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AcceleratedFailureTime

lifelines' parametric accelerated failure time regressions, right-, left- and interval-censored, fitted to their maximum.

public static class AcceleratedFailureTime

Example — how a dose stretches or shrinks time, on ten patients.

using Lodestar.Survival;

double[] dose = [1.0, 2.0, 0.5, 3.0, 0.0, 1.5, 0.0, 2.5, 1.0, 0.5];
double[] months = [5, 8, 12, 3, 15, 9, 20, 6, 11, 14];
bool[] died = [true, true, false, true, true, true, false, true, true, false];

AftSummary fit = AcceleratedFailureTime.Fit(AftModel.Weibull, dose, months, died, featureCount: 1);

double perUnit = Math.Round(fit.ExpCoefficients[0], 6);   // => 0.57744
double concordance = fit.ConcordanceIndex;                // => 0.9

Remarks — an accelerated failure time model says a covariate multiplies time. Above, each unit of dose multiplies a patient's time scale by 0.577: every percentile of the survival curve comes 0.577 times as soon. CoxProportionalHazards says instead that a covariate multiplies the hazard, and leaves the baseline's shape free; this fixes the shape to a ParametricModel's and reads the effect on the time axis, where it is often what a reader asked for. The Weibull is the one model that is both, so its coefficients and a Cox fit's describe the same curves in two units.

The primary parameter's log (lambda_ for the Weibull, mu_ itself for the log-normal, alpha_ for the log-logistic) is linear in the covariates; the ancillary one's log is an intercept, or linear in the same covariates when AftOptions.Ancillary says so. The design holds covariates only: the intercept is AftOptions.FitIntercept's to add.

The fit is lifelines' likelihood taken to its maximum, by Newton's method on exact derivatives, from the univariate fit lifelines itself starts from; lifelines' optimiser stops short of it, so a default lifelines fit differs in about the sixth significant figure. Reference behaviour is lifelines 0.30.3's WeibullAFTFitter, LogNormalAFTFitter and LogLogisticAFTFitter, with their weights, delayed entry, ridge penalty and robust errors. Thread-safe.

Applies to — net10.0, netstandard2.0.

See also — the estimators index, AftSummary, AftOptions, ParametricSurvival, Python → C# equivalence.

Members

Member	What it does
AcceleratedFailureTime.Fit	Fits a regression to right-censored durations.
AcceleratedFailureTime.FitIntervalCensored	Fits a regression to events known to lie between two times.
AcceleratedFailureTime.FitLeftCensored	Fits a regression to durations some of which are upper bounds.