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LogRank

The log-rank family: two groups or more, weighted, pairwise.

public static class LogRank

Example — Freireich's two arms, which is what the test was published to compare.

using Lodestar.Survival;

double[] treatment = [6, 6, 6, 7, 10, 13, 16, 22, 23, 6, 9, 10, 11, 17, 19, 20, 25, 32, 32, 34, 35];
bool[] treatmentObserved = [true, true, true, true, true, true, true, true, true,
                            false, false, false, false, false, false, false, false, false, false, false, false];
double[] control = [1, 1, 2, 2, 3, 4, 4, 5, 5, 8, 8, 8, 8, 11, 11, 12, 12, 15, 17, 22, 23];
bool[] controlObserved = [true, true, true, true, true, true, true, true, true, true, true,
                          true, true, true, true, true, true, true, true, true, true];

LogRankResult result = LogRank.Test(treatment, treatmentObserved, control, controlObserved);

double statistic = result.Statistic;  // => 16.79…
double p = result.PValue;  // => 4.168…

Remarks — at each time carrying an event in either arm, the first group's observed events are compared against what the pooled risk sets would give it. The statistic is the squared total difference over the summed variance, so it is never negative and is zero when the two curves agree step for step.

Ties are handled by the hypergeometric variance, not by an approximation of it. With one event at a time it reduces to the familiar n₁n₂/n²; with several it carries the (n - d) / (n - 1) factor that a naive implementation drops, and that factor is what makes a heavily tied comparison come out at the reference's number.

Its p-value is the published chi-squared tail, not a second one: Distributions.ChiSquaredSf on one degree of freedom. Decision 0003 published that member for this call rather than let a second far-tail approximation into the tree, and a test asserts the two routes agree.

A time that only censors, or a time where one subject remains, contributes nothing: the hypergeometric variance is zero there and the term carries no information. Where no time compares both groups at all, the result is a statistic of zero and a p-value of one — there is nothing to reject rather than an error to raise.

The weightings, the truncation and the subject weights are LogRankOptions and the weighted overloads: Wilcoxon, Tarone-Ware, Peto and Fleming-Harrington weigh each time before it is summed, and a truncation censors every event past it.

Reference behaviour is lifelines.statistics 0.30.3 — logrank_test, multivariate_logrank_test and pairwise_logrank_test — matched under every weighting, with and without subject weights.

Applies to — net10.0, netstandard2.0.

See also — the estimators index, KaplanMeier.

Members

Member	What it does
LogRank.MultiGroup	Compares several groups at once.
LogRank.Pairwise	Runs the two-sample test on every pair of groups.
LogRank.Test	Compares the survival of two right-censored samples, under any weighting.