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Fits the Cox model on start-stop intervals.

public static CoxSummary Fit(ReadOnlySpan<double> design, ReadOnlySpan<double> starts, ReadOnlySpan<double> stops, ReadOnlySpan<bool> eventObserved, int featureCount, CoxOptions options = null)

public static CoxSummary Fit(ReadOnlySpan<double> design, ReadOnlySpan<double> starts, ReadOnlySpan<double> stops, ReadOnlySpan<bool> eventObserved, ReadOnlySpan<double> weights, ReadOnlySpan<int> strata, int featureCount, CoxOptions options = null)

The second overload weighs and stratifies the intervals, lifelines' weights_col and strata.

Parameters — design holds the covariates row-major, featureCount values per interval. starts and stops bound each interval (start, stop], starts non-negative and each stop after its start. eventObserved is true where the interval ends in the subject's event. weights holds one positive, finite weight per interval and strata one label per interval, or either is empty. options sets the level, the iteration budget and the penalty; null takes the defaults.

Returns — a CoxSummary: the coefficient table, the likelihood-ratio test and one baseline. ConcordanceIndex is NaN, as lifelines computes none for this fitter.

Exceptions — ArgumentOutOfRangeException when featureCount is below one. ArgumentException when the spans disagree in length, an interval is not finite and non-negative with its stop after its start, a covariate is not finite or does not vary, no interval ends in an event, a covariate is collinear with the others or separates the events, or CoxOptions.Robust is asked for. InvalidOperationException when the fit does not converge. ArgumentException also when the covariates are too many for their square to fit in one array (#1311). ArgumentException naming design also when it is more cells than one array holds (#1614).

Example — one interval per subject from zero is the ordinary fit.

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];
double[] zeros = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0];

double ordinary = CoxProportionalHazards.Fit(design, months, died, featureCount: 2).Coefficients[0];
double varying = CoxTimeVarying.Fit(design, zeros, months, died, featureCount: 2).Coefficients[0];

double same = Math.Round(varying - ordinary, 9);   // => 0

Remarks — no robust variance: lifelines' time-varying fitter raises NotImplementedError for robust=True, so there is nothing to match and it is refused. The penalty is the proportional hazards fit's; with an L1 part the answer is lifelines' own loop, which sharpens its smoothed absolute value by 1.5^i here rather than 1.3^i. The baseline is lifelines': Breslow's cumulative hazard at every distinct event time, pooled over the strata, the weighted events over the unweighted partial hazards of the intervals at risk.

Applies to — net10.0, netstandard2.0.

See also — CoxTimeVarying, CoxOptions.