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KaplanMeier

The Kaplan-Meier estimator of a survival function.

public static class KaplanMeier

Example — the treatment arm of Freireich's leukaemia trial, the data every survival text opens with.

using Lodestar.Survival;

double[] durations = [6, 6, 6, 7, 10, 13, 16, 22, 23, 6, 9, 10, 11, 17, 19, 20, 25, 32, 32, 34, 35];
bool[] observed = [true, true, true, true, true, true, true, true, true,
                   false, false, false, false, false, false, false, false, false, false, false, false];

KaplanMeierCurve curve = KaplanMeier.Estimate(durations, observed);

double atSix = curve.Survival[1];  // => 0.857142…
int atRisk = curve.Steps[1].AtRisk;  // => 21

Remarks — the estimate is the running product of 1 - d/n over the times carrying an event. Nine of those 21 subjects had the event; the other twelve were censored, and they contribute by being in the risk set rather than by being dropped.

A censoring leaves the risk set without moving the curve. That step is still reported — it has a Censored count and no Events — because a reader comparing against lifelines' event table expects to see it, and because the next step's AtRisk only makes sense if it is there.

Bounds are built on the log-log transform, not on the estimate. This is lifelines' default and it is not interchangeable with the plain Greenwood interval: at S = 0.857 on 21 subjects the latter reaches 1.0067, outside the range a probability can take, where the transform gives [0.6197, 0.9516]. The transform also means the bounds are not symmetric about the estimate.

Where the curve reaches zero the transform is undefined and both bounds collapse onto it — zero, not NaN, which is what lifelines reports too.

Reference behaviour is lifelines.KaplanMeierFitter 0.30.3, matched over 8 samples.

Applies to — net10.0, netstandard2.0.

See also — the estimators index, NelsonAalen.

Members

Member	What it does
KaplanMeier.Estimate	The survival function of a right-censored sample.