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BreslowFlemingHarrington

The Breslow-Fleming-Harrington estimator of a survival function: the exponential of minus the Nelson-Aalen hazard.

public static class BreslowFlemingHarrington

Example — where Kaplan-Meier reaches zero, this does not.

using Lodestar.Survival;

SurvivalCurve smooth = BreslowFlemingHarrington.Estimate([1, 2, 3], [true, true, true]);
KaplanMeierCurve product = KaplanMeier.Estimate([1, 2, 3], [true, true, true]);

double bfhLast = Math.Round(smooth.Survival[3], 6);   // => 0.15988
double kmLast = product.Survival[3];                  // => 0

Remarks — exp(−H), with H the NelsonAalen cumulative hazard, lies above the Kaplan-Meier product at every step, by little while the risk set is large and by much at its end: above, exp(−1/3 − 1/2 − 1) where the product's last factor is 1 − 1/1. Prefer it on small samples where a curve pinned to zero by the last subject is not believable; prefer KaplanMeier everywhere else, being the estimator every reader expects.

Reference behaviour is lifelines.BreslowFlemingHarringtonFitter 0.30.3, right-censored with delayed entry. There are no weights: lifelines' fitter passes none on to the Nelson-Aalen fit it wraps, so its weights has no effect there. Thread-safe.

Applies to — net10.0, netstandard2.0.

See also — the estimators index, SurvivalCurve, NelsonAalen, Python → C# equivalence.

Members

Member	What it does
BreslowFlemingHarrington.Estimate	The survival function of a right-censored sample, entries allowed.