, "d": 100, "e": 3.16227766016838e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 36, "distinctConcentrations": 12, "drcLL4": { "estimates": { "b": 0.458537332265013, "c": 5.75530083607359, "d": 101.80115182622, "e": 3.49138890971945e-06 }, "standardErrors": { "b": 0.0632029553556318, "c": 4.45902127389139, "d": 3.75889814410066, "e": 8.5094386203129e-07 }, "wald": { "b": { "lower": 0.329797125095906, "upper": 0.587277539434119 }, "c": { "lower": -3.32742827591372, "upper": 14.8380299480609 }, "d": { "lower": 94.1445268618307, "upper": 109.457776790609 } }, "dfResidual": 32, "tQuantile": 2.0369333434601, "rss": 603.539338074247, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 101.80115182622, "bottom": 5.75530083607359, "logIC50": -5.45700177194271, "hill": -0.458537332265013 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -12.5652161756777, "lnIC50StandardError": 0.243727554823835, "waldLogIC50": { "lower": -5.67261249043975, "upper": -5.24139560759688 }, "logIC50": -5.45700404901831, "dfResidual": 32 }, "nls": { "estimates": { "top": 101.801426818408, "bottom": 5.75504273449301, "logIC50": -5.45700271361294, "hill": -0.458532513061419 }, "standardErrors": { "top": 3.70440892359995, "bottom": 4.47964195073625, "logIC50": 0.106388434085747, "hill": 0.062755767877746 }, "wald": { "top": { "lower": 94.2557927641164, "upper": 109.3470608727 }, "bottom": { "lower": -3.36968932172431, "upper": 14.8797747907103 }, "logIC50": { "lower": -5.67370886236071, "upper": -5.24029656486517 }, "hill": { "lower": -0.586361829146043, "upper": -0.330703196976796 } }, "dfResidual": 32, "tQuantile": 2.0369333434601, "objective": 603.539337960491, "rss": 603.539337960491, "minimumFitted": 12.4319248543421, "startedFrom": "truth", "convergenceTolerance": 1e-06, "earlierAttempts": ["start truth, tol 1e-08: number of iterations exceeded maximum of 1000"], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -5.6723249637722, "upper": -5.21827357493872, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 4.48458886741724e-05, "logIC50Difference": -9.4167023245717e-07, "objectiveDrcMinusNls": 1.13755731945275e-07 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 101.801426818408, "bottom": 5.75504273449301, "logIC50": -5.45700271361294, "hill": -0.458532513061419 }, "objective": 603.539337960491, "df": 32, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 603.539337960491, "polishedObjective": 603.53933796046, "relativeImprovement": 5.16125322352426e-14, "minimumAttained": true, "polishedEstimates": { "top": 101.801422298787, "bottom": 5.75504608193281, "logIC50": -5.45700266508633, "hill": -0.458532584044348 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 603.539337960491, "threshold": 681.793823132712, "lower": -5.67229125998712, "upper": -5.21836204257782, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.98202649519756, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -5.30766119431932, "absoluteIC50_M": 4.92423539714825e-06, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 4.92423391448774e-06, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 56.3233333333333, "objectiveFlat": 33579.390586, "objectiveFull": 603.539337960491, "weighted": false, "n": 36, "parametersFull": 4, "df1": 3, "df2": 32, "F": 582.799481639501, "p": 5.43133006639254e-28, "alpha": 0.05, "noResponse": false, "working": "F = ((33579.3906 - 603.539338) / 3) / (603.539338 / 32) = 582.799482; p = P(F(3, 32) > F) = 5.43133e-28 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 12, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 5.43133006639254e-28, "fires": false }, "iii": { "concentrationsBelowIC50": 6, "concentrationsAboveIC50": 6, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 1.46182054812992, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.91882326174285, "bendPoint_M": 1.20552643542171e-07, "concentrationsAtOrBeyond": 3, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -3.99518216548302, "bendPoint_M": 0.000101115523469047, "concentrationsAtOrBeyond": 3, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 5, "concentrationsPredictedAbove50": 7, "fires": false }, "vi": { "profileWidthLog10": 0.453929217409295, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 101.801426818408, "bottom": 5.75504273449301, "logIC50": -5.45700271361294, "hill": -0.458532513061419 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 603.539337960491, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -5.67370886236071, "upper": -5.24029656486517, "standardError": 0.106388434085747, "dfResidual": 32, "tQuantile": 2.0369333434601, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -5.67229125998712, "upper": -5.21836204257782, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 582.799481639501, "p": 5.43133006639254e-28, "df1": 3, "df2": 32, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -5.45700271361294, "ic50_M": 3.49138133943344e-06, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -5.30766119431932, "absoluteIC50_M": 4.92423539714825e-06 } }, "warnings": ["NaNs produced"] }, { "id": "C06", "description": "Hill -0.5, 4-fold series", "truth": { "top": 95, "bottom": 5, "logIC50": -6.5, "hill": -0.5, "ic50_M": 3.16227766016838e-07, "drcLL4": { "b": 0.5, "c": 5, "d": 95, "e": 3.16227766016838e-07 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 20, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 0.489453768603886, "c": 3.96460144800307, "d": 95.5213869608335, "e": 3.45202737138592e-07 }, "standardErrors": { "b": 0.0384649657013022, "c": 2.34647538720421, "d": 1.83817628594579, "e": 4.81461460020087e-08 }, "wald": { "b": { "lower": 0.407911683979331, "upper": 0.57099585322844 }, "c": { "lower": -1.00970415982338, "upper": 8.93890705582952 }, "d": { "lower": 91.6246273113542, "upper": 99.4181466103128 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "rss": 64.1732339349279, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 95.5213869608335, "bottom": 3.96460144800307, "logIC50": -6.46192576938941, "hill": -0.489453768603886 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -14.8791362519159, "lnIC50StandardError": 0.139472124023998, "waldLogIC50": { "lower": -6.59033361802768, "upper": -6.33351992135976 }, "logIC50": -6.46192676969372, "dfResidual": 16 }, "nls": { "estimates": { "top": 95.5215903816177, "bottom": 3.96434933175708, "logIC50": -6.46192466539404, "hill": -0.489448696403292 }, "standardErrors": { "top": 1.80683165290162, "bottom": 2.35344501001362, "logIC50": 0.0609744996017541, "hill": 0.0380403071034125 }, "wald": { "top": { "lower": 91.6912783858309, "upper": 99.3519023774046 }, "bottom": { "lower": -1.02473121639661, "upper": 8.95342987991078 }, "logIC50": { "lower": -6.59118483021717, "upper": -6.33266450057092 }, "hill": { "lower": -0.57009054501582, "upper": -0.408806847790764 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "objective": 64.1732338650603, "rss": 64.1732338650603, "minimumFitted": 9.33997258931657, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.58814574112661, "upper": -6.32758438391248, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-05, "earlierAttempts": ["confint at tol 1e-06: step factor 5.82077e-11 reduced below 'minFactor' of 1e-10"] }, "agreementWithDrc": { "maxRelativeDifference": 6.35918261378298e-05, "logIC50Difference": 1.10399536357164e-06, "objectiveDrcMinusNls": 6.98676245747265e-08 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 95.5215903816177, "bottom": 3.96434933175708, "logIC50": -6.46192466539404, "hill": -0.489448696403292 }, "objective": 64.1732338650603, "df": 16, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 64.1732338650603, "polishedObjective": 64.1732338650602, "relativeImprovement": 1.55011641170501e-15, "minimumAttained": true, "polishedEstimates": { "top": 95.5215902731525, "bottom": 3.96434948324795, "logIC50": -6.46192466609726, "hill": -0.489448699006474 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 64.1732338650603, "threshold": 82.1978848210921, "lower": -6.5881449306217, "upper": -6.32760179030053, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.996560409121245, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -6.47188865007501, "absoluteIC50_M": 3.37373797742093e-07, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 3.37373715055998e-07, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 53.2611, "objectiveFlat": 18657.2287598, "objectiveFull": 64.1732338650603, "weighted": false, "n": 20, "parametersFull": 4, "df1": 3, "df2": 16, "F": 1545.23867401634, "p": 6.53035685269458e-20, "alpha": 0.05, "noResponse": false, "working": "F = ((18657.2288 - 64.1732339) / 3) / (64.1732339 / 16) = 1545.23867; p = P(F(3, 16) > F) = 6.53036e-20 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 6.53035685269458e-20, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 1.36948418599225, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -7.8314088513863, "bendPoint_M": 1.47431793457793e-08, "concentrationsAtOrBeyond": 3, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.09244047940179, "bendPoint_M": 8.08275696710191e-06, "concentrationsAtOrBeyond": 2, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 5, "concentrationsPredictedAbove50": 5, "fires": false }, "vi": { "profileWidthLog10": 0.260543140321166, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 95.5215903816177, "bottom": 3.96434933175708, "logIC50": -6.46192466539404, "hill": -0.489448696403292 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 64.1732338650603, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.59118483021717, "upper": -6.33266450057092, "standardError": 0.0609744996017541, "dfResidual": 16, "tQuantile": 2.11990529922125, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.5881449306217, "upper": -6.32760179030053, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 1545.23867401634, "p": 6.53035685269458e-20, "df1": 3, "df2": 16, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -6.46192466539404, "ic50_M": 3.45203614660001e-07, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -6.47188865007501, "absoluteIC50_M": 3.37373797742093e-07 } }, "warnings": [] }, { "id": "C07", "description": "Hill -3 (steep), 2-fold series of 12", "truth": { "top": 100, "bottom": 0, "logIC50": -6, "hill": -3, "ic50_M": 1e-06, "drcLL4": { "b": 3, "c": 0, "d": 100, "e": 1e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 36, "distinctConcentrations": 12, "drcLL4": { "estimates": { "b": 3.05836412743751, "c": -0.773701023439875, "d": 98.6277747497446, "e": 1.00221806416788e-06 }, "standardErrors": { "b": 0.150017251974089, "c": 0.633081281898128, "d": 0.818140756917436, "e": 2.01983065400794e-08 }, "wald": { "b": { "lower": 2.75278898479723, "upper": 3.36393927007779 }, "c": { "lower": -2.06324539565864, "upper": 0.515843348778886 }, "d": { "lower": 96.9612765623358, "upper": 100.294272937153 } }, "dfResidual": 32, "tQuantile": 2.0369333434601, "rss": 206.206838668668, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 98.6277747497446, "bottom": -0.773701023439875, "logIC50": -5.99903777371714, "hill": -3.05836412743751 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -13.8132810727709, "lnIC50StandardError": 0.0201531073056508, "waldLogIC50": { "lower": -6.01685976825349, "upper": -5.98120372551256 }, "logIC50": -5.99903174688302, "dfResidual": 32 }, "nls": { "estimates": { "top": 98.6278015985682, "bottom": -0.773687450027187, "logIC50": -5.99903843656464, "hill": -3.0583639082611 }, "standardErrors": { "top": 0.823494507995378, "bottom": 0.633266359828088, "logIC50": 0.00872245101129942, "hill": 0.154537248555578 }, "wald": { "top": { "lower": 96.9503981770761, "upper": 100.30520502006 }, "bottom": { "lower": -2.06360881365262, "upper": 0.516233913598248 }, "logIC50": { "lower": -6.01680548786625, "upper": -5.98127138526303 }, "hill": { "lower": -3.37314598265054, "upper": -2.74358183387166 } }, "dfResidual": 32, "tQuantile": 2.0369333434601, "objective": 206.206838631496, "rss": 206.206838631496, "minimumFitted": -0.773610959870522, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.01679006729723, "upper": -5.98113419618236, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 1.75434855029983e-05, "logIC50Difference": -6.6284750044332e-07, "objectiveDrcMinusNls": 3.71726684988971e-08 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 98.6278015985682, "bottom": -0.773687450027187, "logIC50": -5.99903843656464, "hill": -3.0583639082611 }, "objective": 206.206838631496, "df": 32, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 206.206838631496, "polishedObjective": 206.206838631495, "relativeImprovement": 2.20529713710963e-15, "minimumAttained": true, "polishedEstimates": { "top": 98.6278016329003, "bottom": -0.773687428854537, "logIC50": -5.99903843748892, "hill": -3.05836390687486 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 206.206838631496, "threshold": 232.943471989362, "lower": -6.01679017823279, "upper": -5.98113424807846, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.997134745534895, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -6.00517049597145, "absoluteIC50_M": 9.88165083185768e-07, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 9.88166327616189e-07, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 39.4819722222222, "objectiveFlat": 71968.0716469722, "objectiveFull": 206.206838631496, "weighted": false, "n": 36, "parametersFull": 4, "df1": 3, "df2": 32, "F": 3712.09750544157, "p": 9.517248968319e-41, "alpha": 0.05, "noResponse": false, "working": "F = ((71968.0716 - 206.206839) / 3) / (206.206839 / 32) = 3712.09751; p = P(F(3, 32) > F) = 9.51725e-41 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 12, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 9.517248968319e-41, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 7, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.219166936860676, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.21820537342532, "bendPoint_M": 6.0505468291014e-07, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.77987149970396, "bendPoint_M": 1.66007802342109e-06, "concentrationsAtOrBeyond": 6, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 7, "concentrationsPredictedAbove50": 5, "fires": false }, "vi": { "profileWidthLog10": 0.0356559301543253, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 98.6278015985682, "bottom": -0.773687450027187, "logIC50": -5.99903843656464, "hill": -3.0583639082611 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 206.206838631496, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.01680548786625, "upper": -5.98127138526303, "standardError": 0.00872245101129942, "dfResidual": 32, "tQuantile": 2.0369333434601, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.01679017823279, "upper": -5.98113424807846, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 3712.09750544157, "p": 9.517248968319e-41, "df1": 3, "df2": 32, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -5.99903843656464, "ic50_M": 1.00221653452093e-06, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -6.00517049597145, "absoluteIC50_M": 9.88165083185768e-07 } }, "warnings": ["NaNs produced"] }, { "id": "C08", "description": "Hill -3 on a 3-fold series (few points on the slope)", "truth": { "top": 100, "bottom": 0, "logIC50": -5.3, "hill": -3, "ic50_M": 5.01187233627272e-06, "drcLL4": { "b": 3, "c": 0, "d": 100, "e": 5.01187233627272e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 20, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 2.70797758723331, "c": -4.78056145851156, "d": 100.912073658779, "e": 5.62155378033931e-06 }, "standardErrors": { "b": 0.219673834538005, "c": 1.63671132100247, "d": 0.905932201070637, "e": 2.37266482856997e-07 }, "wald": { "b": { "lower": 2.24228986129594, "upper": 3.17366531317068 }, "c": { "lower": -8.25023446120011, "upper": -1.310888455823 }, "d": { "lower": 98.9915831849939, "upper": 102.832564132564 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "rss": 148.838193872597, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 100.912073658779, "bottom": -4.78056145851156, "logIC50": -5.2501436301671, "hill": -2.70797758723331 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -12.0888487541301, "lnIC50StandardError": 0.0421960143001166, "waldLogIC50": { "lower": -5.2889686229209, "upper": -5.21127199004249 }, "logIC50": -5.2501203064817, "dfResidual": 16 }, "nls": { "estimates": { "top": 100.912074809732, "bottom": -4.78055859487097, "logIC50": -5.25014370929863, "hill": -2.70797766425308 }, "standardErrors": { "top": 0.904165172331804, "bottom": 1.62555013380825, "logIC50": 0.018385908405823, "hill": 0.21088114591099 }, "wald": { "top": { "lower": 98.9953302695348, "upper": 102.82881934993 }, "bottom": { "lower": -8.2265709376809, "upper": -1.33454625206105 }, "logIC50": { "lower": -5.28912009395914, "upper": -5.21116732463813 }, "hill": { "lower": -3.15502572297564, "upper": -2.26092960553052 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "objective": 148.838193872409, "rss": 148.838193872409, "minimumFitted": -4.73705704894912, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -5.28896927998348, "upper": -5.21132107649234, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 5.99017627941171e-07, "logIC50Difference": -7.91315342141274e-08, "objectiveDrcMinusNls": 1.88038029591553e-10 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 100.912074809732, "bottom": -4.78055859487097, "logIC50": -5.25014370929863, "hill": -2.70797766425308 }, "objective": 148.838193872409, "df": 16, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 148.838193872409, "polishedObjective": 148.838193872408, "relativeImprovement": 1.90957097039007e-15, "minimumAttained": true, "polishedEstimates": { "top": 100.912074806707, "bottom": -4.78055857393644, "logIC50": -5.25014370952164, "hill": -2.70797766753745 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 148.838193872409, "threshold": 190.643107414984, "lower": -5.28896948268277, "upper": -5.21132102654016, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.99634825093157, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -5.2618888801419, "absoluteIC50_M": 5.47155941907294e-06, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 5.47156026052079e-06, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 67.97395, "objectiveFlat": 40758.05623095, "objectiveFull": 148.838193872409, "weighted": false, "n": 20, "parametersFull": 4, "df1": 3, "df2": 16, "F": 1455.154020368, "p": 1.05402021778573e-19, "alpha": 0.05, "noResponse": false, "working": "F = ((40758.0562 - 148.838194) / 3) / (148.838194 / 16) = 1455.15402; p = P(F(3, 16) > F) = 1.05402e-19 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 1.05402021778573e-19, "fires": false }, "iii": { "concentrationsBelowIC50": 7, "concentrationsAboveIC50": 3, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.247525028890411, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -5.49766873818905, "bendPoint_M": 3.17929818276385e-06, "concentrationsAtOrBeyond": 6, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.00261868040822, "bendPoint_M": 9.93988407894742e-06, "concentrationsAtOrBeyond": 3, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 3, "concentrationsPredictedAbove50": 7, "fires": false }, "vi": { "profileWidthLog10": 0.0776484561426045, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 100.912074809732, "bottom": -4.78055859487097, "logIC50": -5.25014370929863, "hill": -2.70797766425308 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 148.838193872409, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -5.28912009395914, "upper": -5.21116732463813, "standardError": 0.018385908405823, "dfResidual": 16, "tQuantile": 2.11990529922125, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -5.28896948268277, "upper": -5.21132102654016, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 1455.154020368, "p": 1.05402021778573e-19, "df1": 3, "df2": 16, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -5.25014370929863, "ic50_M": 5.62155275605244e-06, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -5.2618888801419, "absoluteIC50_M": 5.47155941907294e-06 } }, "warnings": [] }, { "id": "C09", "description": "Hill -3, Bottom 15", "truth": { "top": 100, "bottom": 15, "logIC50": -7.2, "hill": -3, "ic50_M": 6.30957344480193e-08, "drcLL4": { "b": 3, "c": 15, "d": 100, "e": 6.30957344480193e-08 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 36, "distinctConcentrations": 12, "drcLL4": { "estimates": { "b": 3.21145215305973, "c": 15.1958896624444, "d": 99.5420732174166, "e": 6.27351959060637e-08 }, "standardErrors": { "b": 0.11686706381884, "c": 