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CoxProportionalHazards

The Cox proportional hazards model, fitted by Newton-Raphson on Efron's partial likelihood.

public static class CoxProportionalHazards

Example — how much a dose and a treatment move the hazard, on ten patients.

using Lodestar.Survival;

// One row per patient: dose in mg, then 1 if on the new treatment.
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 summary = CoxProportionalHazards.Fit(design, months, died, featureCount: 2);

double perMilligram = summary.HazardRatios[0];  // => 4.0687…
double p = summary.PValues[0];                  // => 0.02669…

Remarks — the model assumes the covariates multiply the hazard by the same factor at every time. That is the "proportional" in its name, and a hazard ratio of 4.07 per milligram means nothing if the dose's effect fades after the first months. TestProportionalHazards tests it covariate by covariate, and the guide says how to read a failure.

It answers a different question from its neighbours. KaplanMeier says what survival looks like, and LogRank whether two groups differ. This says by how much each covariate changes the hazard, holding the others fixed.

Reference behaviour is lifelines.CoxPHFitter 0.30.3, right-censored, with its strata, subject weights, elastic-net penalty, robust and clustered variances, baselines and predictions. The divergences are recorded in decision 0003 and the equivalence table.

Applies to — net10.0, netstandard2.0.

See also — the estimators index, CoxSummary, CoxOptions.

Members

Member	What it does
CoxProportionalHazards.Fit	Fits the model and reports its inference table.
CoxProportionalHazards.TestProportionalHazards	Tests each covariate for a hazard ratio that drifts with time.