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AalenAdditive

Aalen's additive hazards model: each covariate adds to the hazard, by an amount that moves with time.

public static class AalenAdditive

Example — how much a treatment takes off the hazard, month by month, on twelve patients.

using Lodestar.Survival;

// 1 if on the new treatment; months to death or to the end of follow-up.
double[] treated = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1];
double[] months = [3, 10, 5, 4, 8, 18, 12, 6, 9, 20, 7, 15];
bool[] died = [true, true, true, false, true, true, true, true, true, false, true, true];

AalenSummary fit = AalenAdditive.Fit(treated, months, died, featureCount: 1);

double perMonth = fit.Slopes[0];              // => -0.200022…
double concordance = fit.ConcordanceIndex;    // => 0.598214…

Remarks — the model assumes nothing about how an effect changes with time. Where CoxProportionalHazards fixes each covariate's hazard ratio for the whole follow-up, this estimates a separate increment at every event time, and reports their running sum: a cumulative coefficient whose slope at a time is the covariate's effect then. A straight line means a constant effect; a bend means the effect moved. The slope above says the treatment takes about 0.2 a month off the hazard, averaged over the follow-up.

The price is that nothing keeps the hazard positive. An increment may take either sign, so a predicted cumulative hazard may fall and a predicted survival curve rise.

At each distinct event time the increments are a ridge-penalised least squares of that time's deaths on the covariates of the subjects at risk, the covariates scaled to unit sample deviation and weighted by the square roots of the weights. AalenOptions sets the two penalties and the intercept, which, when fitted, is the last coefficient.

Reference behaviour is lifelines 0.30.3's AalenAdditiveFitter, whose readings are kept on purpose; AalenAdditive.Fit lists them. Thread-safe.

Applies to — net10.0, netstandard2.0.

See also — the estimators index, AalenSummary, AalenOptions, Python → C# equivalence.

Members

Member	What it does
AalenAdditive.Fit	Fits the model to right-censored durations.