0.342846737203809, "d": 0.54162652619411, "e": 8.57908299656392e-10 }, "wald": { "b": { "lower": 2.97340173401486, "upper": 3.44950257210461 }, "c": { "lower": 14.4975337117374, "upper": 15.8942456131513 }, "d": { "lower": 98.4388160865093, "upper": 100.645330348324 } }, "dfResidual": 32, "tQuantile": 2.0369333434601, "rss": 69.9163059449958, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 99.5420732174166, "bottom": 15.1958896624444, "logIC50": -7.20248874147777, "hill": -3.21145215305973 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -16.5843650237666, "lnIC50StandardError": 0.013674254032292, "waldLogIC50": { "lower": -7.21459485614539, "upper": -7.19040157523684 }, "logIC50": -7.20249821569111, "dfResidual": 32 }, "nls": { "estimates": { "top": 99.5421036446912, "bottom": 15.1958996278532, "logIC50": -7.20248943573308, "hill": -3.21144894462742 }, "standardErrors": { "top": 0.542905051097626, "bottom": 0.342596437607789, "logIC50": 0.00595230634535607, "hill": 0.117136395306467 }, "wald": { "top": { "lower": 98.4362422437775, "upper": 100.647965045605 }, "bottom": { "lower": 14.4980535207392, "upper": 15.8937457349671 }, "logIC50": { "lower": -7.21461388699843, "upper": -7.19036498446774 }, "hill": { "lower": -3.45004797395988, "upper": -2.97284991529495 } }, "dfResidual": 32, "tQuantile": 2.0369333434601, "objective": 69.9163059150233, "rss": 69.9163059150233, "minimumFitted": 15.1959067544655, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -7.21464144660376, "upper": -7.19045094665771, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 9.99059666682585e-07, "logIC50Difference": -6.94255311017855e-07, "objectiveDrcMinusNls": 2.99724973729099e-08 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 99.5421036446912, "bottom": 15.1958996278532, "logIC50": -7.20248943573308, "hill": -3.21144894462742 }, "objective": 69.9163059150233, "df": 32, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 69.9163059150233, "polishedObjective": 69.9163059150231, "relativeImprovement": 2.43906273866482e-15, "minimumAttained": true, "polishedEstimates": { "top": 99.5421036429144, "bottom": 15.1958996410135, "logIC50": -7.20248943578377, "hill": -3.21144894563307 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 69.9163059150233, "threshold": 78.9816048614224, "lower": -7.21464141279969, "upper": -7.19045085122905, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.99856309031075, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -7.15474026277832, "absoluteIC50_M": 7.00260673629771e-08, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 7.00261519780763e-08, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 44.5961388888889, "objectiveFlat": 48657.4114143056, "objectiveFull": 69.9163059150233, "weighted": false, "n": 36, "parametersFull": 4, "df1": 3, "df2": 32, "F": 7412.67158936291, "p": 1.52427857348119e-45, "alpha": 0.05, "noResponse": false, "working": "F = ((48657.4114 - 69.9163059) / 3) / (69.9163059 / 32) = 7412.67159; p = P(F(3, 32) > F) = 1.52428e-45 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 12, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 1.52427857348119e-45, "fires": false }, "iii": { "concentrationsBelowIC50": 4, "concentrationsAboveIC50": 8, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.208719572110961, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -7.41120900784404, "bendPoint_M": 3.87963610329971e-08, "concentrationsAtOrBeyond": 3, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -6.99376986362212, "bendPoint_M": 1.01444880847246e-07, "concentrationsAtOrBeyond": 7, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 8, "concentrationsPredictedAbove50": 4, "fires": false }, "vi": { "profileWidthLog10": 0.0241905615706361, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 99.5421036446912, "bottom": 15.1958996278532, "logIC50": -7.20248943573308, "hill": -3.21144894462742 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 69.9163059150233, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -7.21461388699843, "upper": -7.19036498446774, "standardError": 0.00595230634535607, "dfResidual": 32, "tQuantile": 2.0369333434601, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -7.21464141279969, "upper": -7.19045085122905, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 7412.67158936291, "p": 1.52427857348119e-45, "df1": 3, "df2": 32, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -7.20248943573308, "ic50_M": 6.27350956187933e-08, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -7.15474026277832, "absoluteIC50_M": 7.00260673629771e-08 } }, "warnings": ["NaNs produced"] }, { "id": "C10", "description": "Bottom 20 (partial inhibition)", "truth": { "top": 100, "bottom": 20, "logIC50": -6, "hill": -1, "ic50_M": 1e-06, "drcLL4": { "b": 1, "c": 20, "d": 100, "e": 1e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 30, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 0.960633819083199, "c": 19.634059045161, "d": 101.027431497261, "e": 9.59396914691087e-07 }, "standardErrors": { "b": 0.0792295920981795, "c": 1.59538218283261, "d": 1.4231464631891, "e": 8.70393767514182e-08 }, "wald": { "b": { "lower": 0.797775060113725, "upper": 1.12349257805267 }, "c": { "lower": 16.3547040024623, "upper": 22.9134140878598 }, "d": { "lower": 98.1021120466753, "upper": 103.952750947847 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "rss": 272.278310162598, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 101.027431497261, "bottom": 19.634059045161, "logIC50": -6.01800168250843, "hill": -0.960633819083199 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -13.8569626702446, "lnIC50StandardError": 0.0907238257438651, "waldLogIC50": { "lower": -6.09899204488757, "upper": -5.93701280236556 }, "logIC50": -6.01800242362656, "dfResidual": 26 }, "nls": { "estimates": { "top": 101.027460723074, "bottom": 19.6340527878394, "logIC50": -6.01800237601521, "hill": -0.960632172284655 }, "standardErrors": { "top": 1.41355814737727, "bottom": 1.61974274289542, "logIC50": 0.0394613158735947, "hill": 0.0799949298805482 }, "wald": { "top": { "lower": 98.1218503379069, "upper": 103.933071108242 }, "bottom": { "lower": 16.3046238967897, "upper": 22.9634816788891 }, "logIC50": { "lower": -6.09911627248097, "upper": -5.93688847954945 }, "hill": { "lower": -1.12506410559629, "upper": -0.796200238973016 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "objective": 272.278310154503, "rss": 272.278310154503, "minimumFitted": 20.5610039896221, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.09915226130488, "upper": -5.93640571513816, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 1.71428333175553e-06, "logIC50Difference": -6.9350678355562e-07, "objectiveDrcMinusNls": 8.09507127996767e-09 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 101.027460723074, "bottom": 19.6340527878394, "logIC50": -6.01800237601521, "hill": -0.960632172284655 }, "objective": 272.278310154503, "df": 26, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 272.278310154503, "polishedObjective": 272.278310154503, "relativeImprovement": 8.35078179066889e-16, "minimumAttained": true, "polishedEstimates": { "top": 101.027460721707, "bottom": 19.6340527891197, "logIC50": -6.01800237620952, "hill": -0.96063217327133 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 272.278310154503, "threshold": 316.52564333565, "lower": -6.09915158374385, "upper": -5.93640642817023, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.991266040366326, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -5.7833473947652, "absoluteIC50_M": 1.64684454367426e-06, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 1.64684501944626e-06, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 62.5104666666667, "objectiveFlat": 31174.6700894667, "objectiveFull": 272.278310154503, "weighted": false, "n": 30, "parametersFull": 4, "df1": 3, "df2": 26, "F": 983.628584304292, "p": 7.17165402459381e-27, "alpha": 0.05, "noResponse": false, "working": "F = ((31174.6701 - 272.27831) / 3) / (272.27831 / 26) = 983.628584; p = P(F(3, 26) > F) = 7.17165e-27 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 7.17165402459381e-27, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.697761608363258, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.71576398437847, "bendPoint_M": 1.92413710954584e-07, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.32024076765195, "bendPoint_M": 4.78364819078965e-06, "concentrationsAtOrBeyond": 3, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 4, "concentrationsPredictedAbove50": 6, "fires": false }, "vi": { "profileWidthLog10": 0.162745155573622, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 101.027460723074, "bottom": 19.6340527878394, "logIC50": -6.01800237601521, "hill": -0.960632172284655 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 272.278310154503, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.09911627248097, "upper": -5.93688847954945, "standardError": 0.0394613158735947, "dfResidual": 26, "tQuantile": 2.05552943864287, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.09915158374385, "upper": -5.93640642817023, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 983.628584304292, "p": 7.17165402459381e-27, "df1": 3, "df2": 26, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -6.01800237601521, "ic50_M": 9.59395382671305e-07, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -5.7833473947652, "absoluteIC50_M": 1.64684454367426e-06 } }, "warnings": ["NaNs produced"] }, { "id": "C11", "description": "Bottom -10 (undershoot below the 0% control)", "truth": { "top": 100, "bottom": -10, "logIC50": -6, "hill": -1.2, "ic50_M": 1e-06, "drcLL4": { "b": 1.2, "c": -10, "d": 100, "e": 1e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 20, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 1.15777011450539, "c": -9.27220074704226, "d": 99.1493591028686, "e": 9.43469283478873e-07 }, "standardErrors": { "b": 0.0739448533522486, "c": 1.4630796647296, "d": 1.32268350018979, "e": 5.69572950839011e-08 }, "wald": { "b": { "lower": 1.00101402803382, "upper": 1.31452620097696 }, "c": { "lower": -12.3737910814854, "upper": -6.17061041259912 }, "d": { "lower": 96.3453953416237, "upper": 101.953322864113 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "rss": 127.389002923167, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 99.1493591028686, "bottom": -9.27220074704226, "logIC50": -6.0252722345905, "hill": -1.15777011450539 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -13.8737026828783, "lnIC50StandardError": 0.0603705781159745, "waldLogIC50": { "lower": -6.08085348678125, "upper": -5.9696915506995 }, "logIC50": -6.02527251874038, "dfResidual": 16 }, "nls": { "estimates": { "top": 99.149373760412, "bottom": -9.27221072092852, "logIC50": -6.02527236279612, "hill": -1.15776891966752 }, "standardErrors": { "top": 1.31720611359862, "bottom": 1.47054021278337, "logIC50": 0.0262340259073702, "hill": 0.0740155932252424 }, "wald": { "top": { "lower": 96.3570215400276, "upper": 101.941725980796 }, "bottom": { "lower": -12.3896167107259, "upper": -6.15480473113109 }, "logIC50": { "lower": -6.08088601333707, "upper": -5.96965871225518 }, "hill": { "lower": -1.31467496797072, "upper": -1.00086287136433 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "objective": 127.389002920852, "rss": 127.389002920852, "minimumFitted": -8.78427852294949, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.0808980919842, "upper": -5.96949935142132, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 1.07567626347721e-06, "logIC50Difference": -1.28205625671285e-07, "objectiveDrcMinusNls": 2.31496244396112e-09 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 99.149373760412, "bottom": -9.27221072092852, "logIC50": -6.02527236279612, "hill": -1.15776891966752 }, "objective": 127.389002920852, "df": 16, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 127.389002920852, "polishedObjective": 127.389002920852, "relativeImprovement": 2.23109599563023e-16, "minimumAttained": true, "polishedEstimates": { "top": 99.1493737608748, "bottom": -9.27221072156726, "logIC50": -6.02527236280257, "hill": -1.15776891956856 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 127.389002920852, "threshold": 163.169376995711, "lower": -6.08089797666968, "upper": -5.96949962051755, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.996841364366462, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -6.09552225097106, "absoluteIC50_M": 8.02560440832286e-07, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 8.02560721645278e-07, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 47.69665, "objectiveFlat": 40330.38871855, "objectiveFull": 127.389002920852, "weighted": false, "n": 20, "parametersFull": 4, "df1": 3, "df2": 16, "F": 1683.15940596987, "p": 3.30318759919967e-20, "alpha": 0.05, "noResponse": false, "working": "F = ((40330.3887 - 127.389003) / 3) / (127.389003 / 16) = 1683.15941; p = P(F(3, 16) > F) = 3.30319e-20 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 3.30318759919967e-20, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.578951670054608, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.60422403285073, "bendPoint_M": 2.48757376062415e-07, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.44632069274152, "bendPoint_M": 3.57832108303756e-06, "concentrationsAtOrBeyond": 4, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 5, "concentrationsPredictedAbove50": 5, "fires": false }, "vi": { "profileWidthLog10": 0.111398356152126, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 99.149373760412, "bottom": -9.27221072092852, "logIC50": -6.02527236279612, "hill": -1.15776891966752 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 127.389002920852, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.08088601333707, "upper": -5.96965871225518, "standardError": 0.0262340259073702, "dfResidual": 16, "tQuantile": 2.11990529922125, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.08089797666968, "upper": -5.96949962051755, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 1683.15940596987, "p": 3.30318759919967e-20, "df1": 3, "df2": 16, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -6.02527236279612, "ic50_M": 9.43469004962666e-07, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -6.09552225097106, "absoluteIC50_M": 8.02560440832286e-07 } }, "warnings": [] }, { "id": "C12", "description": "Top 90, Bottom 40", "truth": { "top": 90, "bottom": 40, "logIC50": -5, "hill": -1, "ic50_M": 1e-05, "drcLL4": { "b": 1, "c": 40, "d": 90, "e": 1e-05 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 30, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 1.06005888509509, "c": 40.7740413799582, "d": 90.6154398060303, "e": 9.96261183897721e-06 }, "standardErrors": { "b": 0.0901537262497584, "c": 0.931542158402711, "d": 0.843960466312764, "e": 8.45554018734687e-07 }, "wald": { "b": { "lower": 0.874745246785359, "upper": 1.24537252340482 }, "c": { "lower": 38.8592290500246, "upper": 42.6888537098919 }, "d": { "lower": 88.8806542224736, "upper": 92.3502253895869 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "rss": 109.81583772434, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 90.6154398060303, "bottom": 40.7740413799582, "logIC50": -5.00162679023543, "hill": -1.06005888509509 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -11.5166730854036, "lnIC50StandardError": 0.0848732190264485, "waldLogIC50": { "lower": -5.0773943257241, "upper": -4.92586081602488 }, "logIC50": -5.00162757087449, "dfResidual": 26 }, "nls": { "estimates": { "top": 90.6154511971473, "bottom": 40.7740374668291, "logIC50": -5.0016271781394, "hill": -1.06005751214191 }, "standardErrors": { "top": 0.823299319635037, "bottom": 0.948780062618828, "logIC50": 0.0369951732148321, "hill": 0.0890548873806751 }, "wald": { "top": { "lower": 88.9231352088228, "upper": 92.3077671854717 }, "bottom": { "lower": 38.8237921173187, "upper": 42.7242828163395 }, "logIC50": { "lower": -5.07767184577018, "upper": -4.92558251050862 }, "hill": { "lower": -1.24311245480791, "upper": -0.877002569475906 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "objective": 109.815837722905, "rss": 109.815837722905, "minimumFitted": 41.1477022948946, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -5.07790099398061, "upper": -4.92573378621057, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 1.29516689833214e-06, "logIC50Difference": -3.87903974718995e-07, "objectiveDrcMinusNls": 1.43541001307312e-09 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 90.6154511971473, "bottom": 40.7740374668291, "logIC50": -5.0016271781394, "hill": -1.06005751214191 }, "objective": 109.815837722905, "df": 26, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 109.815837722905, "polishedObjective": 109.815837722904, "relativeImprovement": 1.81168736803555e-15, "minimumAttained": true, "polishedEstimates": { "top": 90.6154512102863, "bottom": 40.7740374480128, "logIC50": -5.001627178273, "hill": -1.06005750762271 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 109.815837722905, "threshold": 127.661761467381, "lower": -5.0779004347824, "upper": -4.92573441221242, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.991080119917898, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -4.39441522198969, "absoluteIC50_M": 4.03259658506997e-05, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 4.03259343107734e-05, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 67.2051666666667, "objectiveFlat": 12311.3580801667, "objectiveFull": 109.815837722905, "weighted": false, "n": 30, "parametersFull": 4, "df1": 3, "df2": 26, "F": 962.945797502729, "p": 9.42981975722595e-27, "alpha": 0.05, "noResponse": false, "working": "F = ((12311.3581 - 109.815838) / 3) / (109.815838 / 26) = 962.945798; p = P(F(3, 26) > F) = 9.42982e-27 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 9.42981975722595e-27, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.632316871397351, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -5.63394404953675, "bendPoint_M": 2.32303605544705e-06, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -4.36931030674205, "bendPoint_M": 4.27257498300364e-05, "concentrationsAtOrBeyond": 3, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 3, "concentrationsPredictedAbove50": 7, "fires": false }, "vi": { "profileWidthLog10": 0.152166022569985, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 90.6154511971473, "bottom": 40.7740374668291, "logIC50": -5.0016271781394, "hill": -1.06005751214191 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 109.815837722905, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -5.07767184577018, "upper": -4.92558251050862, "standardError": 0.0369951732148321, "dfResidual": 26, "tQuantile": 2.05552943864287, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -5.0779004347824, "upper": -4.92573441221242, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 962.945797502729, "p": 9.42981975722595e-27, "df1": 3, "df2": 26, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -5.0016271781394, "ic50_M": 9.96260294055651e-06, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -4.39441522198969, "absoluteIC50_M": 4.03259658506997e-05 } }, "warnings": [] }, { "id": "C13", "description": "No lower plateau: IC50 half a log below the top concentration", "truth": { "top": 100, "bottom": 0, "logIC50": -4.5, "hill": -1, "ic50_M": 3.16227766016838e-05, "drcLL4": { "b": 1, "c": 0, "d": 100, "e": 3.16227766016838e-05 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 20, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 0.908222891607846, "c": -10.3209035665932, "d": 101.250051206912, "e": 3.72157750657555e-05 }, "standardErrors": { "b": 0.164574978688182, "c": 20.737964364299, "d": 1.38444213886618, "e": 1.75142954277576e-05 }, "wald": { "b": { "lower": 0.559339522167543, "upper": 1.25710626104815 }, "c": { "lower": -54.2834241175322, "upper": 33.6416169843457 }, "d": { "lower": 98.3151649802645, "upper": 104.18493743356 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "rss": 248.431777793376, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 101.250051206912, "bottom": -10.3209035665932, "logIC50": -4.42927293184407, "hill": -0.908222891607846 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -10.1985268988602, "lnIC50StandardError": 0.470952938641327, "waldLogIC50": { "lower": -4.86275298282702, "upper": -3.99557492860676 }, "logIC50": -4.42916395571689, "dfResidual": 16 }, "nls": { "estimates": { "top": 101.250060101305, "bottom": -10.3211464622679, "logIC50": -4.42927053473361, "hill": -0.908220750591176 }, "standardErrors": { "top": 