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Tests each covariate for a hazard ratio that drifts with time: lifelines' proportional_hazard_test.

public static IReadOnlyList<TestResult> TestProportionalHazards(ReadOnlySpan<double> design, ReadOnlySpan<double> durations, ReadOnlySpan<bool> eventObserved, CoxSummary fit, CoxTimeTransform transform = CoxTimeTransform.Rank)

public static IReadOnlyList<TestResult> TestProportionalHazards(ReadOnlySpan<double> design, ReadOnlySpan<double> durations, ReadOnlySpan<bool> eventObserved, ReadOnlySpan<double> weights, ReadOnlySpan<int> strata, CoxSummary fit, CoxTimeTransform transform)

The second overload takes the weights and strata a fit was made with.

Parameters — design, durations and eventObserved are what the model was fitted on, and weights and strata too, or empty. fit is that model. transform is the CoxTimeTransform the residuals are correlated with, the rank by default.

Returns — one TestResult per covariate, in the design's column order: a chi-squared statistic on one degree of freedom and its p-value.

Exceptions — ArgumentNullException when fit is null. ArgumentException when the spans disagree with each other or with the fit's covariate count, a value is not finite, no event is observed, a weight or stratum span is neither empty nor one value per subject, the strata are not the ones the fit was stratified by, or the fit is a CoxTimeVarying one, which lifelines' test does not take either. ArgumentOutOfRangeException when transform names no time scale. ArgumentException naming design also when it is more cells than one array holds (#1614).

Example — neither covariate drifts on this sample.

using Lodestar.Stats;
using Lodestar.Survival;

double[] design = [1.0, 0.0, 2.0, 1.0, 1.5, 0.0, 3.0, 1.0, 2.5, 0.0,
                   0.5, 1.0, 2.0, 0.0, 1.0, 1.0, 3.5, 0.0, 0.5, 1.0];
double[] months = [12, 5, 20, 3, 15, 9, 8, 14, 2, 18];
bool[] died = [true, true, false, true, true, true, true, false, true, true];

CoxSummary fit = CoxProportionalHazards.Fit(design, months, died, featureCount: 2);
IReadOnlyList<TestResult> tests = CoxProportionalHazards.TestProportionalHazards(design, months, died, fit);

double first = Math.Round(tests[0].PValue, 6);    // => 0.326668
double second = Math.Round(tests[1].PValue, 6);   // => 0.945687

Remarks — lifelines' approximation, which R left in 2019. The Schoenfeld residual of each event is its covariates less the Efron-weighted mean of its risk set at the fitted coefficients, scaled by the number of events times the model-based covariance; covariate k's statistic is (Σ gᵢ sᵢₖ)² / (d · seₖ² · Σ gᵢ²), g the transformed event times less their mean. The standard error is the fit's own, robust where the fit was. So the numbers match lifelines and not a current cox.zph. The rank transform counts events along the fit's sorted order, strata first, as lifelines does; the Kaplan-Meier one pools the strata and takes the weights.

Applies to — net10.0, netstandard2.0.

See also — CoxTimeTransform, CoxProportionalHazards.Fit.