Development build. This page describes main, not a released package. The latest published Lodestar.Survival is 0.2.0 — read its documentation.

Home › Survival › Survival estimators

LogRankWeighting

Which member of the log-rank family LogRank runs: lifelines' weightings=.

public enum LogRankWeighting { LogRank, Wilcoxon, TaroneWare, Peto, FlemingHarrington }

Members — LogRank, the default, weighs every event time one: lifelines' weightings=None. Wilcoxon weighs it by the pooled number at risk, Gehan and Breslow's generalised Wilcoxon test. TaroneWare weighs it by that number's square root. Peto weighs it by Peto and Peto's modified survival estimate. FlemingHarrington weighs it by S^p (1 − S)^q, S the pooled Kaplan-Meier curve just before the time, with p and q from LogRankOptions.

Example — the early weightings and the late one on Freireich's two arms.

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];

double wilcoxon = LogRank.Test(treatment, treatmentObserved, control, controlObserved,
    new LogRankOptions { Weighting = LogRankWeighting.Wilcoxon }).Statistic;
double late = LogRank.Test(treatment, treatmentObserved, control, controlObserved,
    new LogRankOptions { Weighting = LogRankWeighting.FlemingHarrington, P = 0, Q = 1 }).Statistic;

double early = Math.Round(wilcoxon, 6);   // => 13.457852
double lateOnly = Math.Round(late, 6);    // => 13.048449

Remarks — the weight says where a difference counts. Wilcoxon, Tarone-Ware and Peto weigh the early times, where most subjects are still at risk; Fleming-Harrington with q > 0 weighs the late ones, and with p = q = 0 it is the log-rank test itself. Choose before looking at the data: picking the weighting that rejects is a multiple comparison the p-value does not know about.

Peto's weight includes the time it weighs, ∏ (1 − d/(n + 1)) up to and including it, as lifelines computes it; the pooled curve under Fleming-Harrington is the one just before.

Applies to — net10.0, netstandard2.0.

See also — LogRankOptions, LogRank.Test.