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ParametricSurvival

lifelines' parametric univariate fitters, right-, left- and interval-censored, fitted to their maximum.

public static class ParametricSurvival

Example — a Weibull curve through ten patients, three of them censored.

using Lodestar.Survival;

double[] months = [5, 8, 12, 3, 15, 9, 20, 6, 11, 14];
bool[] died = [true, true, false, true, true, true, false, true, true, false];

ParametricFit fit = ParametricSurvival.Fit(ParametricModel.Weibull, months, died);

double scale = Math.Round(fit.Parameters[0], 6);        // => 13.682221
double shape = Math.Round(fit.Parameters[1], 6);        // => 1.702463
double median = Math.Round(fit.MedianSurvivalTime, 6);  // => 11.032146

Remarks — a parametric fit trades the data's own shape for a smooth one. KaplanMeier steps only where an event happened and stops at the last duration; a fitted model has a hazard at every time, a median even where fewer than half had the event, and a curve past the end of follow-up — each as good as the model is. Compare models on the same data by ParametricFit.Aic, lower being better.

Six models, lifelines' six fitters: ParametricModel names them and their parameters. Every fit takes lifelines' weights and delayed entry (entry) through the overloads that carry them, and the three censoring schemes are three methods: Fit for right-censored durations, FitLeftCensored for durations some of which are only upper bounds, FitIntervalCensored for events known to lie between two times.

The fit is lifelines' likelihood taken to its maximum, by Newton's method on exact first and second derivatives. lifelines' own optimiser, Nelder-Mead then L-BFGS-B, stops 1e-6 to 1e-3 short of that maximum, so a default lifelines fit differs from this one in about the sixth significant figure; the frozen reference is lifelines driven to its maximum. Reference behaviour is lifelines 0.30.3's ExponentialFitter, WeibullFitter, LogNormalFitter, LogLogisticFitter, PiecewiseExponentialFitter and GeneralizedGammaFitter. Thread-safe.

Applies to — net10.0, netstandard2.0.

See also — the estimators index, ParametricFit, AcceleratedFailureTime, Python → C# equivalence.

Members

Member	What it does
ParametricSurvival.CompareAt	Tests whether two fitted curves differ at one time.
ParametricSurvival.Fit	Fits a model to right-censored durations.
ParametricSurvival.FitIntervalCensored	Fits a model to events known to lie between two times.
ParametricSurvival.FitLeftCensored	Fits a model to durations some of which are upper bounds.