1.41518008703203, "bottom": 21.2253648291849, "logIC50": 0.208406765239152, "hill": 0.172861493160345 }, "wald": { "top": { "lower": 98.250012335453, "upper": 104.250107867156 }, "bottom": { "lower": -55.3169098415613, "upper": 34.6746169170255 }, "logIC50": { "lower": -4.87107314075765, "upper": -3.98746792870957 }, "hill": { "lower": -1.27467074597309, "upper": -0.541770755209262 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "objective": 248.431777790911, "rss": 248.431777790911, "minimumFitted": 21.9809957486843, "startedFrom": "truth", "convergenceTolerance": 1e-06, "earlierAttempts": ["start truth, tol 1e-08: step factor 5.82077e-11 reduced below 'minFactor' of 1e-10"], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -4.71547965895861, "upper": -3.4232041487084, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 2.3534342036986e-05, "logIC50Difference": 2.39711045857405e-06, "objectiveDrcMinusNls": 2.46541276283097e-09 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 101.250060101305, "bottom": -10.3211464622679, "logIC50": -4.42927053473361, "hill": -0.908220750591176 }, "objective": 248.431777790911, "df": 16, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 248.431777790911, "polishedObjective": 248.431777790907, "relativeImprovement": 1.64742457441285e-14, "minimumAttained": true, "polishedEstimates": { "top": 101.250059686011, "bottom": -10.3211394051332, "logIC50": -4.4292706016865, "hill": -0.908220823210613 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 248.431777790911, "threshold": 318.210029740679, "lower": -4.71599111893992, "upper": -3.42441032440203, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.982068406881163, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -4.50719785367712, "absoluteIC50_M": 3.1102990400283e-05, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 3.11029638376366e-05, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 83.23675, "objectiveFlat": 13854.41751575, "objectiveFull": 248.431777790911, "weighted": false, "n": 20, "parametersFull": 4, "df1": 3, "df2": 16, "F": 292.093297863805, "p": 3.54004949365083e-14, "alpha": 0.05, "noResponse": false, "working": "F = ((13854.4175 - 248.431778) / 3) / (248.431778 / 16) = 292.093298; p = P(F(3, 16) > F) = 3.54005e-14 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 3.54004949365083e-14, "fires": false }, "iii": { "concentrationsBelowIC50": 9, "concentrationsAboveIC50": 1, "fires": true }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.738027895908046, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -5.16729843064166, "bendPoint_M": 6.80301720585879e-06, "concentrationsAtOrBeyond": 7, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -3.69124263882556, "bendPoint_M": 0.000203590430720334, "concentrationsAtOrBeyond": 0, "fires": true } }, "fires": true }, "v": { "concentrationsPredictedBelow50": 2, "concentrationsPredictedAbove50": 8, "fires": false }, "vi": { "profileWidthLog10": 1.29158079453789, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 101.250060101305, "bottom": -10.3211464622679, "logIC50": -4.42927053473361, "hill": -0.908220750591176 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 248.431777790911, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -4.87107314075765, "upper": -3.98746792870957, "standardError": 0.208406765239152, "dfResidual": 16, "tQuantile": 2.11990529922125, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -4.71599111893992, "upper": -3.42441032440203, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 292.093297863805, "p": 3.54004949365083e-14, "df1": 3, "df2": 16, "noResponse": false }, "relativeIC50": { "shown": false, "withheldBy": "iii", "reason": "IC50 not bracketed: only one concentration above it", "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -4.50719785367712, "absoluteIC50_M": 3.1102990400283e-05 } }, "warnings": [] }, { "id": "C14", "description": "No lower plateau, Hill -1.5, Bottom 10, 8 points", "truth": { "top": 100, "bottom": 10, "logIC50": -4.3, "hill": -1.5, "ic50_M": 5.01187233627273e-05, "drcLL4": { "b": 1.5, "c": 10, "d": 100, "e": 5.01187233627273e-05 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 24, "distinctConcentrations": 8, "drcLL4": { "estimates": { "b": 1.32528989613874, "c": -3.42376598679554, "d": 99.615206395719, "e": 6.4412164989563e-05 }, "standardErrors": { "b": 0.22555566836706, "c": 21.4847303707993, "d": 0.780277593896129, "e": 2.27542817727078e-05 }, "wald": { "b": { "lower": 0.854789016601434, "upper": 1.79579077567605 }, "c": { "lower": -48.2401282146457, "upper": 41.3925962410546 }, "d": { "lower": 97.9875758561311, "upper": 101.242836935307 } }, "dfResidual": 20, "tQuantile": 2.08596344726586, "rss": 132.407080762765, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 99.615206395719, "bottom": -3.42376598679554, "logIC50": -4.19103210330925, "hill": -1.32528989613874 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -9.6497983128639, "lnIC50StandardError": 0.353996355494146, "waldLogIC50": { "lower": -4.51154739188476, "upper": -3.87016092562744 }, "logIC50": -4.1908541587561, "dfResidual": 20 }, "nls": { "estimates": { "top": 99.615213403484, "bottom": -3.4241306181461, "logIC50": -4.19102950092458, "hill": -1.32528590446269 }, "standardErrors": { "top": 0.786272451028685, "bottom": 21.9757655640508, "logIC50": 0.156882981486224, "hill": 0.231568682797786 }, "wald": { "top": { "lower": 97.975077811046, "upper": 101.255348995922 }, "bottom": { "lower": -49.26477431044, "upper": 42.4165130741478 }, "logIC50": { "lower": -4.51828166580293, "upper": -3.86377733604623 }, "hill": { "lower": -1.80832971231037, "upper": -0.842242096615002 } }, "dfResidual": 20, "tQuantile": 2.08596344726586, "objective": 132.407080760561, "rss": 132.407080760561, "minimumFitted": 33.490312943708, "startedFrom": "truth", "convergenceTolerance": 1e-06, "earlierAttempts": ["start truth, tol 1e-08: step factor 5.82077e-11 reduced below 'minFactor' of 1e-10"], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -4.3834596089353, "upper": -3.43652020820775, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 0.000106500079726932, "logIC50Difference": 2.6023846722012e-06, "objectiveDrcMinusNls": 2.20367724068637e-09 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 99.615213403484, "bottom": -3.4241306181461, "logIC50": -4.19102950092458, "hill": -1.32528590446269 }, "objective": 132.407080760561, "df": 20, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 132.407080760561, "polishedObjective": 132.407080760557, "relativeImprovement": 3.32713699026345e-14, "minimumAttained": true, "polishedEstimates": { "top": 99.6152134312115, "bottom": -3.42414286476599, "logIC50": -4.1910294134235, "hill": -1.32528581780785 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 132.407080760561, "threshold": 161.21385325827, "lower": -4.38964961194861, "upper": -3.43811818126704, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.988833677129636, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -4.2152677424633, "absoluteIC50_M": 6.09161233672187e-05, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 6.09160758106057e-05, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 86.0375, "objectiveFlat": 11857.715588, "objectiveFull": 132.407080760561, "weighted": false, "n": 24, "parametersFull": 4, "df1": 3, "df2": 20, "F": 590.366640005854, "p": 1.10944078336797e-19, "alpha": 0.05, "noResponse": false, "working": "F = ((11857.7156 - 132.407081) / 3) / (132.407081 / 20) = 590.36664; p = P(F(3, 20) > F) = 1.10944e-19 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 8, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 1.10944078336797e-19, "fires": false }, "iii": { "concentrationsBelowIC50": 7, "concentrationsAboveIC50": 1, "fires": true }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.50577180917848, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -4.69680131010306, "bendPoint_M": 2.01001218365401e-05, "concentrationsAtOrBeyond": 6, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -3.6852576917461, "bendPoint_M": 0.000206415501118991, "concentrationsAtOrBeyond": 0, "fires": true } }, "fires": true }, "v": { "concentrationsPredictedBelow50": 1, "concentrationsPredictedAbove50": 7, "fires": true }, "vi": { "profileWidthLog10": 0.951531430681576, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 99.615213403484, "bottom": -3.4241306181461, "logIC50": -4.19102950092458, "hill": -1.32528590446269 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 132.407080760561, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -4.51828166580293, "upper": -3.86377733604623, "standardError": 0.156882981486224, "dfResidual": 20, "tQuantile": 2.08596344726586, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -4.38964961194861, "upper": -3.43811818126704, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 590.366640005854, "p": 1.10944078336797e-19, "df1": 3, "df2": 20, "noResponse": false }, "relativeIC50": { "shown": false, "withheldBy": "iii", "reason": "IC50 not bracketed: only one concentration above it", "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": false, "withheldBy": "v", "reason": "below 50 percent only at 100 M" } }, "warnings": [] }, { "id": "C15", "description": "No upper plateau: IC50 near the lowest concentration", "truth": { "top": 100, "bottom": 0, "logIC50": -8.3, "hill": -1, "ic50_M": 5.01187233627271e-09, "drcLL4": { "b": 1, "c": 0, "d": 100, "e": 5.01187233627271e-09 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 20, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 1.16545509502716, "c": -0.598731354709045, "d": 68.5040379970818, "e": 1.06416244591969e-08 }, "standardErrors": { "b": 0.26350977944611, "c": 0.874579836814402, "d": 16.1939900754496, "e": 5.03033226641266e-09 }, "wald": { "b": { "lower": 0.606839317182729, "upper": 1.72407087287159 }, "c": { "lower": -2.45275778536396, "upper": 1.25529507594587 }, "d": { "lower": 34.1743126205998, "upper": 102.833763373564 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "rss": 129.482833416024, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 68.5040379970818, "bottom": -0.598731354709045, "logIC50": -7.97299207130646, "hill": -1.16545509502716 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -18.3596825736857, "lnIC50StandardError": 0.475903761358306, "waldLogIC50": { "lower": -8.41165589851172, "upper": -7.53536176398228 }, "logIC50": -7.973508831247, "dfResidual": 16 }, "nls": { "estimates": { "top": 68.5306437437621, "bottom": -0.599079562389216, "logIC50": -7.97333398480237, "hill": -1.16506004688614 }, "standardErrors": { "top": 17.1486552931451, "bottom": 0.894087538795578, "logIC50": 0.216517626822645, "hill": 0.286824110617504 }, "wald": { "top": { "lower": 32.1771185133052, "upper": 104.884168974219 }, "bottom": { "lower": -2.49446047384965, "upper": 1.29630134907122 }, "logIC50": { "lower": -8.4323308492785, "upper": -7.51433712032623 }, "hill": { "lower": -1.77309999892861, "upper": -0.557020094843673 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "objective": 129.482811178895, "rss": 129.482811178895, "minimumFitted": -0.597455951558116, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -9.84394051236387, "upper": -7.71759143917191, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 0.000581575822666947, "logIC50Difference": -0.000341913495908841, "objectiveDrcMinusNls": 2.22371290874435e-05 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 68.5306437437621, "bottom": -0.599079562389216, "logIC50": -7.97333398480237, "hill": -1.16506004688614 }, "objective": 129.482811178895, "df": 16, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 129.482811178895, "polishedObjective": 129.482811178895, "relativeImprovement": 2.1950179465239e-16, "minimumAttained": true, "polishedEstimates": { "top": 68.5306439066424, "bottom": -0.599079535414363, "logIC50": -7.97333398701331, "hill": -1.16506004465046 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 129.482811178895, "threshold": 165.851283449015, "lower": -9.87139048881269, "upper": -7.71313469536227, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.973770958374611, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -8.34778001545678, "absoluteIC50_M": 4.48972751918359e-09, "withinTestedRange": false, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 4.48906586363322e-09, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 8.53755, "objectiveFlat": 4936.61998895, "objectiveFull": 129.482811178895, "weighted": false, "n": 20, "parametersFull": 4, "df1": 3, "df2": 16, "F": 198.003616964191, "p": 7.39067075037193e-13, "alpha": 0.05, "noResponse": false, "working": "F = ((4936.61999 - 129.482811) / 3) / (129.482811 / 16) = 198.003617; p = P(F(3, 16) > F) = 7.39067e-13 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 7.39067075037193e-13, "fires": false }, "iii": { "concentrationsBelowIC50": 1, "concentrationsAboveIC50": 9, "fires": true }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.575328500338092, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -8.54866248514046, "bendPoint_M": 2.82707620256637e-09, "concentrationsAtOrBeyond": 0, "fires": true }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -7.39800548446427, "bendPoint_M": 3.99939699112441e-08, "concentrationsAtOrBeyond": 8, "fires": false } }, "fires": true }, "v": { "concentrationsPredictedBelow50": 10, "concentrationsPredictedAbove50": 0, "fires": true }, "vi": { "profileWidthLog10": 2.15825579345042, "lowerUnbounded": false, "upperUnbounded": false, "fires": true } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 68.5306437437621, "bottom": -0.599079562389216, "logIC50": -7.97333398480237, "hill": -1.16506004688614 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 129.482811178895, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -8.4323308492785, "upper": -7.51433712032623, "standardError": 0.216517626822645, "dfResidual": 16, "tQuantile": 2.11990529922125, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -9.87139048881269, "upper": -7.71313469536227, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 198.003616964191, "p": 7.39067075037193e-13, "df1": 3, "df2": 16, "noResponse": false }, "relativeIC50": { "shown": false, "withheldBy": "iii", "reason": "IC50 not bracketed: only one concentration below it", "poorlyDetermined": true, "poorlyDeterminedReason": "poorly determined: profile interval 2.16 log units wide" }, "absoluteIC50": { "shown": false, "withheldBy": "v", "reason": "above 50 percent at no tested concentration" } }, "warnings": ["NaNs produced"] }, { "id": "C16", "description": "Triplicates with one excluded well (outlier near the IC50)", "truth": { "top": 100, "bottom": 0, "logIC50": -6, "hill": -1, "ic50_M": 1e-06, "drcLL4": { "b": 1, "c": 0, "d": 100, "e": 1e-06 } }, "expectedRule": null, "excludedWells": 1, "fixed": {}, "weighting": "none", "n": 29, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 0.977221117509355, "c": -1.10313736463458, "d": 99.4356834379734, "e": 1.05985918289299e-06 }, "standardErrors": { "b": 0.0499870597882786, "c": 1.23422285816728, "d": 1.02556478959519, "e": 6.09365402622065e-08 }, "wald": { "b": { "lower": 0.874270840736611, "upper": 1.0801713942821 }, "c": { "lower": -3.64506692371946, "upper": 1.4387921944503 }, "d": { "lower": 97.3234932154558, "upper": 101.547873660491 } }, "dfResidual": 25, "tQuantile": 2.0595385527533, "rss": 144.994987815485, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 99.4356834379734, "bottom": -1.10313736463458, "logIC50": -5.97475183299473, "hill": -0.977221117509355 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -13.7573729923826, "lnIC50StandardError": 0.0574948745108833, "waldLogIC50": { "lower": -6.02617724975402, "upper": -5.92332510239915 }, "logIC50": -5.97475117607659, "dfResidual": 25 }, "nls": { "estimates": { "top": 99.4357075021827, "bottom": -1.10316002077455, "logIC50": -5.97475193755496, "hill": -0.977219485275384 }, "standardErrors": { "top": 1.0170054245796, "bottom": 1.22577202286162, "logIC50": 0.0250242278894109, "hill": 0.0489966823541883 }, "wald": { "top": { "lower": 97.3411456219018, "upper": 101.530269382464 }, "bottom": { "lower": -3.62768475874445, "upper": 1.42136471719534 }, "logIC50": { "lower": -6.02629029964609, "upper": -5.92321357546383 }, "hill": { "lower": -1.07813004154084, "upper": -0.876308929009926 } }, "dfResidual": 25, "tQuantile": 2.0595385527533, "objective": 144.994987809169, "rss": 144.994987809169, "minimumFitted": 0.0649733382447777, "startedFrom": "truth", "convergenceTolerance": 1e-06, "earlierAttempts": ["start truth, tol 1e-08: number of iterations exceeded maximum of 1000"], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.02590491095235, "upper": -5.92292172966007, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 2.05379136784364e-05, "logIC50Difference": -1.04560226255046e-07, "objectiveDrcMinusNls": 6.31644070381299e-09 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 99.4357075021827, "bottom": -1.10316002077455, "logIC50": -5.97475193755496, "hill": -0.977219485275384 }, "objective": 144.994987809169, "df": 25, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 144.994987809169, "polishedObjective": 144.994987809166, "relativeImprovement": 1.97978750565424e-14, "minimumAttained": true, "polishedEstimates": { "top": 99.4357070674475, "bottom": -1.10315931446399, "logIC50": -5.97475194002146, "hill": -0.977219517866534 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 144.994987809169, "threshold": 169.595991892573, "lower": -6.02590512446201, "upper": -5.92292181072272, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.99694970548764, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -5.98949478938694, "absoluteIC50_M": 1.02448407187357e-06, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 1.02448433107849e-06, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 53.0169310344828, "objectiveFlat": 47534.7502418621, "objectiveFull": 144.994987809169, "weighted": false, "n": 29, "parametersFull": 4, "df1": 3, "df2": 25, "F": 2723.64330025576, "p": 1.46980464217381e-31, "alpha": 0.05, "noResponse": false, "working": "F = ((47534.7502 - 144.994988) / 3) / (144.994988 / 25) = 2723.6433; p = P(F(3, 25) > F) = 1.4698e-31 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 1.46980464217381e-31, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.685917810357559, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.66066974791252, "bendPoint_M": 2.18439036411446e-07, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.2888341271974, "bendPoint_M": 5.14240020981151e-06, "concentrationsAtOrBeyond": 3, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 5, "concentrationsPredictedAbove50": 5, "fires": false }, "vi": { "profileWidthLog10": 0.102983313739297, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 99.4357075021827, "bottom": -1.10316002077455, "logIC50": -5.97475193755496, "hill": -0.977219485275384 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 144.994987809169, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.02629029964609, "upper": -5.92321357546383, "standardError": 0.0250242278894109, "dfResidual": 25, "tQuantile": 2.0595385527533, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.02590512446201, "upper": -5.92292181072272, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 2723.64330025576, "p": 1.46980464217381e-31, "df1": 3, "df2": 25, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -5.97475193755496, "ic50_M": 1.05985892772257e-06, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -5.98949478938694, "absoluteIC50_M": 1.02448407187357e-06 } }, "warnings": [] }, { "id": "C17", "description": "Triplicates with one excluded well (outlier on the top plateau)", "truth": { "top": 100, "bottom": 5, "logIC50": -6.8, "hill": -1.3, "ic50_M": 1.58489319246111e-07, "drcLL4": { "b": 1.3, "c": 5, "d": 100, "e": 1.58489319246111e-07 } }, "expectedRule": null, "excludedWells": 1, "fixed": {}, "weighting": "none", "n": 29, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 1.21937280732905, "c": 4.57591720440599, "d": 101.890120034041, "e": 1.63918949198665e-07 }, "standardErrors": { "b": 0.0762827677790942, "c": 0.90347551536306, "d": 1.84001116251277, "e": 1.02013111261727e-08 }, "wald": { "b": { "lower": 1.06226550617728, "upper": 1.37648010848082 }, "c": { "lower": 2.71517454904711, "upper": 6.43665985976486 }, "d": { "lower": 98.1005461073493, "upper": 105.679693960732 } }, "dfResidual": 25, "tQuantile": 2.0595385527533, "rss": 215.716786392586, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 101.890120034041, "bottom": 