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KaplanMeier.CompareAt

Tests whether two survival curves differ at one time: lifelines' survival_difference_at_fixed_point_in_time_test.

public static TestResult CompareAt(double time, KaplanMeierCurve curveA, KaplanMeierCurve curveB)

Parameters — time is the time both curves are read at, non-negative. curveA and curveB are two curves from KaplanMeier.Estimate.

Returns — a TestResult: the chi-squared statistic on one degree of freedom and its upper-tail p-value.

Exceptions — ArgumentNullException when a curve is null, and ArgumentException when one holds no step or not one estimate per step, or is not a right-censored curve from Estimate, the product of its steps' 1 − d/n: a curve from EstimateLeftCensored is refused. ArgumentOutOfRangeException when time is negative or NaN.

Example — Freireich's arms at week 10, where the log-rank test reads the whole curve instead.

using Lodestar.Stats;
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];

TestResult atTen = KaplanMeier.CompareAt(10,
    KaplanMeier.Estimate(treatment, treatmentObserved), KaplanMeier.Estimate(control, controlObserved));

double statistic = Math.Round(atTen.Statistic, 6);   // => 4.737596
double p = Math.Round(atTen.PValue, 6);              // => 0.02951

Remarks — Klein, Logan, Harhoff and Andersen's test on the log(−log S) scale: the squared difference of the two transformed estimates over the sum of their delta-method variances.

Two readings of the curve, as lifelines takes them. Each estimate is the curve's step at time, while its Greenwood sum is interpolated linearly between the times on either side, which is numpy.interp over lifelines' _cumulative_sq_. A step where every subject left at risk has the event adds nothing to that sum, where KaplanMeier.Estimate's bounds read it as infinite. A curve at one or at zero at time leaves the transform undefined, and the statistic is NaN, as lifelines' is.

Applies to — net10.0, netstandard2.0.

See also — KaplanMeier.RestrictedMean, LogRank.