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ParametricSurvival.CompareAt

Tests whether two fitted survival functions differ at one time: lifelines' survival_difference_at_fixed_point_in_time_test on two parametric fitters.

public static TestResult CompareAt(double time, ParametricFit fitA, ParametricFit fitB)

Parameters — time is the time both fits are read at, positive and finite. fitA and fitB are two fits from ParametricSurvival, of the same model or not.

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

Exceptions — ArgumentNullException when a fit is null. ArgumentOutOfRangeException when time is not positive and finite.

Example — two arms of ten, each fitted with a Weibull curve, compared at five months.

using Lodestar.Stats;
using Lodestar.Survival;

double[] armA = [5, 8, 12, 3, 15, 9, 20, 6, 11, 14];
bool[] diedA = [true, true, false, true, true, true, false, true, true, false];
double[] armB = [2, 4, 7, 1, 6, 3, 9, 5, 4, 8];
bool[] diedB = [true, true, true, true, false, true, true, true, true, false];

TestResult atFive = ParametricSurvival.CompareAt(5.0,
    ParametricSurvival.Fit(ParametricModel.Weibull, armA, diedA),
    ParametricSurvival.Fit(ParametricModel.Weibull, armB, diedB));

double statistic = Math.Round(atFive.Statistic, 6);   // => 5.84045
double p = Math.Round(atFive.PValue, 6);              // => 0.015662

Remarks — the statistic is KaplanMeier.CompareAt's, on the log(−log S) scale: (log(−log S_A) − log(−log S_B))² over σ²_A/(log S_A)² + σ²_B/(log S_B)².

σ² is the delta-method variance of S itself, not of log S. A Kaplan-Meier curve hands the formula Greenwood's variance of log S, which is what its denominator expects; lifelines hands it a parametric fit's variance of S unchanged, and this keeps that reading so the statistic is the one lifelines reports. The two differ by a factor of S² in each variance.

Applies to — net10.0, netstandard2.0.

See also — ParametricFit.SurvivalBounds, KaplanMeier.CompareAt, LogRank.