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CoxOptions

What a CoxProportionalHazards or CoxTimeVarying fit may be told.

public sealed record CoxOptions

Properties — ConfidenceLevel is the two-sided level the intervals are reported at; 0.95 by default. MaximumIterations is how many Newton-Raphson iterations are allowed; 100 by default, and not read by an L1 fit, which keeps lifelines' own limits of 500 steps, 50 for the time-varying fit. Penalizer is lifelines' penalizer, zero by default, and L1Ratio its l1_ratio, the share of the penalty that is L1, zero by default. Robust asks for the Huber sandwich standard errors, lifelines' robust=True; clusters passed to the fit ask for it too.

Exceptions — ArgumentOutOfRangeException when ConfidenceLevel does not lie strictly inside (0, 1), when MaximumIterations is below one, when Penalizer is negative or not finite, or when L1Ratio lies outside [0, 1]. Each is thrown where the setting is set, not where the fit reads it.

Example — a narrower level moves both ends inward without moving the estimate.

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 ninetyFive = CoxProportionalHazards.Fit(design, months, died, 2);
CoxSummary ninety = CoxProportionalHazards.Fit(
    design, months, died, 2, new CoxOptions { ConfidenceLevel = 0.9 });

double wide = ninetyFive.ConfidenceLower[0];  // => 0.16213876109…
double narrow = ninety.ConfidenceLower[0];    // => 0.36168950449…

Remarks — there is no intercept. The baseline hazard absorbs what an intercept would carry, so a column of ones is collinear with it and is refused.

The penalty is lifelines' elastic net on the standardised coefficients, n · penalizer · Σ (l1 · |βⱼσⱼ| + (1 − l1) · (βⱼσⱼ)² / 2) with σⱼ the covariate's sample standard deviation, so it does not depend on the units a covariate is recorded in. A ridge penalty, L1Ratio = 0, is fitted to its optimum, as the unpenalised fit is. With an L1 part the answer is lifelines' own loop, reproduced step for step: the absolute value is smoothed and sharpened at every Newton step, so the answer is where lifelines' stopping rules fire rather than a stationary point, and its default and tightened fits differ by a factor of 29 (#1160). LogLikelihood is the penalised one, as lifelines' log_likelihood_ is.

Applies to — net10.0, netstandard2.0.

See also — CoxProportionalHazards.Fit, CoxSummary.