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The event time at which each subject's survival reaches a level: lifelines' predict_percentile.

public double[] PredictPercentile(ReadOnlySpan<double> design, double probability)

Parameters — design holds the subjects' covariates row-major, FeatureCount per row; empty for the one subject of a fit with no covariate. probability is the survival level, in [0, 1]; a half for the median.

Returns — one time per subject, among EventTimes; infinity where the last survival is still above the level.

Exceptions — ArgumentException when design is not whole rows of finite covariates. ArgumentOutOfRangeException when probability lies outside [0, 1]. ArgumentException naming design also when it, with any intercept column, or its rows times the event times, is more cells than one array holds (#1614, #1616).

Example — by when a quarter are still alive: month 9 untreated, never within the fit on treatment.

using Lodestar.Survival;

double[] treated = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1];
double[] months = [3, 10, 5, 4, 8, 18, 12, 6, 9, 20, 7, 15];
bool[] died = [true, true, true, false, true, true, true, true, true, false, true, true];

AalenSummary fit = AalenAdditive.Fit(treated, months, died, featureCount: 1);

double[] times = fit.PredictPercentile([0.0, 1.0], 0.25);
double untreated = times[0];                              // => 9
bool neverOnTreatment = double.IsPositiveInfinity(times[1]);   // => True

Remarks — the level is a survival probability, as lifelines' is: 0.25 is the time a quarter are still event-free.

The time is where numpy's searchsorted lands, not necessarily the first crossing. lifelines reads the percentile off the curve by a binary search that assumes it falls, and an additive model's curve need not: where it rises and falls back across the level, the search may land on a later crossing than the first. This lands where numpy's does, measured identical on 20,000 random curves.

Applies to — net10.0, netstandard2.0.

See also — AalenSummary, AalenSummary.PredictMedian, AalenSummary.PredictSurvivalFunction.