4.57591720440599, "logIC50": -6.78537083863983, "hill": -1.21937280732905 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -15.6239021401954, "lnIC50StandardError": 0.0622398661680559, "waldLogIC50": { "lower": -6.84104469885382, "upper": -6.72970427171274 }, "logIC50": -6.78537448528328, "dfResidual": 25 }, "nls": { "estimates": { "top": 101.890299438551, "bottom": 4.57593832179437, "logIC50": -6.78537448577041, "hill": -1.219368331825 }, "standardErrors": { "top": 1.85712925421365, "bottom": 0.917449916023496, "logIC50": 0.0267561406903838, "hill": 0.080039103056566 }, "wald": { "top": { "lower": 98.0654701420524, "upper": 105.71512873505 }, "bottom": { "lower": 2.68641484952371, "upper": 6.46546179406504 }, "logIC50": { "lower": -6.84047978904514, "upper": -6.73026918249567 }, "hill": { "lower": -1.38421195029779, "upper": -1.05452471335221 } }, "dfResidual": 25, "tQuantile": 2.0595385527533, "objective": 215.716786233572, "rss": 215.716786233572, "minimumFitted": 4.61498689722913, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.84262839192627, "upper": -6.73077191906162, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 4.61489739481566e-06, "logIC50Difference": -3.64713057532384e-06, "objectiveDrcMinusNls": 1.59013438860711e-07 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 101.890299438551, "bottom": 4.57593832179437, "logIC50": -6.78537448577041, "hill": -1.219368331825 }, "objective": 215.716786233572, "df": 25, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 215.716786233572, "polishedObjective": 215.716786233572, "relativeImprovement": 3.9526422481971e-16, "minimumAttained": true, "polishedEstimates": { "top": 101.890299484951, "bottom": 4.57593837273043, "logIC50": -6.78537448734507, "hill": -1.2193683312635 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 215.716786233572, "threshold": 252.317013725403, "lower": -6.84262719657129, "upper": -6.73077079519529, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.994787038195944, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -6.73797272007268, "absoluteIC50_M": 1.82821505068345e-07, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 1.82822379064418e-07, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 38.1848620689655, "objectiveFlat": 41380.8491874483, "objectiveFull": 215.716786233572, "weighted": false, "n": 29, "parametersFull": 4, "df1": 3, "df2": 25, "F": 1590.24606290345, "p": 1.19153753223168e-28, "alpha": 0.05, "noResponse": false, "working": "F = ((41380.8492 - 215.716786) / 3) / (215.716786 / 25) = 1590.24606; p = P(F(3, 25) > F) = 1.19154e-28 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 1.19153753223168e-28, "fires": false }, "iii": { "concentrationsBelowIC50": 4, "concentrationsAboveIC50": 6, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.549704492141125, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -7.33507897791153, "bendPoint_M": 4.62296943501259e-08, "concentrationsAtOrBeyond": 3, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -6.23566999362928, "bendPoint_M": 5.81205889381297e-07, "concentrationsAtOrBeyond": 5, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 6, "concentrationsPredictedAbove50": 4, "fires": false }, "vi": { "profileWidthLog10": 0.111856401376, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 101.890299438551, "bottom": 4.57593832179437, "logIC50": -6.78537448577041, "hill": -1.219368331825 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 215.716786233572, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.84047978904514, "upper": -6.73026918249567, "standardError": 0.0267561406903838, "dfResidual": 25, "tQuantile": 2.0595385527533, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.84262719657129, "upper": -6.73077079519529, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 1590.24606290345, "p": 1.19153753223168e-28, "df1": 3, "df2": 25, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -6.78537448577041, "ic50_M": 1.63917572641222e-07, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -6.73797272007268, "absoluteIC50_M": 1.82821505068345e-07 } }, "warnings": ["NaNs produced"] }, { "id": "C18", "description": "Quadruplicates with one excluded well, Hill -0.8", "truth": { "top": 100, "bottom": 0, "logIC50": -5.5, "hill": -0.8, "ic50_M": 3.16227766016838e-06, "drcLL4": { "b": 0.8, "c": 0, "d": 100, "e": 3.16227766016838e-06 } }, "expectedRule": null, "excludedWells": 1, "fixed": {}, "weighting": "none", "n": 39, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 0.725925855579873, "c": -0.915891704642046, "d": 100.686072339893, "e": 3.53132333059978e-06 }, "standardErrors": { "b": 0.0645050852522359, "c": 3.70883360743479, "d": 1.4977497151242, "e": 4.74340934952058e-07 }, "wald": { "b": { "lower": 0.594973570596845, "upper": 0.856878140562902 }, "c": { "lower": -8.44522421565674, "upper": 6.61344080637264 }, "d": { "lower": 97.6454787686849, "upper": 103.726665911101 } }, "dfResidual": 35, "tQuantile": 2.03010792825034, "rss": 478.436266671588, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 100.686072339893, "bottom": -0.915891704642046, "logIC50": -5.45206251628946, "hill": -0.725925855579873 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -12.5538284329929, "lnIC50StandardError": 0.134326268451476, "waldLogIC50": { "lower": -5.57048914047744, "upper": -5.33362768994052 }, "logIC50": -5.45205841520898, "dfResidual": 35 }, "nls": { "estimates": { "top": 100.686119892139, "bottom": -0.916014034594259, "logIC50": -5.45206126789718, "hill": -0.725923115421495 }, "standardErrors": { "top": 1.47459595893568, "bottom": 3.72332682835738, "logIC50": 0.0591392872207739, "hill": 0.0637299379797669 }, "wald": { "top": { "lower": 97.6925309449376, "upper": 103.67970883934 }, "bottom": { "lower": -8.47476934830978, "upper": 6.64274127912126 }, "logIC50": { "lower": -5.57212040375515, "upper": -5.33200213203921 }, "hill": { "lower": -0.855301767781123, "upper": -0.596544463061868 } }, "dfResidual": 35, "tQuantile": 2.03010792825034, "objective": 478.436266646526, "rss": 478.436266646526, "minimumFitted": 7.32675357546276, "startedFrom": "truth", "convergenceTolerance": 1e-06, "earlierAttempts": ["start truth, tol 1e-08: step factor 5.82077e-11 reduced below 'minFactor' of 1e-10"], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -5.56028258276478, "upper": -5.31531315519153, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 0.000133563773526387, "logIC50Difference": 1.24839228288209e-06, "objectiveDrcMinusNls": 2.50616949415416e-08 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 100.686119892139, "bottom": -0.916014034594259, "logIC50": -5.45206126789718, "hill": -0.725923115421495 }, "objective": 478.436266646526, "df": 35, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 478.436266646526, "polishedObjective": 478.436266646524, "relativeImprovement": 5.70292073475821e-15, "minimumAttained": true, "polishedEstimates": { "top": 100.68611970009, "bottom": -0.916015070750632, "logIC50": -5.45206124435839, "hill": -0.72592310761912 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 478.436266646526, "threshold": 534.773342708262, "lower": -5.56029651555886, "upper": -5.31533765148345, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.989563910466002, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -5.45476864965794, "absoluteIC50_M": 3.50938770601692e-06, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 3.50938478026939e-06, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 64.9163076923077, "objectiveFlat": 45844.4003463077, "objectiveFull": 478.436266646526, "weighted": false, "n": 39, "parametersFull": 4, "df1": 3, "df2": 35, "F": 1106.24887331213, "p": 1.01242755144183e-34, "alpha": 0.05, "noResponse": false, "working": "F = ((45844.4003 - 478.436267) / 3) / (478.436267 / 35) = 1106.24887; p = P(F(3, 35) > F) = 1.01243e-34 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 1.01242755144183e-34, "fires": false }, "iii": { "concentrationsBelowIC50": 6, "concentrationsAboveIC50": 4, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.923365347292512, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.37542661518969, "bendPoint_M": 4.2128246684813e-07, "concentrationsAtOrBeyond": 5, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -4.52869592060467, "bendPoint_M": 2.96008429947552e-05, "concentrationsAtOrBeyond": 2, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 4, "concentrationsPredictedAbove50": 6, "fires": false }, "vi": { "profileWidthLog10": 0.244958864075413, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 100.686119892139, "bottom": -0.916014034594259, "logIC50": -5.45206126789718, "hill": -0.725923115421495 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 478.436266646526, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -5.57212040375515, "upper": -5.33200213203921, "standardError": 0.0591392872207739, "dfResidual": 35, "tQuantile": 2.03010792825034, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -5.56029651555886, "upper": -5.31533765148345, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 1106.24887331213, "p": 1.01242755144183e-34, "df1": 3, "df2": 35, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -5.45206126789718, "ic50_M": 3.53133348150732e-06, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -5.45476864965794, "absoluteIC50_M": 3.50938770601692e-06 } }, "warnings": [] }, { "id": "C19", "description": "Rising (agonist) curve, Hill +1", "truth": { "top": 100, "bottom": 0, "logIC50": -7, "hill": 1, "ic50_M": 1e-07, "drcLL4": { "b": -1, "c": 0, "d": 100, "e": 1e-07 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 30, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": -1.04924520236627, "c": 2.59625770958634, "d": 98.7384204018647, "e": 1.00153918727781e-07 }, "standardErrors": { "b": 0.0770714149423182, "c": 1.38152493367945, "d": 1.6087056390377, "e": 7.45237397459881e-09 }, "wald": { "b": { "lower": -1.20766776465806, "upper": -0.89082264007447 }, "c": { "lower": -0.243507461810912, "upper": 5.43602288098358 }, "d": { "lower": 95.4316786027119, "upper": 102.045162201018 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "rss": 305.327093665808, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 98.7384204018647, "bottom": 2.59625770958634, "logIC50": -6.99933205337434, "hill": 1.04924520236627 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -16.116558234801, "lnIC50StandardError": 0.0744100527700845, "waldLogIC50": { "lower": -7.06575854169439, "upper": -6.93290607559856 }, "logIC50": -6.99933230864648, "dfResidual": 26 }, "nls": { "estimates": { "top": 98.738428844708, "bottom": 2.59624079493348, "logIC50": -6.99933228855033, "hill": 1.04924408737172 }, "standardErrors": { "top": 1.59798852920142, "bottom": 1.38183248261633, "logIC50": 0.0323151339091928, "hill": 0.0763824049172251 }, "wald": { "top": { "lower": 95.4537163803208, "upper": 102.023141309095 }, "bottom": { "lower": -0.244156552357365, "upper": 5.43663814222432 }, "logIC50": { "lower": -7.06575699761436, "upper": -6.9329075794863 }, "hill": { "lower": 0.892237805470021, "upper": 1.20625036927341 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "objective": 305.327093662471, "rss": 305.327093662471, "minimumFitted": 2.97074497318574, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -7.06552495566765, "upper": -6.93221700645192, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 6.51501305039123e-06, "logIC50Difference": -2.3517598979339e-07, "objectiveDrcMinusNls": 3.33642447003513e-09 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 98.738428844708, "bottom": 2.59624079493348, "logIC50": -6.99933228855033, "hill": 1.04924408737172 }, "objective": 305.327093662471, "df": 26, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 305.327093662471, "polishedObjective": 305.327093662471, "relativeImprovement": 7.44688827695671e-16, "minimumAttained": true, "polishedEstimates": { "top": 98.7384290178306, "bottom": 2.59624073179631, "logIC50": -6.99933228705072, "hill": 1.04924407737832 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 305.327093662471, "threshold": 354.945110003356, "lower": -7.06552465700872, "upper": -6.93221717576951, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.993284067998018, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -7.01082507817486, "absoluteIC50_M": 9.75382415715825e-08, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 9.75382800657945e-08, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 47.7088666666667, "objectiveFlat": 45463.1008134667, "objectiveFull": 305.327093662471, "weighted": false, "n": 30, "parametersFull": 4, "df1": 3, "df2": 26, "F": 1281.79706407236, "p": 2.35866148441371e-28, "alpha": 0.05, "noResponse": false, "working": "F = ((45463.1008 - 305.327094) / 3) / (305.327094 / 26) = 1281.79706; p = P(F(3, 26) > F) = 2.35866e-28 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 2.35866148441371e-28, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.638833477973525, "plateaus": { "top": { "free": true, "side": "high concentrations", "bendPointLog10": -6.3604988105768, "bendPoint_M": 4.36014758133364e-07, "concentrationsAtOrBeyond": 3, "fires": false }, "bottom": { "free": true, "side": "low concentrations", "bendPointLog10": -7.63816576652385, "bendPoint_M": 2.30056354419289e-08, "concentrationsAtOrBeyond": 4, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 5, "concentrationsPredictedAbove50": 5, "fires": false }, "vi": { "profileWidthLog10": 0.133307481239206, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 98.738428844708, "bottom": 2.59624079493348, "logIC50": -6.99933228855033, "hill": 1.04924408737172 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 305.327093662471, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -7.06575699761436, "upper": -6.9329075794863, "standardError": 0.0323151339091928, "dfResidual": 26, "tQuantile": 2.05552943864287, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -7.06552465700872, "upper": -6.93221717576951, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 1281.79706407236, "p": 2.35866148441371e-28, "df1": 3, "df2": 26, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -6.99933228855033, "ic50_M": 1.00153864493174e-07, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -7.01082507817486, "absoluteIC50_M": 9.75382415715825e-08 } }, "warnings": [] }, { "id": "C20", "description": "Rising curve, Hill +2, Bottom 10, Top 120", "truth": { "top": 120, "bottom": 10, "logIC50": -8, "hill": 2, "ic50_M": 1e-08, "drcLL4": { "b": -2, "c": 10, "d": 120, "e": 1e-08 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 20, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": -2.23140781805109, "c": 11.9065073015618, "d": 119.745131253691, "e": 9.70241312598817e-09 }, "standardErrors": { "b": 0.197219309756234, "c": 1.23981851560009, "d": 1.29973373771154, "e": 4.21944310997571e-10 }, "wald": { "b": { "lower": -2.64949407791208, "upper": -1.81332155819009 }, "c": { "lower": 9.27820946026855, "upper": 14.5348051428551 }, "d": { "lower": 116.98981881554, "upper": 122.500443691843 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "rss": 177.738286197931, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 119.745131253691, "bottom": 11.9065073015618, "logIC50": -8.01312023718087, "hill": 2.23140781805109 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -18.4509440024178, "lnIC50StandardError": 0.0434907016376986, "waldLogIC50": { "lower": -8.0531834535482, "upper": -7.97310287876369 }, "logIC50": -8.01314316615594, "dfResidual": 16 }, "nls": { "estimates": { "top": 119.745129856525, "bottom": 11.9065035177588, "logIC50": -8.0131203554833, "hill": 2.23140718831615 }, "standardErrors": { "top": 1.30089144956498, "bottom": 1.23465705885563, "logIC50": 0.0188394130534081, "hill": 0.194669914171258 }, "wald": { "top": { "lower": 116.98736317888, "upper": 122.502896534169 }, "bottom": { "lower": 9.28914747596981, "upper": 14.5238595595478 }, "logIC50": { "lower": -8.05305812704944, "upper": -7.97318258391717 }, "hill": { "lower": 1.81872540566555, "upper": 2.64408897096674 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "objective": 177.738286197445, "rss": 177.738286197445, "minimumFitted": 11.9073805102402, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -8.05399774570673, "upper": -7.97392915427782, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 3.17792861925398e-07, "logIC50Difference": -1.18302430962558e-07, "objectiveDrcMinusNls": 4.85897544422187e-10 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 119.745129856525, "bottom": 11.9065035177588, "logIC50": -8.0131203554833, "hill": 2.23140718831615 }, "objective": 177.738286197445, "df": 16, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 177.738286197445, "polishedObjective": 177.738286197445, "relativeImprovement": 6.39630549803569e-16, "minimumAttained": true, "polishedEstimates": { "top": 119.745129878507, "bottom": 11.9065035198455, "logIC50": -8.01312035443775, "hill": 2.23140719710842 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 177.738286197445, "threshold": 227.660510422092, "lower": -8.05399686633441, "upper": -7.9739284809419, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.996345566076874, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -8.1308321973966, "absoluteIC50_M": 7.39891098791337e-09, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 7.39891317356282e-09, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 62.81615, "objectiveFlat": 48636.33874255, "objectiveFull": 177.738286197445, "weighted": false, "n": 20, "parametersFull": 4, "df1": 3, "df2": 16, "F": 1454.08102345178, "p": 1.06023445544632e-19, "alpha": 0.05, "noResponse": false, "working": "F = ((48636.3387 - 177.738286) / 3) / (177.738286 / 16) = 1454.08102; p = P(F(3, 16) > F) = 1.06023e-19 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 1.06023445544632e-19, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.300389930214684, "plateaus": { "top": { "free": true, "side": "high concentrations", "bendPointLog10": -7.71273042526862, "bendPoint_M": 1.93762431050381e-08, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": true, "side": "low concentrations", "bendPointLog10": -8.31351028569799, "bendPoint_M": 4.8583602440908e-09, "concentrationsAtOrBeyond": 5, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 5, "concentrationsPredictedAbove50": 5, "fires": false }, "vi": { "profileWidthLog10": 0.0800683853925142, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 119.745129856525, "bottom": 11.9065035177588, "logIC50": -8.0131203554833, "hill": 2.23140718831615 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 177.738286197445, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -8.05305812704944, "upper": -7.97318258391717, "standardError": 0.0188394130534081, "dfResidual": 16, "tQuantile": 2.11990529922125, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -8.05399686633441, "upper": -7.9739284809419, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 1454.08102345178, "p": 1.06023445544632e-19, "df1": 3, "df2": 16, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -8.0131203554833, "ic50_M": 9.70241048303749e-09, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -8.1308321973966, "absoluteIC50_M": 7.39891098791337e-09 } }, "warnings": [] }, { "id": "C21", "description": "Nanomolar potency on a 100 nM top concentration", "truth": { "top": 100, "bottom": 0, "logIC50": -9, "hill": -1, "ic50_M": 1e-09, "drcLL4": { "b": 1, "c": 0, "d": 100, "e": 1e-09 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 30, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 1.05674858504585, "c": 1.08992211374172, "d": 99.3720800768941, "e": 9.11841547260443e-10 }, "standardErrors": { "b": 0.055983355776728, "c": 1.187534411553, "d": 1.07878094008103, "e": 5.13219742307144e-11 }, "wald": { "b": { "lower": 0.94167314917277, "upper": 1.17182402091893 }, "c": { "lower": -1.3510898286069, "upper": 3.53093405609034 }, "d": { "lower": 97.1546140967107, "upper": 101.589546057077 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "rss": 185.00837309579, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 99.3720800768941, "bottom": 1.08992211374172, "logIC50": -9.04008062343602, "hill": -1.05674858504585 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -20.8155560867308, "lnIC50StandardError": 0.0562847722887618, "waldLogIC50": { "lower": -9.09032684907242, "upper": -8.98983544335727 }, "logIC50": -9.04008114621484, "dfResidual": 26 }, "nls": { "estimates": { "top": 99.3720955650497, "bottom": 1.08991905345378, "logIC50": -9.04008089329665, "hill": -1.0567477873222 }, "standardErrors": { "top": 1.0893453181603, "bottom": 1.2092231500979, "logIC50": 0.0243721255345381, "hill": 0.058377094012329 }, "wald": { "top": { "lower": 97.1329141947234, "upper": 101.611276935376 }, "bottom": { "lower": -1.39567472946091, "upper": 3.57551283636848 }, "logIC50": { "lower": -9.09017851481519, "upper": -8.9899832717781 }, "hill": { "lower": -1.17674362260696, "upper": -0.936751952037435 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "objective": 185.008373092616, "rss": 185.008373092616, "minimumFitted": 1.77163101577454, "startedFrom": "truth", "convergenceTolerance": 1e-06, "earlierAttempts": ["start truth, tol 1e-08: number of iterations exceeded maximum of 1000"], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -9.09031499051321, "upper": -8.98967575925344, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 2.80780424687482e-06, "logIC50Difference": -2.69860626289642e-07, "objectiveDrcMinusNls": 3.17390913551208e-09 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 99.3720955650497, "bottom": 1.08991905345378, "logIC50": -9.04008089329665, "hill": -1.0567477873222 }, "objective": 185.008373092616, "df": 26, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 185.008373092616, "polishedObjective": 185.008373092496, "relativeImprovement": 6.52901612289449e-13, "minimumAttained": true, "polishedEstimates": { "top": 99.372097772534, "bottom": 1.08991601378438, "logIC50": -9.04008087644365, "hill": -1.05674756015471 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 185.008373092616, "threshold": 215.0736659207, "lower": -9.09031487540844, "upper": -8.98967597484896, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.99611918589773, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -9.03621698233184, "absoluteIC50_M": 9.1998981134027e-10, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 9.19990158189364e-10, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 52.4217, "objectiveFlat": 47672.5677183, "objectiveFull": 185.008373092616, "weighted": false, "n": 30, "parametersFull": 4, "df1": 3, "df2": 26, "F": 2224.54173710524, "p": 1.89171303515431e-31, "alpha": 0.05, "noResponse": false, "working": "F = ((47672.5677 - 185.008373) / 3) / (185.008373 / 26) = 2224.54174; p = P(F(3, 26) > F) = 1.89171e-31 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 1.89171303515431e-31, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.634297282303617, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -9.67437817560026, "bendPoint_M": 2.11651730846387e-10, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -8.40578361099303, "bendPoint_M": 3.92840621095741e-09, "concentrationsAtOrBeyond": 3, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 5, "concentrationsPredictedAbove50": 5, "fires": false }, "vi": { "profileWidthLog10": 0.100638900559487, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 99.3720955650497, "bottom": 1.08991905345378, "logIC50": -9.04008089329665, "hill": -1.0567477873222 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 185.008373092616, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -9.09017851481519, "upper": -8.9899832717781, "standardError": 0.0243721255345381, "dfResidual": 26, "tQuantile": 2.05552943864287, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -9.09031487540844, "upper": -8.98967597484896, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 2224.54173710524, "p": 1.89171303515431e-31, "df1": 3, "df2": 26, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -9.04008089329665, "ic50_M": 9.11840980663205e-10, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -9.03621698233184, "absoluteIC50_M": 9.1998981134027e-10 } }, "warnings": ["NaNs produced"] }, { "id": "C22", "description": "Raw luminescence counts, not normalised", "truth": { "top": 50000, "bottom": 2000, "logIC50": -6.2, "hill": -1.1, "ic50_M": 6.30957344480193e-07, "drcLL4": { "b": 1.1, "c": 2000, "d": 50000, "e": 6.30957344480193e-07 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 20, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 1.27139323740093, "c": 1851.94083526119, "d": 49268.2734870436, "e": 7.13405080945541e-07 }, "standardErrors": { "b": 0.111607199282721, "c": 797.706767865031, "d": 791.054642415916, "e": 5.48953323039551e-08 }, "wald": { "b": { "lower": 1.03479654421024, "upper": 1.50798993059161 }, "c": { "lower": 160.878030839454, "upper": 3543.00363968293 }, "d": { "lower": 47591.3125586125, "upper": 50945.2344154746 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "rss": 46879717.7395591, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 49268.2734870436, "bottom": 1851.94083526119, "logIC50": -6.14666380189596, "hill": -1.27139323740093 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -14.1532171583693, "lnIC50StandardError": 0.0769488878624955, "waldLogIC50": { "lower": -6.21750812036341, "upper": -6.07582010575303 }, "logIC50": -6.14666411305822, "dfResidual": 16 }, "nls": { "estimates": { "top": 49268.2725466527, "bottom": 1851.96547062384, "logIC50": -6.14666452192314, "hill": -1.27139489454564 }, "standardErrors": { "top": 794.075685757882, "bottom": 794.32518880963, "logIC50": 0.033403356785798, "hill": 0.111542609447647 }, "wald": { "top": { "lower": 47584.9072924319, "upper": 50951.6378008736 }, "bottom": { "lower": 168.071293561383, "upper": 3535.8596476863 }, "logIC50": { "lower": -6.21747647498513, "upper": -6.07585256886115 }, "hill": { "lower": -1.50785466340267, "upper": -1.0349351256886 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "objective": 46879717.7364988, "rss": 46879717.7364988, "minimumFitted": 1940.24501671286, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.21759751288898, "upper": -6.07546589582935, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 1.33024566337893e-05, "logIC50Difference": -7.20027172995685e-07, "objectiveDrcMinusNls": 0.00306021422147751 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 49268.2725466527, "bottom": 1851.96547062384, "logIC50": -6.14666452192314, "hill": -1.27139489454564 }, "objective": 46879717.7364988, "df": 16, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 46879717.7364988, "polishedObjective": 46879717.7364988, "relativeImprovement": 1.74822696302955e-15, "minimumAttained": true, "polishedEstimates": { "top": 49268.2725338638, "bottom": 1851.96547437834, "logIC50": -6.14666452132186, "hill": -1.27139489685944 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 46879717.7364988, "threshold": 60047053.9953272, "lower": -6.21759725816897, "upper": -6.07546640857957, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.99419428508762, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 25563.9, "objectiveFlat": 8074753659.8, "objectiveFull": 46879717.7364988, "weighted": false, "n": 20, "parametersFull": 4, "df1": 3, "df2": 16, "F": 913.301738113301, "p": 4.29803204573218e-18, "alpha": 0.05, "noResponse": false, "working": "F = ((8.07475366e+09 - 46879717.7) / 3) / (46879717.7 / 16) = 913.301738; p = P(F(3, 16) > F) = 4.29803e-18 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 4.29803204573218e-18, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.527210115798346, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.67387463772148, "bendPoint_M": 2.11897270394597e-07, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.61945440612479, "bendPoint_M": 2.40184840976883e-06, "concentrationsAtOrBeyond": 4, "fires": false } }, "fires": false }, "v": { "applies": false, "note": "the response is not on a percent-of-control scale, so no absolute IC50" }, "vi": { "profileWidthLog10": 0.142130849589404, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 49268.2725466527, "bottom": 1851.96547062384, "logIC50": -6.14666452192314, "hill": -1.27139489454564 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 46879717.7364988, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.21747647498513, "upper": -6.07585256886115, "standardError": 0.033403356785798, "dfResidual": 16, "tQuantile": 2.11990529922125, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.21759725816897, "upper": -6.07546640857957, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 913.301738113301, "p": 4.29803204573218e-18, "df1": 3, "df2": 16, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -6.14666452192314, "ic50_M": 7.13403898175234e-07, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": null }, "warnings": ["NaNs produced"] }, { "id": "C23", "description": "High noise (SD 10)", "truth": { "top": 100, "bottom": 0, "logIC50": -6, "hill": -1, "ic50_M": 1e-06, "drcLL4": { "b": 1, "c": 0, "d": 100, "e": 1e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 30, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 1.50405402776474, "c": 6.14212731003569, "d": 97.385961086589, "e": 8.5037446495684e-07 }, "standardErrors": { "b": 0.350400023398592, "c": 3.3517934778302, "d": 3.30959279597312, "e": 1.30194944149629e-07 }, "wald": { "b": { "lower": 0.783796464367784, "upper": 2.2243115911617 }, "c": { "lower": -0.747582855895472, "upper": 13.0318374759669 }, "d": { "lower": 90.5829956645459, "upper": 104.188926508632 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "rss": 2226.71222928223, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 97.385961086589, "bottom": 6.14212731003569, "logIC50": -6.07038978928302, "hill": -1.50405402776474 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -13.9775946937432, "lnIC50StandardError": 0.153104861946903, "waldLogIC50": { "lower": -6.20706973573348, "upper": -5.9337147558122 }, "logIC50": -6.07039224577284, "dfResidual": 26 }, "nls": { "estimates": { "top": 97.3859838293495, "bottom": 6.14213391707799, "logIC50": -6.07039046759661, "hill": -1.50405174601032 }, "standardErrors": { "top": 3.14551660146034, "bottom": 3.31711174365014, "logIC50": 0.0668507121524871, "hill": 0.304953010183072 }, "wald": { "top": { "lower": 90.9202818553079, "upper": 103.851685803391 }, "bottom": { "lower": -0.676286923262858, "upper": 12.9605547574188 }, "logIC50": { "lower": -6.20780407442029, "upper": -5.93297686077293 }, "hill": { "lower": -2.13089163584438, "upper": -0.877211856176256 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "objective": 2226.71222927052, "rss": 2226.71222927052, "minimumFitted": 6.21226253554095, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.21331748744048, "upper": -5.93399807607023, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 1.51706945241051e-06, "logIC50Difference": -6.78313591073731e-07, "objectiveDrcMinusNls": 1.17106537800282e-08 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 97.3859838293495, "bottom": 6.14213391707799, "logIC50": -6.07039046759661, "hill": -1.50405174601032 }, "objective": 2226.71222927052, "df": 26, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 2226.71222927052, "polishedObjective": 2226.71222927052, "relativeImprovement": 6.12671019957673e-16, "minimumAttained": true, "polishedEstimates": { "top": 97.3859838167802, "bottom": 6.14213392087646, "logIC50": -6.07039046592051, "hill": -1.5040517443261 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 2226.71222927052, "threshold": 2588.57020411676, "lower": -6.21330609600022, "upper": -5.93400651312987, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.955013556143479, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -6.04804921182059, "absoluteIC50_M": 8.95263313572471e-07, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 8.95264266643425e-07, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 53.2289333333333, "objectiveFlat": 49497.4049598667, "objectiveFull": 2226.71222927052, "weighted": false, "n": 30, "parametersFull": 4, "df1": 3, "df2": 26, "F": 183.983961471623, "p": 1.26601119741371e-17, "alpha": 0.05, "noResponse": false, "working": "F = ((49497.405 - 2226.71223) / 3) / (2226.71223 / 26) = 183.983961; p = P(F(3, 26) > F) = 1.26601e-17 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 1.26601119741371e-17, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.445657705166636, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.51604817276325, "bendPoint_M": 3.04755693011521e-07, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.62473276242997, "bendPoint_M": 2.37283334926512e-06, "concentrationsAtOrBeyond": 4, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 5, "concentrationsPredictedAbove50": 5, "fires": false }, "vi": { "profileWidthLog10": 0.279299582870344, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 97.3859838293495, "bottom": 6.14213391707799, "logIC50": -6.07039046759661, "hill": -1.50405174601032 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 2226.71222927052, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.20780407442029, "upper": -5.93297686077293, "standardError": 0.0668507121524871, "dfResidual": 26, "tQuantile": 2.05552943864287, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.21330609600022, "upper": -5.93400651312987, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 183.983961471623, "p": 1.26601119741371e-17, "df1": 3, "df2": 26, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -6.07039046759661, "ic50_M": 8.50373136779461e-07, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -6.04804921182059, "absoluteIC50_M": 8.95263313572471e-07 } }, "warnings": ["NaNs produced"] }, { "id": "C24", "description": "1/Y^2 weighting, proportional noise (CV 5%)", "truth": { "top": 100, "bottom": 10, "logIC50": -6, "hill": -1, "ic50_M": 1e-06, "drcLL4": { "b": 1, "c": 10, "d": 100, "e": 1e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "1/Y^2", "n": 30, "distinctConcentrations": 10, "drcLL4": { "role": "start values for nls only: an unweighted fit, because drc cannot weight by the fitted curve", "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 97.4378416815488, "bottom": 9.76355813492074, "logIC50": -5.96315953480017, "hill": -0.975565943593871 } }, "nls": { "estimates": { "top": 96.9093383708917, "bottom": 10.3263794652519, "logIC50": -5.95771603411967, "hill": -1.02331638785196 }, "standardErrors": { "top": 1.71079215219013, "bottom": 0.395556048517319, "logIC50": 0.0299112173349981, "hill": 0.0488685747987764 }, "wald": { "top": { "lower": 93.3927547386657, "upper": 100.425922003118 }, "bottom": { "lower": 9.51330236289135, "upper": 11.1394565676125 }, "logIC50": { "lower": -6.0191994218974, "upper": -5.89623264634193 }, "hill": { "lower": -1.12376718197536, "upper": -0.92286559372855 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "objective": 0.0665961698971556, "rss": 152.353824287498, "minimumFitted": 11.1770890342397, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "~(y - (bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))))/(bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill)))", "objectiveIs": "sum(((y - f) / f)^2): 1/Y^2 weighting by the fitted curve", "covariance": "(J^T J)^-1 s^2 with J the Jacobian of the weighted residuals (y - f) / f, s^2 = objective / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.02241749780243, "upper": -5.89695537241835, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "irlsCrossCheck": { "estimates": { "top": 96.7435141545059, "bottom": 10.317829021618, "logIC50": -5.95704615321202, "hill": -1.0287437069121 }, "steps": 6, "objectiveAtFixedPoint": 0.0668264485916543 } }, "status": "fitted", "bestFit": { "source": "nls (weighted by the fitted curve)", "estimates": { "top": 96.9093383708917, "bottom": 10.3263794652519, "logIC50": -5.95771603411967, "hill": -1.02331638785196 }, "objective": 0.0665961698971556, "df": 26, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 0.0665961698971556, "polishedObjective": 0.0665961698971555, "relativeImprovement": 1.25032305875061e-15, "minimumAttained": true, "polishedEstimates": { "top": 96.9093382754524, "bottom": 10.3263794570656, "logIC50": -5.95771603296313, "hill": -1.02331638821512 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 0.0665961698971556, "threshold": 0.0774185630446509, "lower": -6.02241593999354, "upper": -5.89695283164086, "lowerUnbounded": false, "upperUnbounded": false }, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -5.88661634954652, "absoluteIC50_M": 1.29832568963754e-06, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": null, "drcEDCall": "not applicable: weighted curve, drc cannot weight by the fitted curve" }, "flatLineFTest": { "reducedModel": "flat line y = c fitted by the full model's objective: c = sum(y^2) / sum(y), minimising sum(((y - c) / c)^2) (one parameter)", "constant": 78.1108872387998, "objectiveFlat": 8.12776092560679, "objectiveFull": 0.0665961698971556, "weighted": true, "n": 30, "parametersFull": 4, "df1": 3, "df2": 26, "F": 1049.06074914979, "p": 3.12753450359691e-27, "alpha": 0.05, "noResponse": false, "working": "F = ((8.12776093 - 0.0665961699) / 3) / (0.0665961699 / 26) = 1049.06075; p = P(F(3, 26) > F) = 3.12753e-27 (approximate for a nonlinear model)", "crossCheckMean": { "constant": 56.9486666666667, "objectiveFlat": 11.1480505922994, "F": 1442.11404062926, "p": 5.14859290162192e-29, "note": "the earlier reduced model, y = mean(y) with weighted residuals: superseded by the CSO's confirmation (item 8), kept as a cross-check" } }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 3.12753450359691e-27, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.655019559479393, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.61273559359906, "bendPoint_M": 2.43929545394481e-07, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.30269647464027, "bendPoint_M": 4.98085071516372e-06, "concentrationsAtOrBeyond": 3, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 4, "concentrationsPredictedAbove50": 6, "fires": false }, "vi": { "profileWidthLog10": 0.125463108352686, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 96.9093383708917, "bottom": 10.3263794652519, "logIC50": -5.95771603411967, "hill": -1.02331638785196 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 0.0665961698971556, "objectiveIs": "sum(((y - f) / f)^2) (1/Y^2 weighting by the fitted curve)", "waldLogIC50": { "lower": -6.0191994218974, "upper": -5.89623264634193, "standardError": 0.0299112173349981, "dfResidual": 26, "tQuantile": 2.05552943864287, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.02241593999354, "upper": -5.89695283164086, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 1049.06074914979, "p": 3.12753450359691e-27, "df1": 3, "df2": 26, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -5.95771603411967, "ic50_M": 1.10225979271117e-06, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -5.88661634954652, "absoluteIC50_M": 1.29832568963754e-06 } }, "warnings": [] }, { "id": "C25", "description": "1/Y^2 weighting, proportional noise (CV 8%), Hill -2", "truth": { "top": 1000, "bottom": 50, "logIC50": -5.5, "hill": -2, "ic50_M": 3.16227766016838e-06, "drcLL4": { "b": 2, "c": 50, "d": 1000, "e": 3.16227766016838e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "1/Y^2", "n": 24, "distinctConcentrations": 12, "drcLL4": { "role": "start values for nls only: an unweighted fit, because drc cannot weight by the fitted curve", "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 991.409342916178, "bottom": 55.5318578740914, "logIC50": -5.47411320692083, "hill": -2.19530461953249 } }, "nls": { "estimates": { "top": 1005.20551189238, "bottom": 49.2183549981148, "logIC50": -5.48598258240165, "hill": -1.94694510964357 }, "standardErrors": { "top": 22.9475462304152, "bottom": 2.06587655393725, "logIC50": 0.0216378516962443, "hill": 0.0941085818956478 }, "wald": { "top": { "lower": 957.337769251291, "upper": 1053.07325453347 }, "bottom": { "lower": 44.9090120200381, "upper": 53.5276979761915 }, "logIC50": { "lower": -5.53111835011738, "upper": -5.44084681468593 }, "hill": { "lower": -2.14325217155191, "upper": -1.75063804773522 } }, "dfResidual": 20, "tQuantile": 2.08596344726586, "objective": 0.0940987655907584, "rss": 31413.0610995127, "minimumFitted": 50.4395089648379, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "~(y - (bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))))/(bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill)))", "objectiveIs": "sum(((y - f) / f)^2): 1/Y^2 weighting by the fitted curve", "covariance": "(J^T J)^-1 s^2 with J the Jacobian of the weighted residuals (y - f) / f, s^2 = objective / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -5.53115166356946, "upper": -5.44235129412737, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "irlsCrossCheck": { "estimates": { "top": 1002.76615220377, "bottom": 48.8214285133355, "logIC50": -5.48628043439297, "hill": -1.94509246125 }, "steps": 6, "objectiveAtFixedPoint": 0.0945503987366879 } }, "status": "fitted", "bestFit": { "source": "nls (weighted by the fitted curve)", "estimates": { "top": 1005.20551189238, "bottom": 49.2183549981148, "logIC50": -5.48598258240165, "hill": -1.94694510964357 }, "objective": 0.0940987655907584, "df": 20, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 0.0940987655907584, "polishedObjective": 0.0940987655907583, "relativeImprovement": 1.76977298956331e-15, "minimumAttained": true, "polishedEstimates": { "top": 1005.20551181816, "bottom": 49.2183549404487, "logIC50": -5.48598258205429, "hill": -1.94694511076836 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 0.0940987655907584, "threshold": 0.114571097713163, "lower": -5.53115055500343, "upper": -5.44235084300572, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "reducedModel": "flat line y = c fitted by the full model's objective: c = sum(y^2) / sum(y), minimising sum(((y - c) / c)^2) (one parameter)", "constant": 868.443690542159, "objectiveFlat": 8.23395765423514, "objectiveFull": 0.0940987655907584, "weighted": true, "n": 24, "parametersFull": 4, "df1": 3, "df2": 20, "F": 576.68903076052, "p": 1.39863072466191e-19, "alpha": 0.05, "noResponse": false, "working": "F = ((8.23395765 - 0.0940987656) / 3) / (0.0940987656 / 20) = 576.689031; p = P(F(3, 20) > F) = 1.39863e-19 (approximate for a nonlinear model)", "crossCheckMean": { "constant": 570.496666666667, "objectiveFlat": 12.5342162203901, "F": 881.351799300054, "p": 2.09699923153185e-21, "note": "the earlier reduced model, y = mean(y) with weighted residuals: superseded by the CSO's confirmation (item 8), kept as a cross-check" } }, "ruleChecks": { "i": { "distinctConcentrations": 12, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 1.39863072466191e-19, "fires": false }, "iii": { "concentrationsBelowIC50": 7, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.344278966191062, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -5.83026154859271, "bendPoint_M": 1.47821788122786e-06, "concentrationsAtOrBeyond": 5, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.14170361621059, "bendPoint_M": 7.21599766146702e-06, "concentrationsAtOrBeyond": 4, "fires": false } }, "fires": false }, "v": { "applies": false, "note": "the response is not on a percent-of-control scale, so no absolute IC50" }, "vi": { "profileWidthLog10": 0.0887997119977122, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 1005.20551189238, "bottom": 49.2183549981148, "logIC50": -5.48598258240165, "hill": -1.94694510964357 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 0.0940987655907584, "objectiveIs": "sum(((y - f) / f)^2) (1/Y^2 weighting by the fitted curve)", "waldLogIC50": { "lower": -5.53111835011738, "upper": -5.44084681468593, "standardError": 0.0216378516962443, "dfResidual": 20, "tQuantile": 2.08596344726586, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -5.53115055500343, "upper": -5.44235084300572, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 576.68903076052, "p": 1.39863072466191e-19, "df1": 3, "df2": 20, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -5.48598258240165, "ic50_M": 3.26600930404048e-06, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": null }, "warnings": [] }, { "id": "C26", "description": "Bottom fixed at 0 (three free parameters)", "truth": { "top": 100, "bottom": 0, "logIC50": -6, "hill": -1, "ic50_M": 1e-06, "drcLL4": { "b": 1, "c": 0, "d": 100, "e": 1e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": { "bottom": 0 }, "weighting": "none", "n": 20, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 0.844261028729716, "d": 102.648058576176, "e": 9.18968838221395e-07 }, "standardErrors": { "b": 0.0627925422286726, "d": 2.29063465515105, "e": 1.01583962260782e-07 }, "wald": { "b": { "lower": 0.711780344963906, "upper": 0.976741712495526 }, "d": { "lower": 97.8152418976139, "upper": 107.480875254739 } }, "dfResidual": 17, "tQuantile": 2.10981557783332, "rss": 271.661922448659, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, 0, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 102.648058576176, "bottom": 0, "logIC50": -6.0366992150752, "hill": -0.844261028729716 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -13.900013913225, "lnIC50StandardError": 0.110541795870295, "waldLogIC50": { "lower": -6.13798671725802, "upper": -5.93541196452603 }, "logIC50": -6.03669934089203, "dfResidual": 17 }, "nls": { "estimates": { "top": 102.648094416569, "logIC50": -6.0366998824359, "hill": -0.84425971090686 }, "standardErrors": { "top": 2.27273642253057, "logIC50": 0.0474287125508042, "hill": 0.0629478339905614 }, "wald": { "top": { "lower": 97.8530397080048, "upper": 107.443149125133 }, "logIC50": { "lower": -6.13676571901216, "upper": -5.93663404585963 }, "hill": { "lower": -0.977068031651012, "upper": -0.711451390162708 } }, "dfResidual": 17, "tQuantile": 2.10981557783332, "objective": 271.661922441306, "rss": 271.661922441306, "minimumFitted": 1.92150046836457, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ 0L + (top - 0L)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.14304110879971, "upper": -5.93862155855091, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 1.56091873418177e-06, "logIC50Difference": -6.67360694706076e-07, "objectiveDrcMinusNls": 7.35303729015868e-09 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 102.648094416569, "bottom": 0, "logIC50": -6.0366998824359, "hill": -0.84425971090686 }, "objective": 271.661922441306, "df": 17, "freeParameters": ["top", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 271.661922441306, "polishedObjective": 271.661922441306, "relativeImprovement": 1.88318909455484e-15, "minimumAttained": true, "polishedEstimates": { "top": 102.648094343299, "bottom": 0, "logIC50": -6.03669988162282, "hill": -0.8442597138914 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 271.661922441306, "threshold": 342.794547742103, "lower": -6.14303025171453, "upper": -5.93861860522103, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.991205980905479, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -6.01015277612491, "absoluteIC50_M": 9.76893508878133e-07, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 9.76894129117083e-07, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 53.4973, "objectiveFlat": 30891.6684762, "objectiveFull": 271.661922441306, "weighted": false, "n": 20, "parametersFull": 3, "df1": 2, "df2": 17, "F": 958.06601590689, "p": 3.35423075215891e-18, "alpha": 0.05, "noResponse": false, "working": "F = ((30891.6685 - 271.661922) / 2) / (271.661922 / 17) = 958.066016; p = P(F(2, 17) > F) = 3.35423e-18 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 3.35423075215891e-18, "fires": false }, "iii": { "concentrationsBelowIC50": 5, "concentrationsAboveIC50": 5, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.793940822852767, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.83064070528866, "bendPoint_M": 1.47692790025173e-07, "concentrationsAtOrBeyond": 4, "fires": false }, "bottom": { "free": false, "side": "high concentrations", "bendPointLog10": -5.24275905958313, "bendPoint_M": 5.71795772874658e-06, "concentrationsAtOrBeyond": 3, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 5, "concentrationsPredictedAbove50": 5, "fires": false }, "vi": { "profileWidthLog10": 0.204411646493505, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 102.648094416569, "bottom": 0, "logIC50": -6.0366998824359, "hill": -0.84425971090686 }, "freeParameters": ["top", "logIC50", "hill"], "fixed": { "bottom": 0 }, "objective": 271.661922441306, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.13676571901216, "upper": -5.93663404585963, "standardError": 0.0474287125508042, "dfResidual": 17, "tQuantile": 2.10981557783332, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.14303025171453, "upper": -5.93861860522103, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 958.06601590689, "p": 3.35423075215891e-18, "df1": 2, "df2": 17, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -6.0366998824359, "ic50_M": 9.18967426084615e-07, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -6.01015277612491, "absoluteIC50_M": 9.76893508878133e-07 } }, "warnings": [] }, { "id": "C27", "description": "Top fixed at 100 and Bottom at 0 (two free parameters)", "truth": { "top": 100, "bottom": 0, "logIC50": -5, "hill": -1.5, "ic50_M": 1e-05, "drcLL4": { "b": 1.5, "c": 0, "d": 100, "e": 1e-05 } }, "expectedRule": null, "excludedWells": 0, "fixed": { "top": 100, "bottom": 0 }, "weighting": "none", "n": 30, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 1.59098321120205, "e": 1.01087903792084e-05 }, "standardErrors": { "b": 0.134769883085386, "e": 6.1279057410343e-07 }, "wald": { "b": { "lower": 1.31491962019104, "upper": 1.86704680221307 } }, "dfResidual": 28, "tQuantile": 2.04840714179524, "rss": 747.136914054436, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, 0, 100, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 100, "bottom": 0, "logIC50": -4.9953008091038, "hill": -1.59098321120205 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -11.5021064902996, "lnIC50StandardError": 0.0606202984269808, "waldLogIC50": { "lower": -5.04922991897666, "upper": -4.94137283902474 }, "logIC50": -4.9953013790007, "dfResidual": 28 }, "nls": { "estimates": { "logIC50": -4.99530084023999, "hill": -1.59098301857363 }, "standardErrors": { "logIC50": 0.026279392577945, "hill": 0.137567939747729 }, "wald": { "logIC50": { "lower": -5.04913173567869, "upper": -4.94146994480128 }, "hill": { "lower": -1.87277816883494, "upper": -1.30918786831233 } }, "dfResidual": 28, "tQuantile": 2.04840714179524, "objective": 747.136914054348, "rss": 747.136914054348, "minimumFitted": 2.54277142241025, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ 0L + (100L - 0L)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -5.04942360107503, "upper": -4.94138343106703, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 1.21075079355395e-07, "logIC50Difference": -3.11361896265794e-08, "objectiveDrcMinusNls": 8.89031070983037e-11 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 100, "bottom": 0, "logIC50": -4.99530084023999, "hill": -1.59098301857363 }, "objective": 747.136914054348, "df": 28, "freeParameters": ["logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 747.136914054348, "polishedObjective": 747.136914054347, "relativeImprovement": 7.60816629342359e-16, "minimumAttained": true, "polishedEstimates": { "top": 100, "bottom": 0, "logIC50": -4.99530083881451, "hill": -1.59098303380051 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 747.136914054348, "threshold": 859.099965339214, "lower": -5.04942334285241, "upper": -4.94138361060183, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.982429021195832, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -4.99530084023999, "absoluteIC50_M": 1.01087896544715e-05, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 1.01087903792084e-05, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 74.3302666666667, "objectiveFlat": 42521.0753698667, "objectiveFull": 747.136914054348, "weighted": false, "n": 30, "parametersFull": 2, "df1": 1, "df2": 28, "F": 1565.53672393928, "p": 4.02919658060459e-26, "alpha": 0.05, "noResponse": false, "working": "F = ((42521.0754 - 747.136914) / 1) / (747.136914 / 28) = 1565.53672; p = P(F(1, 28) > F) = 4.0292e-26 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 4.02919658060459e-26, "fires": false }, "iii": { "concentrationsBelowIC50": 7, "concentrationsAboveIC50": 3, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.421306979240903, "plateaus": { "top": { "free": false, "side": "low concentrations", "bendPointLog10": -5.41660781948089, "bendPoint_M": 3.83170601304884e-06, "concentrationsAtOrBeyond": 7, "fires": false }, "bottom": { "free": false, "side": "high concentrations", "bendPointLog10": -4.57399386099909, "bendPoint_M": 2.66689636236057e-05, "concentrationsAtOrBeyond": 2, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 3, "concentrationsPredictedAbove50": 7, "fires": false }, "vi": { "profileWidthLog10": 0.108039732250582, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 100, "bottom": 0, "logIC50": -4.99530084023999, "hill": -1.59098301857363 }, "freeParameters": ["logIC50", "hill"], "fixed": { "top": 100, "bottom": 0 }, "objective": 747.136914054348, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -5.04913173567869, "upper": -4.94146994480128, "standardError": 0.026279392577945, "dfResidual": 28, "tQuantile": 2.04840714179524, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -5.04942334285241, "upper": -4.94138361060183, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 1565.53672393928, "p": 4.02919658060459e-26, "df1": 1, "df2": 28, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -4.99530084023999, "ic50_M": 1.01087896544715e-05, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -4.99530084023999, "absoluteIC50_M": 1.01087896544715e-05 } }, "warnings": ["NaNs produced"] }, { "id": "C28", "description": "Exactly four distinct concentrations: the minimum that is fitted", "truth": { "top": 100, "bottom": 0, "logIC50": -6, "hill": -1, "ic50_M": 1e-06, "drcLL4": { "b": 1, "c": 0, "d": 100, "e": 1e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 12, "distinctConcentrations": 4, "drcLL4": { "estimates": { "b": 1.06949646338223, "c": 1.68993930101809, "d": 101.396377327026, "e": 9.39075977306045e-07 }, "standardErrors": { "b": 0.14525045106244, "c": 1.66188940680723, "d": 3.85891708532446, "e": 8.75079215256876e-08 }, "wald": { "b": { "lower": 0.734548322591975, "upper": 1.40444460417249 }, "c": { "lower": -2.14238454333137, "upper": 5.52226314536755 }, "d": { "lower": 92.4976985708575, "upper": 110.295056083194 } }, "dfResidual": 8, "tQuantile": 2.30600413520417, "rss": 42.6993720354334, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 101.396377327026, "bottom": 1.68993930101809, "logIC50": -6.02729926908648, "hill": -1.06949646338223 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -13.8783729288231, "lnIC50StandardError": 0.0931901878125516, "waldLogIC50": { "lower": -6.12062934401864, "upper": -5.933972217548 }, "logIC50": -6.02730078078332, "dfResidual": 8 }, "nls": { "estimates": { "top": 101.396535128943, "bottom": 1.68996898601668, "logIC50": -6.02730154111724, "hill": -1.0694908897582 }, "standardErrors": { "top": 3.8590666370956, "bottom": 1.66191254259967, "logIC50": 0.0404712964644486, "hill": 0.145253540922241 }, "wald": { "top": { "lower": 92.497511505772, "upper": 110.295558752114 }, "bottom": { "lower": -2.14240820956582, "upper": 5.52234618159918 }, "logIC50": { "lower": -6.12062851812133, "upper": -5.93397456411315 }, "hill": { "lower": -1.40444615577794, "upper": -0.734535623738468 } }, "dfResidual": 8, "tQuantile": 2.30600413520417, "objective": 42.699372, "rss": 42.699372, "minimumFitted": 2.36233333333333, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -6.16185693928488, "upper": -5.94922951007345, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 1.75657188188334e-05, "logIC50Difference": -2.27203075731097e-06, "objectiveDrcMinusNls": 3.54333451468847e-08 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 101.396535128943, "bottom": 1.68996898601668, "logIC50": -6.02730154111724, "hill": -1.0694908897582 }, "objective": 42.699372, "df": 8, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 42.699372, "polishedObjective": 42.699372, "relativeImprovement": 0, "minimumAttained": true, "polishedEstimates": { "top": 101.396535128943, "bottom": 1.68996898601668, "logIC50": -6.02730154111724, "hill": -1.0694908897582 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 42.699372, "threshold": 71.0819385086283, "lower": -6.16185761419451, "upper": -5.94922597114675, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.997311719469135, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -6.00215263502955, "absoluteIC50_M": 9.95055638466905e-07, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 9.95057115571829e-07, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 38.5865833333333, "objectiveFlat": 15883.5253649167, "objectiveFull": 42.699372, "weighted": false, "n": 12, "parametersFull": 4, "df1": 3, "df2": 8, "F": 989.293300327174, "p": 1.28390064124543e-10, "alpha": 0.05, "noResponse": false, "working": "F = ((15883.5254 - 42.699372) / 3) / (42.699372 / 8) = 989.2933; p = P(F(3, 8) > F) = 1.2839e-10 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 4, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 1.28390064124543e-10, "fires": false }, "iii": { "concentrationsBelowIC50": 1, "concentrationsAboveIC50": 3, "fires": true }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.626739559913759, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.654041101031, "bendPoint_M": 2.21798650268259e-07, "concentrationsAtOrBeyond": 1, "fires": true }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.40056198120348, "bendPoint_M": 3.97592349239873e-06, "concentrationsAtOrBeyond": 2, "fires": false } }, "fires": true }, "v": { "concentrationsPredictedBelow50": 3, "concentrationsPredictedAbove50": 1, "fires": true }, "vi": { "profileWidthLog10": 0.212631643047763, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 101.396535128943, "bottom": 1.68996898601668, "logIC50": -6.02730154111724, "hill": -1.0694908897582 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 42.699372, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -6.12062851812133, "upper": -5.93397456411315, "standardError": 0.0404712964644486, "dfResidual": 8, "tQuantile": 2.30600413520417, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -6.16185761419451, "upper": -5.94922597114675, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 989.293300327174, "p": 1.28390064124543e-10, "df1": 3, "df2": 8, "noResponse": false }, "relativeIC50": { "shown": false, "withheldBy": "iii", "reason": "IC50 not bracketed: only one concentration below it", "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": false, "withheldBy": "v", "reason": "above 50 percent only at 100 nM" } }, "warnings": ["NaNs produced"] }, { "id": "C29", "description": "Three distinct concentrations: must refuse", "truth": { "top": 100, "bottom": 0, "logIC50": -6, "hill": -1, "ic50_M": 1e-06, "drcLL4": { "b": 1, "c": 0, "d": 100, "e": 1e-06 } }, "expectedRule": { "outcome": "refuse", "rule": "i", "reason": "fewer than four distinct concentrations (rule (i), CSO ruling, 6 October 2026); a rule, not an oracle value" }, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 9, "distinctConcentrations": 3, "status": "refused", "expected": { "status": "refused", "withheldBy": "i", "reason": "only 3 concentrations: at least four are needed" } }, { "id": "C30", "description": "Flat: no response at any concentration", "truth": { "top": 100, "bottom": 100, "logIC50": null, "hill": null, "note": "Top equals Bottom: no IC50 and no Hill slope exist; every concentration has the same expected response", "drcLL4": null }, "expectedRule": { "outcome": "not determinable", "rule": "ii", "reason": "the true curve is flat (Top = Bottom), so no IC50 exists; a fit still converges numerically, so rule (ii) (no response: flat-line F-test p >= 0.05, CSO ruling, 6 October 2026) is what withholds it. The design intent only: reference.R computes the test on the data, and a flat curve still gives p < 0.05 one time in 20." }, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 20, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": -0.163032326916907, "c": 94.9827560641562, "d": 100.805795253145, "e": 1.22698250127588e-08 }, "standardErrors": { "b": 0.796222731198634, "c": 7.74872800557002, "d": 9.59414304824454, "e": 5.45817733941434e-08 }, "wald": { "b": { "lower": -1.85094911414531, "upper": 1.5248844603115 }, "c": { "lower": 78.5561865029242, "upper": 111.409325625388 }, "d": { "lower": 80.4671205636844, "upper": 121.144469942605 } }, "dfResidual": 16, "tQuantile": 2.11990529922125, "rss": 123.083276182267, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 100.805795253145, "bottom": 94.9827560641562, "logIC50": -7.91116163095964, "hill": 0.163032326916907 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -16.4016624512215, "lnIC50StandardError": 16.6398713699264, "waldLogIC50": { "lower": -22.4428682804914, "upper": 8.19656528728092 }, "logIC50": -7.12315149660524, "dfResidual": 16 }, "nls": { "error": "start drc, tol 1e-08: singular gradient | start drc, tol 1e-06: singular gradient", "starts": ["drc"] }, "status": "fitted", "bestFit": { "source": "drc LL.4", "estimates": { "top": 100.805795253145, "bottom": 94.9827560641562, "logIC50": -7.91116163095964, "hill": 0.163032326916907 }, "objective": 