Lodestar.Survival 0.1.0. This page is frozen at that release. Read the current documentation for what main says now. A link to a decision or a migration page follows main, and leaves the archive.

The cumulative hazard of a right-censored sample.

public static NelsonAalenCurve Estimate(ReadOnlySpan<double> durations, ReadOnlySpan<bool> eventObserved)

Parameters — durations holds one non-negative time per subject; eventObserved is true where that time ends in the event. The two spans must be the same length.

Returns — a NelsonAalenCurve whose Steps and CumulativeHazard share one index.

Exceptions — ArgumentException when the spans differ in length, the sample is empty, or a duration is negative or NaN.

Example — the increment at a time with three tied events.

using Lodestar.Survival;

NelsonAalenCurve curve = NelsonAalen.Estimate([6, 6, 6, 7], [true, true, true, true]);

double atSix = curve.CumulativeHazard[1];  // => 1.083…

Remarks — the increment is not d/n. With d events tied at one time it is the sum of 1 / (n - i) over those events, as though they had been separated by an instant each. Three events among 21 at risk give

1/21 + 1/20 + 1/19 = 0.150251     and not     3/21 = 0.142857

which is a 5% difference at the very first step of the Freireich arm. This is the tie correction lifelines applies by default, and it is the single place an implementation written from the plain definition will disagree with it. The frozen corpus is what caught it here — four of the eight samples carry ties on purpose for that reason.

Censorings contribute nothing to the sum and everything to the denominators after them, which is the same mechanism Kaplan-Meier uses and why the two share a step table.

Applies to — net10.0, netstandard2.0.

See also — NelsonAalen, KaplanMeier.Estimate.