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Fits a parametric model to left-censored durations: lifelines' fit_left_censoring.

public static ParametricFit FitLeftCensored(ParametricModel model, ReadOnlySpan<double> durations, ReadOnlySpan<bool> eventObserved, ParametricOptions options = null)

public static ParametricFit FitLeftCensored(ParametricModel model, ReadOnlySpan<double> durations, ReadOnlySpan<bool> eventObserved, ReadOnlySpan<double> weights, ReadOnlySpan<double> entries, ParametricOptions options = null)

The second overload takes lifelines' weights and entry.

Parameters — model is the ParametricModel to fit. durations holds one positive, finite duration per subject. eventObserved is true where the duration is the event's own time, and false where the event had already happened by it. weights holds one positive, finite weight per subject, or is empty for ones; entries each subject's entry time, non-negative, or is empty for none. options sets the interval level, the iteration budget and the piecewise breakpoints; null takes the defaults.

Returns — a ParametricFit, as Fit returns.

Exceptions — ArgumentException when the spans differ in length or are empty, a duration is not positive and finite, a weight or entry span is neither empty nor one valid value per subject, or the piecewise model is given no breakpoint. ArgumentOutOfRangeException when model names no model. InvalidOperationException when the fit does not converge, or its parameters are not identified.

Example — ten samples under a detection limit: three were only known to be positive by their reading.

using Lodestar.Survival;

double[] readings = [3, 5, 2, 8, 4, 6, 1, 7, 5, 9];
bool[] exact = [true, false, true, true, false, true, false, true, true, true];

ParametricFit fit = ParametricSurvival.FitLeftCensored(ParametricModel.Weibull, readings, exact);

double scale = Math.Round(fit.Parameters[0], 6);        // => 5.050534
double median = Math.Round(fit.MedianSurvivalTime, 6);  // => 4.014061

Remarks — a left-censored subject contributes 1 − S(t), the probability the event came by t, where a right-censored one contributes S(t). The typical case is a measurement below a detection limit, or a subject who already had the event when first examined. Every other part of the fit is Fit's, the maximum reached by Newton's method rather than where lifelines' optimiser stops.

Applies to — net10.0, netstandard2.0.

See also — ParametricSurvival, KaplanMeier.EstimateLeftCensored, ParametricSurvival.FitIntervalCensored.