123.083276182267, "df": 16, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 123.083276182267, "polishedObjective": 113.380949690476, "relativeImprovement": 0.0788273337591665, "minimumAttained": false, "polishedEstimates": { "top": 97.292166659263, "bottom": 99.3992857122825, "logIC50": -7.08030847261808, "hill": -67.6733313775982 }, "limitingModel": { "kind": "step", "description": "|Hill| -> infinity: a step between two adjacent concentrations, each side at the mean of its wells; the best of all splits", "between_M": [4.57247370827617e-08, 1.37174211248285e-07], "lowConcentrationLevel": 97.2921666666667, "highConcentrationLevel": 99.3992857142857, "objective": 113.380949690476 }, "objectiveInfimum": 113.380949690476 }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 98.76715, "objectiveFlat": 132.02874255, "objectiveFull": 113.380949690476, "weighted": false, "n": 20, "parametersFull": 4, "df1": 3, "df2": 16, "F": 0.877174653434289, "p": 0.473575288140507, "alpha": 0.05, "noResponse": true, "working": "F = ((132.028743 - 113.38095) / 3) / (113.38095 / 16) = 0.877174653; p = P(F(3, 16) > F) = 0.473575 (approximate for a nonlinear model)", "pRangeAlongValley": [0.473575288140507, 0.763449235409811] }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 0.473575288140507, "fires": true }, "iii": { "concentrationsBelowIC50": 3, "concentrationsAboveIC50": 7, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.00990482123362287, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -7.09021329385171, "bendPoint_M": 8.1243141096711e-08, "concentrationsAtOrBeyond": 3, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -7.07040365138446, "bendPoint_M": 8.50347322569676e-08, "concentrationsAtOrBeyond": 7, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 0, "concentrationsPredictedAbove50": 10, "fires": true }, "vi": { "fires": null, "note": "not evaluated: with no finite minimum there is no profile" } }, "expected": { "status": "fitted", "engineMustReport": "no finite minimum", "minimumAttained": false, "noFiniteMinimum": "Least squares has no finite minimum on this curve: from the best fit nls and drc found, the objective keeps falling (123.083 -> 113.381 after polishing) toward the limit in minimumCheck.limitingModel (step, objective 113.381), which no finite 4PL reaches. Estimates, Wald and profile bounds depend on where an optimiser stops, so none is recorded. The rules decide the same at the best fit, at the polished point and at the infimum (minimumCheck).", "objectiveInfimum": 113.380949690476, "objectiveIs": "sum((y - f)^2)", "estimates": null, "waldLogIC50": null, "profileLogIC50": null, "flatLineFTest": { "F": 0.877174653434289, "p": 0.473575288140507, "df1": 3, "df2": 16, "noResponse": true, "at": "the infimum (the smallest p any fit can give); pRangeAlongValley in flatLineFTest" }, "rulesAtBestPoint": { "ii": true, "iii": false, "iv": false, "v": true, "at": "the polished point, the best point found (rule (ii) at the infimum); the same outcomes hold at drc's fit" }, "relativeIC50": { "shown": false, "withheldBy": "ii", "reason": "no response: flat-line F-test p = 0.474 (at or above 0.05; approximate)", "poorlyDetermined": null, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": false, "withheldBy": "ii", "reason": "no response: flat-line F-test p = 0.474 (at or above 0.05; approximate)" }, "gate": "The engine reports 'no finite minimum' and shows and exports no estimates, intervals or parameters (CSO confirmation, 6 October 2026, item 1). Assert that, withheldBy and shown exactly, and that the engine's objective is not below objectiveInfimum by more than 1e-6 relative; no estimates, bounds or ruleChecks counts are compared, since they depend on where an optimiser stops." }, "warnings": ["NaNs produced"] }, { "id": "C31", "description": "Shallow curve whose lower plateau lies beyond the highest concentration", "truth": { "top": 100, "bottom": 0, "logIC50": -5, "hill": -0.5, "ic50_M": 1e-05, "drcLL4": { "b": 0.5, "c": 0, "d": 100, "e": 1e-05 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 30, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 0.491449138957889, "c": -4.22180538637766, "d": 100.519573011823, "e": 1.15680015209461e-05 }, "standardErrors": { "b": 0.0506362721518586, "c": 8.69650948302084, "d": 1.50112134189033, "e": 4.03059056042043e-06 }, "wald": { "b": { "lower": 0.387364790886611, "upper": 0.595533487029167 }, "c": { "lower": -22.0977366421639, "upper": 13.6541258694086 }, "d": { "lower": 97.4339739025927, "upper": 103.605172121054 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "rss": 115.791208595325, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 100.519573011823, "bottom": -4.22180538637766, "logIC50": -4.93674166294905, "hill": -0.491449138957889 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -11.3670622901696, "lnIC50StandardError": 0.34857394574466, "waldLogIC50": { "lower": -5.24782616458244, "upper": -4.62547869155995 }, "logIC50": -4.9366524280712, "dfResidual": 26 }, "nls": { "estimates": { "top": 100.519908219097, "bottom": -4.22448293634349, "logIC50": -4.93669528349643, "hill": -0.491433779982894 }, "standardErrors": { "top": 1.49734453398656, "bottom": 8.43547608547172, "logIC50": 0.146388266013219, "hill": 0.0496182621798298 }, "wald": { "top": { "lower": 97.4420724496966, "upper": 103.597743988497 }, "bottom": { "lower": -21.5638523589986, "upper": 13.1148864863116 }, "logIC50": { "lower": -5.23760067375849, "upper": -4.63578989323438 }, "hill": { "lower": -0.593425578587835, "upper": -0.389441981377954 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "objective": 115.791208155546, "rss": 115.791208155546, "minimumFitted": 22.7285503857945, "startedFrom": "truth", "convergenceTolerance": 1e-06, "earlierAttempts": ["start truth, tol 1e-08: step factor 5.82077e-11 reduced below 'minFactor' of 1e-10"], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -5.17811246033967, "upper": -4.48028829675653, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 0.000634219183687049, "logIC50Difference": 4.63794526197603e-05, "objectiveDrcMinusNls": 4.39779498151438e-07 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 100.519908219097, "bottom": -4.22448293634349, "logIC50": -4.93669528349643, "hill": -0.491433779982894 }, "objective": 115.791208155546, "df": 26, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 115.791208155546, "polishedObjective": 115.791208155544, "relativeImprovement": 1.53410338116001e-14, "minimumAttained": true, "polishedEstimates": { "top": 100.519907329721, "bottom": -4.22447725459708, "logIC50": -4.93669537423238, "hill": -0.491433813712593 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 115.791208155546, "threshold": 134.608175852306, "lower": -5.1782745915428, "upper": -4.48039005193395, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.994239729573894, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -4.99923243052334, "absoluteIC50_M": 1.00176895679616e-05, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 1.00175361497109e-05, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 70.5299, "objectiveFlat": 20101.6965507, "objectiveFull": 115.791208155546, "weighted": false, "n": 30, "parametersFull": 4, "df1": 3, "df2": 26, "F": 1495.89232545796, "p": 3.20800478615686e-29, "alpha": 0.05, "noResponse": false, "working": "F = ((20101.6966 - 115.791208) / 3) / (115.791208 / 26) = 1495.89233; p = P(F(3, 26) > F) = 3.208e-29 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 3.20800478615686e-29, "fires": false }, "iii": { "concentrationsBelowIC50": 8, "concentrationsAboveIC50": 2, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 1.36395233067243, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.30064761416887, "bendPoint_M": 5.004404268272e-07, "concentrationsAtOrBeyond": 5, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -3.572742952824, "bendPoint_M": 0.000267458895726149, "concentrationsAtOrBeyond": 0, "fires": true } }, "fires": true }, "v": { "concentrationsPredictedBelow50": 3, "concentrationsPredictedAbove50": 7, "fires": false }, "vi": { "profileWidthLog10": 0.697884539608853, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 100.519908219097, "bottom": -4.22448293634349, "logIC50": -4.93669528349643, "hill": -0.491433779982894 }, "freeParameters": ["top", "bottom", "logIC50", "hill"], "fixed": {}, "objective": 115.791208155546, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -5.23760067375849, "upper": -4.63578989323438, "standardError": 0.146388266013219, "dfResidual": 26, "tQuantile": 2.05552943864287, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -5.1782745915428, "upper": -4.48039005193395, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 1495.89232545796, "p": 3.20800478615686e-29, "df1": 3, "df2": 26, "noResponse": false }, "relativeIC50": { "shown": false, "withheldBy": "iv", "reason": "plateau unbracketed: no concentration at or beyond the bottom plateau's bend point (267 M)", "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -4.99923243052334, "absoluteIC50_M": 1.00176895679616e-05 } }, "warnings": [] }, { "id": "C32", "description": "C31's wells with Bottom fixed at 0: a fixed plateau is exempt from rule (iv)", "truth": { "top": 100, "bottom": 0, "logIC50": -5, "hill": -0.5, "ic50_M": 1e-05, "drcLL4": { "b": 0.5, "c": 0, "d": 100, "e": 1e-05 } }, "expectedRule": null, "excludedWells": 0, "fixed": { "bottom": 0 }, "weighting": "none", "n": 30, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 0.516241181514435, "d": 99.9971285416774, "e": 9.79378301876689e-06 }, "standardErrors": { "b": 0.0188166888984402, "d": 1.0211462429489, "e": 6.69459894172317e-07 }, "wald": { "b": { "lower": 0.4776325250135, "upper": 0.554849838015371 }, "d": { "lower": 97.9019095186056, "upper": 102.092347564749 } }, "dfResidual": 27, "tQuantile": 2.05183051648029, "rss": 117.033637645964, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, 0, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 99.9971285416774, "bottom": 0, "logIC50": -5.00904952200415, "hill": -0.516241181514435 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -11.5337541626789, "lnIC50StandardError": 0.0683554769479219, "waldLogIC50": { "lower": -5.06995726315136, "upper": -4.94813431380886 }, "logIC50": -5.00904578848011, "dfResidual": 27 }, "nls": { "estimates": { "top": 99.9972020821569, "logIC50": -5.00905082433839, "hill": -0.516239403987466 }, "standardErrors": { "top": 1.02314071934487, "logIC50": 0.0296840682065415, "hill": 0.0189088202325019 }, "wald": { "top": { "lower": 97.8978907315515, "upper": 102.096513432762 }, "logIC50": { "lower": -5.06995750133785, "upper": -4.94814414733892 }, "hill": { "lower": -0.555037098371153, "upper": -0.477441709603779 } }, "dfResidual": 27, "tQuantile": 2.05183051648029, "objective": 117.033637607263, "rss": 117.033637607263, "minimumFitted": 23.1567708196461, "startedFrom": "truth", "convergenceTolerance": 1e-08, "earlierAttempts": [], "formula": "y ~ 0L + (top - 0L)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -5.07160951911439, "upper": -4.94941102862068, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 3.44321033040523e-06, "logIC50Difference": -1.30233423778492e-06, "objectiveDrcMinusNls": 3.87010032909529e-08 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 99.9972020821569, "bottom": 0, "logIC50": -5.00905082433839, "hill": -0.516239403987466 }, "objective": 117.033637607263, "df": 27, "freeParameters": ["top", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 117.033637607263, "polishedObjective": 117.033637607262, "relativeImprovement": 2.06423157561875e-15, "minimumAttained": true, "polishedEstimates": { "top": 99.9972019397513, "bottom": 0, "logIC50": -5.00905082183601, "hill": -0.516239407672354 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 117.033637607263, "threshold": 135.28225262243, "lower": -5.07160856687033, "upper": -4.94940941448628, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.994177922380229, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -5.00909790149949, "absoluteIC50_M": 9.79269207262448e-06, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 9.79269354028082e-06, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 70.5299, "objectiveFlat": 20101.6965507, "objectiveFull": 117.033637607263, "weighted": false, "n": 30, "parametersFull": 3, "df1": 2, "df2": 27, "F": 2305.25987948963, "p": 6.73833937633664e-31, "alpha": 0.05, "noResponse": false, "working": "F = ((20101.6966 - 117.033638) / 2) / (117.033638 / 27) = 2305.25988; p = P(F(2, 27) > F) = 6.73834e-31 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 6.73833937633664e-31, "fires": false }, "iii": { "concentrationsBelowIC50": 7, "concentrationsAboveIC50": 3, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 1.29841357401518, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -6.30746439835356, "bendPoint_M": 4.92646726813903e-07, "concentrationsAtOrBeyond": 5, "fires": false }, "bottom": { "free": false, "side": "high concentrations", "bendPointLog10": -3.71063725032321, "bendPoint_M": 0.000194698564576327, "concentrationsAtOrBeyond": 0, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 3, "concentrationsPredictedAbove50": 7, "fires": false }, "vi": { "profileWidthLog10": 0.122199152384051, "lowerUnbounded": false, "upperUnbounded": false, "fires": false } }, "expected": { "status": "fitted", "engineMustReport": "a minimum", "minimumAttained": true, "estimates": { "top": 99.9972020821569, "bottom": 0, "logIC50": -5.00905082433839, "hill": -0.516239403987466 }, "freeParameters": ["top", "logIC50", "hill"], "fixed": { "bottom": 0 }, "objective": 117.033637607263, "objectiveIs": "sum((y - f)^2)", "waldLogIC50": { "lower": -5.06995750133785, "upper": -4.94814414733892, "standardError": 0.0296840682065415, "dfResidual": 27, "tQuantile": 2.05183051648029, "source": "nls: logIC50 +/- t(0.975, n - p) x SE, SE from (J^T J)^-1 s^2 at the nls solution" }, "waldNote": null, "profileLogIC50": { "lower": -5.07160856687033, "upper": -4.94940941448628, "lowerUnbounded": false, "upperUnbounded": false }, "flatLineFTest": { "F": 2305.25987948963, "p": 6.73833937633664e-31, "df1": 2, "df2": 27, "noResponse": false }, "relativeIC50": { "shown": true, "withheldBy": null, "reason": null, "logIC50": -5.00905082433839, "ic50_M": 9.79375364984707e-06, "poorlyDetermined": false, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": true, "withheldBy": null, "reason": null, "logAbsoluteIC50": -5.00909790149949, "absoluteIC50_M": 9.79269207262448e-06 } }, "warnings": ["NaNs produced"] }, { "id": "C33", "description": "Steep step between two tested concentrations: no point on the transition", "truth": { "top": 100, "bottom": 0, "logIC50": -5.67, "hill": -12, "ic50_M": 2.13796208950223e-06, "drcLL4": { "b": 12, "c": 0, "d": 100, "e": 2.13796208950223e-06 } }, "expectedRule": null, "excludedWells": 0, "fixed": {}, "weighting": "none", "n": 30, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 18.5392566606922, "c": -0.293492762168882, "d": 99.5924153657086, "e": 2.17080517992535e-06 }, "standardErrors": { "b": 60.09915677716, "c": 0.83621839336102, "d": 0.681517221954833, "e": 3.86646769941465e-06 }, "wald": { "b": { "lower": -104.996329332374, "upper": 142.074842653758 }, "c": { "lower": -2.01236428685711, "upper": 1.42537876251934 }, "d": { "lower": 98.1915366530384, "upper": 100.993294078379 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "rss": 217.134018100355, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 99.5924153657086, "bottom": -0.293492762168882, "logIC50": -5.66337915078783, "hill": -18.5392566606922 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -13.0430823594208, "lnIC50StandardError": 11.1542321408783, "waldLogIC50": { "lower": -15.6219785318247, "upper": 4.29290114041257 }, "logIC50": -5.66453869570608, "dfResidual": 26 }, "nls": { "error": "start truth, tol 1e-08: singular gradient | start truth, tol 1e-06: singular gradient | start drc, tol 1e-08: singular gradient | start drc, tol 1e-06: singular gradient", "starts": ["truth", "drc"] }, "status": "fitted", "bestFit": { "source": "drc LL.4", "estimates": { "top": 99.5924153657086, "bottom": -0.293492762168882, "logIC50": -5.66337915078783, "hill": -18.5392566606922 }, "objective": 217.134018100355, "df": 26, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 217.134018100355, "polishedObjective": 217.118911194445, "relativeImprovement": 6.95741093114876e-05, "minimumAttained": false, "polishedEstimates": { "top": 99.5919444378434, "bottom": -0.292250022137283, "logIC50": -5.59538235607166, "hill": -95.4635759281741 }, "limitingModel": { "kind": "step", "description": "|Hill| -> infinity: a step between two adjacent concentrations, each side at the mean of its wells; the best of all splits", "between_M": [1.23456790123457e-06, 3.70370370370371e-06], "lowConcentrationLevel": 99.5919444444445, "highConcentrationLevel": -0.29225, "objective": 217.118911194445 }, "objectiveInfimum": 217.118911194445 }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 59.6382666666667, "objectiveFlat": 72050.4554698667, "objectiveFull": 217.118911194445, "weighted": false, "n": 30, "parametersFull": 4, "df1": 3, "df2": 26, "F": 2867.34849619319, "p": 7.0603427262666e-33, "alpha": 0.05, "noResponse": false, "working": "F = ((72050.4555 - 217.118911) / 3) / (217.118911 / 26) = 2867.3485; p = P(F(3, 26) > F) = 7.06034e-33 (approximate for a nonlinear model)", "pRangeAlongValley": [7.0603427262666e-33, 7.06673096923687e-33] }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 7.0603427262666e-33, "fires": false }, "iii": { "concentrationsBelowIC50": 6, "concentrationsAboveIC50": 4, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.00702144501776419, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": -5.60240380108942, "bendPoint_M": 2.49802165510399e-06, "concentrationsAtOrBeyond": 6, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": -5.5883609110539, "bendPoint_M": 2.58011515046558e-06, "concentrationsAtOrBeyond": 4, "fires": false } }, "fires": false }, "v": { "concentrationsPredictedBelow50": 4, "concentrationsPredictedAbove50": 6, "fires": false }, "vi": { "fires": null, "note": "not evaluated: with no finite minimum there is no profile" } }, "expected": { "status": "fitted", "engineMustReport": "no finite minimum", "minimumAttained": false, "noFiniteMinimum": "Least squares has no finite minimum on this curve: from the best fit nls and drc found, the objective keeps falling (217.134 -> 217.119 after polishing) toward the limit in minimumCheck.limitingModel (step, objective 217.119), which no finite 4PL reaches. Estimates, Wald and profile bounds depend on where an optimiser stops, so none is recorded. The rules decide the same at the best fit, at the polished point and at the infimum (minimumCheck).", "objectiveInfimum": 217.118911194445, "objectiveIs": "sum((y - f)^2)", "estimates": null, "waldLogIC50": null, "profileLogIC50": null, "flatLineFTest": { "F": 2867.34849619319, "p": 7.0603427262666e-33, "df1": 3, "df2": 26, "noResponse": false, "at": "the infimum (the smallest p any fit can give); pRangeAlongValley in flatLineFTest" }, "rulesAtBestPoint": { "ii": false, "iii": false, "iv": false, "v": false, "at": "the polished point, the best point found (rule (ii) at the infimum); the same outcomes hold at drc's fit" }, "relativeIC50": { "shown": false, "withheldBy": "noFiniteMinimum", "reason": "IC50 between 1.23 M and 3.7 M", "poorlyDetermined": null, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": false, "withheldBy": "noFiniteMinimum", "reason": "IC50 between 1.23 M and 3.7 M" }, "gate": "The engine reports 'no finite minimum' and shows and exports no estimates, intervals or parameters (CSO confirmation, 6 October 2026, item 1). Assert that, withheldBy and shown exactly, and that the engine's objective is not below objectiveInfimum by more than 1e-6 relative; no estimates, bounds or ruleChecks counts are compared, since they depend on where an optimiser stops." }, "warnings": ["NaNs produced"] } ], "mtt": { "normalisation": { "formula": "percent viability = 100 x (A570 - mean(kill)) / (mean(vehicle) - mean(kill))", "meanVehicle": 1.241875, "meanKill": 0.06, "meanBlank": 0.044, "nVehicle": 8, "nKill": 4, "nBlank": 4 }, "zPrime": { "positive": "vehicle (column 1)", "negative": "kill control (column 12, rows A-D)", "refused": false, "meanPositive": 1.241875, "meanNegative": 0.06, "sdPositive": 0.0722227457245984, "sdNegative": 0.013589211407093, "nPositive": 8, "nNegative": 4, "zPrime": 0.782180119390736, "belowHalf": false, "sd": "sample standard deviation (n - 1 denominator, R sd()); n shown", "working": "Z' = 1 - 3 (0.072223 + 0.013589) / |1.241875 - 0.060000| = 0.782180 (n = 8 and 4)", "crossCheckPopulationSd": 0.798641663109065 }, "compounds": [ { "compound": "Compound A", "truth": { "top": 100, "bottom": 3, "logIC50": -5.69897000433602, "hill": -1.2, "ic50_M": 2e-06, "drcLL4": { "b": 1.2, "c": 3, "d": 100, "e": 2e-06 } }, "normalised": [ { "well": "A2", "concentration_M": 0.0001, "A570": 0.109, "percentViability": 4.14595452141724 }, { "well": "A3", "concentration_M": 3.33333333333333e-05, "A570": 0.123, "percentViability": 5.33051295610788 }, { "well": "A4", "concentration_M": 1.11111111111111e-05, "A570": 0.212, "percentViability": 12.8609201480698 }, { "well": "A5", "concentration_M": 3.7037037037037e-06, "A570": 0.48, "percentViability": 35.5367530407192 }, { "well": "A6", "concentration_M": 1.23456790123457e-06, "A570": 0.942, "percentViability": 74.6271813855103 }, { "well": "A7", "concentration_M": 4.11522633744856e-07, "A570": 1.026, "percentViability": 81.7345319936541 }, { "well": "A8", "concentration_M": 1.37174211248285e-07, "A570": 1.312, "percentViability": 105.933368588049 }, { "well": "A9", "concentration_M": 4.57247370827618e-08, "A570": 1.082, "percentViability": 86.4727657324167 }, { "well": "A10", "concentration_M": 1.52415790275873e-08, "A570": 1.333, "percentViability": 107.710206240085 }, { "well": "A11", "concentration_M": 5.08052634252909e-09, "A570": 1.245, "percentViability": 100.264410364886 }, { "well": "B2", "concentration_M": 0.0001, "A570": 0.099, "percentViability": 3.29984135378107 }, { "well": "B3", "concentration_M": 3.33333333333333e-05, "A570": 0.135, "percentViability": 6.34584875727129 }, { "well": "B4", "concentration_M": 1.11111111111111e-05, "A570": 0.208, "percentViability": 12.5224748810153 }, { "well": "B5", "concentration_M": 3.7037037037037e-06, "A570": 0.451, "percentViability": 33.0830248545743 }, { "well": "B6", "concentration_M": 1.23456790123457e-06, "A570": 0.874, "percentViability": 68.8736118455843 }, { "well": "B7", "concentration_M": 4.11522633744856e-07, "A570": 1.05, "percentViability": 83.765203595981 }, { "well": "B8", "concentration_M": 1.37174211248285e-07, "A570": 1.24, "percentViability": 99.8413537810682 }, { "well": "B9", "concentration_M": 4.57247370827618e-08, "A570": 1.209, "percentViability": 97.2184029613961 }, { "well": "B10", "concentration_M": 1.52415790275873e-08, "A570": 1.184, "percentViability": 95.1031200423056 }, { "well": "B11", "concentration_M": 5.08052634252909e-09, "A570": 1.206, "percentViability": 96.9645690111052 }, { "well": "C2", "concentration_M": 0.0001, "A570": 0.099, "percentViability": 3.29984135378107 }, { "well": "C3", "concentration_M": 3.33333333333333e-05, "A570": 0.156, "percentViability": 8.12268640930724 }, { "well": "C4", "concentration_M": 1.11111111111111e-05, "A570": 0.219, "percentViability": 13.4531993654151 }, { "well": "C5", "concentration_M": 3.7037037037037e-06, "A570": 0.445, "percentViability": 32.5753569539926 }, { "well": "C6", "concentration_M": 1.23456790123457e-06, "A570": 0.833, "percentViability": 65.404547858276 }, { "well": "C7", "concentration_M": 4.11522633744856e-07, "A570": 1.086, "percentViability": 86.8112109994712 }, { "well": "C8", "concentration_M": 1.37174211248285e-07, "A570": 1.111, "percentViability": 88.9264939185616 }, { "well": "C9", "concentration_M": 4.57247370827618e-08, "A570": 1.268, "percentViability": 102.210470650449 }, { "well": "C10", "concentration_M": 1.52415790275873e-08, "A570": 1.209, "percentViability": 97.2184029613961 }, { "well": "C11", "concentration_M": 5.08052634252909e-09, "A570": 1.206, "percentViability": 96.9645690111052 } ], "n": 30, "distinctConcentrations": 10, "drcLL4": { "estimates": { "b": 1.28239129088364, "c": 3.03690981648155, "d": 98.2362738920311, "e": 2.15949796871926e-06 }, "standardErrors": { "b": 0.132953245724371, "c": 2.24709932851172, "d": 1.51052259114645, "e": 1.87359115820035e-07 }, "wald": { "b": { "lower": 1.00910198033407, "upper": 1.5556806014332 }, "c": { "lower": -1.58206900482891, "upper": 7.65588863779201 }, "d": { "lower": 95.1313502381944, "upper": 101.341197545868 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "rss": 565.537675203507, "call": "drm(y ~ conc, data = d, fct = LL.4(fixed = c(NA, NA, NA, NA)), control = drmc(relTol = 1e-12, maxIt = 5000))", "inBriefParameterisation": { "top": 98.2362738920311, "bottom": 3.03690981648155, "logIC50": -5.66564720012513, "hill": -1.28239129088364 }, "note": "cross-check of the minimum only; drc's Wald interval on the linear IC50 scale (e) is never used and not recorded" }, "drcLL24": { "role": "cross-check of the Wald interval on log IC50 only", "call": "drm(..., fct = LL2.4(fixed = ...)): e is log(IC50), natural log", "lnIC50": -13.0456365081878, "lnIC50StandardError": 0.0867613877420516, "waldLogIC50": { "lower": -5.74310028109927, "upper": -5.58819561574386 }, "logIC50": -5.66564794842157, "dfResidual": 26 }, "nls": { "estimates": { "top": 98.2362803419013, "bottom": 3.03690162518932, "logIC50": -5.66564722103455, "hill": -1.28239029833953 }, "standardErrors": { "top": 1.48422483024837, "bottom": 2.25281282244369, "logIC50": 0.03812447684077, "hill": 0.128192734538626 }, "wald": { "top": { "lower": 95.185412509761, "upper": 101.287148174042 }, "bottom": { "lower": -1.59382145109582, "upper": 7.66762470147446 }, "logIC50": { "lower": -5.74401320551361, "upper": -5.58728123655549 }, "hill": { "lower": -1.54589423800381, "upper": -1.01888635867525 } }, "dfResidual": 26, "tQuantile": 2.05552943864287, "objective": 565.537675202529, "rss": 565.537675202529, "minimumFitted": 3.72787387146746, "startedFrom": "truth", "convergenceTolerance": 1e-06, "earlierAttempts": ["start truth, tol 1e-08: number of iterations exceeded maximum of 1000"], "formula": "y ~ bottom + (top - bottom)/(1 + 10^((logIC50 - x) * hill))", "objectiveIs": "sum((y - f)^2)", "covariance": "(J^T J)^-1 s^2, s^2 = RSS / (n - p)", "profileCrossCheck": { "implementation": "confint(fit, parm = \"logIC50\") on the nls fit restarted at its solution with tol 1e-6 (or 1e-5): MASS's profile t-statistic, spline-interpolated; a cross-check only", "lower": -5.74272437089087, "upper": -5.58672435929725, "lowerUnbounded": false, "upperUnbounded": false, "profiledAtTolerance": 1e-06, "earlierAttempts": [] }, "agreementWithDrc": { "maxRelativeDifference": 2.69724579404475e-06, "logIC50Difference": -2.09094181968794e-08, "objectiveDrcMinusNls": 9.77365743892733e-10 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 98.2362803419013, "bottom": 3.03690162518932, "logIC50": -5.66564722103455, "hill": -1.28239029833953 }, "objective": 565.537675202529, "df": 26, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 565.537675202529, "polishedObjective": 565.537675202509, "relativeImprovement": 3.55813081233178e-14, "minimumAttained": true, "polishedEstimates": { "top": 98.2362794104697, "bottom": 3.03690202740698, "logIC50": -5.66564720549404, "hill": -1.28239040593344 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 565.537675202529, "threshold": 657.441925405117, "lower": -5.74272371096611, "upper": -5.58672565330451, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.987851484447233, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -5.6565883027437, "absoluteIC50_M": 2.20501575690542e-06, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 2.20501589746051e-06, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 60.2206945178918, "objectiveFlat": 46551.9982870422, "objectiveFull": 565.537675202529, "weighted": false, "n": 30, "parametersFull": 4, "df1": 3, "df2": 26, "F": 704.72639185335, "p": 5.22372744087219e-25, "alpha": 0.05, "noResponse": false, "working": "F = ((46551.9983 - 565.537675) / 3) / (565.537675 / 26) = 704.726392; p = P(F(3, 26) > F) = 5.22373e-25 (approximate for a nonlinear model)" }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 5.22372744087219e-25, "fires": false }, "iii": { "concentrationsBelowIC50": 6, "concentrationsAboveIC50": 4, "fires": false }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 0.522689738410173, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": 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1.74516150008647e-06, "logIC50Difference": -1.60595890186244e-06, "objectiveDrcMinusNls": 1.75498655607953e-08 } }, "status": "fitted", "bestFit": { "source": "nls", "estimates": { "top": 96.7887786167533, "bottom": 15.5383891117148, "logIC50": -6.73539796787547, "hill": -0.979114748158713 }, "objective": 227.534177214001, "df": 26, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 227.534177214001, "polishedObjective": 227.534177213899, "relativeImprovement": 4.47683982449648e-13, "minimumAttained": true, "polishedEstimates": { "top": 96.7887837478263, "bottom": 15.5383873186002, "logIC50": -6.7353980273425, "hill": -0.97911449396135 } }, "directProfileLogIC50": { "method": "logIC50 held fixed and the other free parameters refitted; bounds where the objective = minimum x (1 + F(0.95; 1, n - p) / (n - p)), found with uniroot (tol 1e-10) after bracketing in 0.05 log10 steps; unbounded if not reached within 10 log10 units", "objectiveMin": 227.534177214001, "threshold": 264.510242415717, "lower": -6.81906612356248, "upper": -6.65706268480167, "lowerUnbounded": false, "upperUnbounded": false }, "rSquared": 0.992074091461632, "absoluteIC50": { "exists": true, "logAbsoluteIC50": -6.5997589794424, "absoluteIC50_M": 2.51328084087626e-07, "withinTestedRange": true, "formula": "logAbsIC50 = logIC50 - log10((Top - Bottom) / (50 - Bottom) - 1) / Hill", "drcED": 2.51328483749891e-07, "drcEDCall": "ED(drc LL.4 fit, 50, type = \"absolute\") (drc's own estimates)" }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 46.2598272518949, "objectiveFlat": 28707.6460840466, "objectiveFull": 227.534177214001, "weighted": false, "n": 30, "parametersFull": 4, "df1": 3, "df2": 26, 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"waldLogIC50": { "lower": -6.77881858657128, "upper": 3.29934047132947 }, "logIC50": -1.7397390576209, "dfResidual": 16 }, "nls": { "error": "start truth, tol 1e-08: number of iterations exceeded maximum of 1000 | start truth, tol 1e-06: number of iterations exceeded maximum of 1000 | start drc, tol 1e-08: number of iterations exceeded maximum of 1000 | start drc, tol 1e-06: number of iterations exceeded maximum of 1000", "starts": ["truth", "drc"] }, "status": "fitted", "bestFit": { "source": "drc LL.4", "estimates": { "top": 102.513381286781, "bottom": -191.700591474271, "logIC50": -3.0430028804389, "hill": -0.607888953731586 }, "objective": 365.664283029819, "df": 16, "freeParameters": ["top", "bottom", "logIC50", "hill"], "note": "the lowest objective found by nls or drc LL.4; expected.estimates, the profile, the rules and R squared use it" }, "minimumCheck": { "method": "optim Nelder-Mead then BFGS (reltol 1e-16), ten rounds, from the best fit", "startObjective": 365.664283029819, "polishedObjective": 352.18230255538, "relativeImprovement": 0.0368698314276955, "minimumAttained": false, "polishedEstimates": { "top": 103.087922845625, "bottom": -3194125.70164625, "logIC50": 5.02842037498604, "hill": -0.522011543963622 }, "limitingModel": { "kind": "power law", "description": "IC50 beyond the tested range with the far plateau at infinity: y -> near + B 10^(k x) (the 4PL's limit), fitted by nls", "parameters": { "near": 103.090060892243, "B": -7572.05238342669, "k": 0.521946300857155 }, "objective": 352.181332364656 }, "objectiveInfimum": 352.181332364656 }, "flatLineFTest": { "reducedModel": "flat line y = mean(y) over the kept wells (one parameter)", "constant": 88.9603384452671, "objectiveFlat": 7576.01085718456, "objectiveFull": 352.181332364656, "weighted": false, "n": 20, "parametersFull": 4, "df1": 3, "df2": 16, "F": 109.395607485373, "p": 7.12834624796413e-11, "alpha": 0.05, "noResponse": false, "working": "F = ((7576.01086 - 352.181332) / 3) / (352.181332 / 16) = 109.395607; p = P(F(3, 16) > F) = 7.12835e-11 (approximate for a nonlinear model)", "pRangeAlongValley": [7.12834624796413e-11, 9.6196604869389e-11] }, "ruleChecks": { "i": { "distinctConcentrations": 10, "anyConcentrationAtOrBelowZero": false, "fires": false }, "ii": { "p": 7.12834624796413e-11, "fires": false }, "iii": { "concentrationsBelowIC50": 10, "concentrationsAboveIC50": 0, "fires": true }, "iv": { "k": 4.6805, "bendHalfWidthLog10": 1.28405637256471, "plateaus": { "top": { "free": true, "side": "low concentrations", "bendPointLog10": 3.74436400242133, "bendPoint_M": 5550.90765449152, "concentrationsAtOrBeyond": 10, "fires": false }, "bottom": { "free": true, "side": "high concentrations", "bendPointLog10": 6.31247674755075, "bendPoint_M": 2053415.08214469, "concentrationsAtOrBeyond": 0, "fires": true } }, "fires": true }, "v": { "concentrationsPredictedBelow50": 1, "concentrationsPredictedAbove50": 9, "fires": true }, "vi": { "fires": null, "note": "not evaluated: with no finite minimum there is no profile" } }, "expected": { "status": "fitted", "engineMustReport": "no finite minimum", "minimumAttained": false, "noFiniteMinimum": "Least squares has no finite minimum on this curve: from the best fit nls and drc found, the objective keeps falling (365.664 -> 352.182 after polishing) toward the limit in minimumCheck.limitingModel (power law, objective 352.181), which no finite 4PL reaches. Estimates, Wald and profile bounds depend on where an optimiser stops, so none is recorded. The rules decide the same at the best fit, at the polished point and at the infimum (minimumCheck).", "objectiveInfimum": 352.181332364656, "objectiveIs": "sum((y - f)^2)", "estimates": null, "waldLogIC50": null, "profileLogIC50": null, "flatLineFTest": { "F": 109.395607485373, "p": 7.12834624796413e-11, "df1": 3, "df2": 16, "noResponse": false, "at": "the infimum (the smallest p any fit can give); pRangeAlongValley in flatLineFTest" }, "rulesAtBestPoint": { "ii": false, "iii": true, "iv": true, "v": true, "at": "the polished point, the best point found (rule (ii) at the infimum); the same outcomes hold at drc's fit" }, "relativeIC50": { "shown": false, "withheldBy": "iii", "reason": "IC50 beyond the highest concentration", "poorlyDetermined": null, "poorlyDeterminedReason": null }, "absoluteIC50": { "shown": false, "withheldBy": "v", "reason": "below 50 percent only at 100 M" }, "gate": "The engine reports 'no finite minimum' and shows and exports no estimates, intervals or parameters (CSO confirmation, 6 October 2026, item 1). Assert that, withheldBy and shown exactly, and that the engine's objective is not below objectiveInfimum by more than 1e-6 relative; no estimates, bounds or ruleChecks counts are compared, since they depend on where an optimiser stops." }, "warnings": [] } ] }, "zPrime": [ { "id": "Z01", "label": "excellent separation", "populationZPrimeOfGenerator": 0.82, "refused": false, "meanPositive": 100.431625, "meanNegative": 0.6880625, "sdPositive": 2.09587165239986, "sdNegative": 3.44151178929164, "nPositive": 16, "nNegative": 16, "zPrime": 0.833451403692599, "belowHalf": false, "sd": "sample standard deviation (n - 1 denominator, R sd()); n shown", "working": "Z' = 1 - 3 (2.095872 + 3.441512) / |100.431625 - 0.688063| = 0.833451 (n = 16 and 16)", "crossCheckPopulationSd": 0.838740015041804 }, { "id": "Z02", "label": "marginal: below the 0.5 convention", "populationZPrimeOfGenerator": 0.266666666666667, "refused": false, "meanPositive": 102.6554375, "meanNegative": 8.233375, "sdPositive": 9.29073948954011, "sdNegative": 8.49683562176728, "nPositive": 16, "nNegative": 16, "zPrime": 0.434848975747356, "belowHalf": true, "sd": "sample standard deviation (n - 1 denominator, R sd()); n shown", "working": "Z' = 1 - 3 (9.290739 + 8.496836) / |102.655438 - 8.233375| = 0.434849 (n = 16 and 16)", "crossCheckPopulationSd": 0.452794873744362 }, { "id": "Z03", "label": "overlapping controls: negative Z'", "populationZPrimeOfGenerator": -1.4, "refused": false, "meanPositive": 48.56975, "meanNegative": 19.581875, "sdPositive": 11.006154971954, "sdNegative": 11.493229148068, "nPositive": 16, "nNegative": 16, "zPrime": -1.3284960474014, "belowHalf": true, "sd": "sample standard deviation (n - 1 denominator, R sd()); n shown", "working": "Z' = 1 - 3 (11.006155 + 11.493229) / |48.569750 - 19.581875| = -1.328496 (n = 16 and 16)", "crossCheckPopulationSd": -1.25455660332385 }, { "id": "Z04", "label": "one negative-control well: Z' refused (a sample SD needs two)", "populationZPrimeOfGenerator": 0.82, "refused": true, "nPositive": 16, "nNegative": 1, "zPrime": null, "reason": "Z' needs at least two wells in each control (sample SD, n - 1): 16 positive, 1 negative" } ], "fTests": [ { "curve": "C01", "comparison": "Hill fixed at -1 (3 free) against Hill free (4 free); true Hill -1", "reducedModel": { "fixed": { "hill": -1 }, "rss": 168.317361937825, "df": 27, "parameters": 3, "from": "nls" }, "fullModel": { "fixed": {}, "rss": 163.430466735332, "df": 26, "parameters": 4, "from": "nls" }, "F": 0.777451584168722, "p": 0.386000731595843, "alpha": 0.05, "preferFull": false, "working": "F = ((168.317362 - 163.430467) / (27 - 26)) / (163.430467 / 26) = 0.777452; p = P(F(1, 26) > F) = 0.386001", "drcAnova": { "F": 0.777451583187598, "p": 0.386000731891221, "rssReduced": 168.317361940166, "rssFull": 163.430466743594, "call": "anova(reduced_drc_fit, full_drc_fit)" } }, { "curve": "C07", "comparison": "Hill fixed at -1 against Hill free; true Hill -3", "reducedModel": { "fixed": { "hill": -1 }, "rss": 3846.34188351296, "df": 33, "parameters": 3, "from": "nls" }, "fullModel": { "fixed": {}, "rss": 206.206838631496, "df": 32, "parameters": 4, "from": "nls" }, "F": 564.890680683834, "p": 6.68805720062637e-22, "alpha": 0.05, "preferFull": true, "working": "F = ((3846.341884 - 206.206839) / (33 - 32)) / (206.206839 / 32) = 564.890681; p = P(F(1, 32) > F) = 6.68806e-22", "drcAnova": { "F": 564.890680585376, "p": 0, "rssReduced": 3846.34188357189, "rssFull": 206.206838668669, "call": "anova(reduced_drc_fit, full_drc_fit)" } }, { "curve": "C04", "comparison": "Hill fixed at -1 against Hill free; true Hill -0.5", "reducedModel": { "fixed": { "hill": -1 }, "rss": 651.790814300759, "df": 21, "parameters": 3, "from": "nls" }, "fullModel": { "fixed": {}, "rss": 89.7094728833959, "df": 20, "parameters": 4, "from": "nls" }, "F": 125.311480126063, "p": 4.59571583065905e-10, "alpha": 0.05, "preferFull": true, "working": "F = ((651.790814 - 89.709473) / (21 - 20)) / (89.709473 / 20) = 125.311480; p = P(F(1, 20) > F) = 4.59572e-10", "drcAnova": { "F": 125.311480054267, "p": 4.59571602995368e-10, "rssReduced": 651.790814302015, "rssFull": 89.7094729278926, "call": "anova(reduced_drc_fit, full_drc_fit)" } }, { "curve": "C10", "comparison": "Bottom fixed at 0 against Bottom free; true Bottom 20", "reducedModel": { "fixed": { "bottom": 0 }, "rss": 874.176951756051, "df": 27, "parameters": 3, "from": "nls" }, "fullModel": { "fixed": {}, "rss": 272.278310154503, "df": 26, "parameters": 4, "from": "nls" }, "F": 57.4756199741363, "p": 4.77443982958419e-08, "alpha": 0.05, "preferFull": true, "working": "F = ((874.176952 - 272.278310) / (27 - 26)) / (272.278310 / 26) = 57.475620; p = P(F(1, 26) > F) = 4.77444e-08", "drcAnova": { "F": 57.4756199819259, "p": 4.77443982127568e-08, "rssReduced": 874.176951863616, "rssFull": 272.278310162598, "call": "anova(reduced_drc_fit, full_drc_fit)" } }, { "curve": "C30", "comparison": "Flat line (y = mean) against the 4PL at drc's fit; true curve flat. drc's fit is not a minimum on C30 (curves[C30].minimumCheck); rule (ii) uses curves[C30].flatLineFTest, taken at the infimum", "reducedModel": { "fixed": "flat line: y = mean, one parameter", "rss": 132.02874255, "df": 19, "parameters": 1, "from": "mean of y (hand)" }, "fullModel": { "fixed": {}, "rss": 123.083276182267, "df": 16, "parameters": 4, "from": "drc LL.4" }, "F": 0.387616867547388, "p": 0.763449235409811, "alpha": 0.05, "preferFull": false, "working": "F = ((132.028743 - 123.083276) / (19 - 16)) / (123.083276 / 16) = 0.387617; p = P(F(3, 16) > F) = 0.763449", "drcAnova": null }, { "curve": "C01", "comparison": "Flat line (y = mean) against the 4PL; true curve Hill -1, IC50 1 uM", "reducedModel": { "fixed": "flat line: y = mean, one parameter", "rss": 47873.4454889667, "df": 29, "parameters": 1, "from": "mean of y (hand)" }, "fullModel": { "fixed": {}, "rss": 163.430466735332, "df": 26, "parameters": 4, "from": "nls" }, "F": 2530.04721285512, "p": 3.57314954879994e-32, "alpha": 0.05, "preferFull": true, "working": "F = ((47873.445489 - 163.430467) / (29 - 26)) / (163.430467 / 26) = 2530.047213; p = P(F(3, 26) > F) = 3.57315e-32", "drcAnova": null } ] }