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Fits an accelerated failure time regression to right-censored durations: lifelines' fit.

public static AftSummary Fit(AftModel model, ReadOnlySpan<double> design, ReadOnlySpan<double> durations, ReadOnlySpan<bool> eventObserved, int featureCount, AftOptions options = null)

public static AftSummary Fit(AftModel model, ReadOnlySpan<double> design, ReadOnlySpan<double> durations, ReadOnlySpan<bool> eventObserved, ReadOnlySpan<double> weights, ReadOnlySpan<double> entries, int featureCount, AftOptions options = null)

The second overload takes lifelines' weights_col and entry_col.

Parameters — model is the AftModel to fit. design holds the covariates row-major, featureCount values per subject, with no intercept column. durations holds one positive, finite duration per subject, and eventObserved is true where it ends in the event. weights holds one positive, finite weight per subject, or is empty for ones; entries each subject's entry time, non-negative and at most its duration, or is empty for none. featureCount is the design's row length, zero for a fit with no covariate. options sets the level, the intercept, the ancillary model, the penalty and the robust errors; null takes the defaults.

Returns — an AftSummary: per coefficient its estimate, standard error, z statistic, p-value and interval, with their exponentials; for the model the log-likelihood, the likelihood-ratio test against the univariate fit, the AIC and the concordance index.

Exceptions — ArgumentException when the spans do not match the subjects, a value is not finite, a duration is not positive, a weight or entry span is neither empty nor one valid value per subject, or the primary parameter has no column at all. ArgumentOutOfRangeException when model names no model, or featureCount is negative. InvalidOperationException when the fit does not converge, or its parameters are not identified. ArgumentException also when the parameters are too many for their square to fit in one array (#1311). ArgumentException naming featureCount also when the parameters are more than one array holds, and naming design when the design is more cells than one array holds or its length only matches the subjects times featureCount once that product wraps int (#1614).

Example — a design that is not a whole number of rows is refused.

using Lodestar.Survival;

double[] dose = [1.0, 2.0, 0.5, 3.0, 0.0, 1.5, 0.0, 2.5, 1.0, 0.5];
double[] months = [5, 8, 12, 3, 15, 9, 20, 6, 11, 14];
bool[] died = [true, true, false, true, true, true, false, true, true, false];

string refusal;
try
{
    // Ten values read as rows of two are five subjects, not the ten durations.
    AcceleratedFailureTime.Fit(AftModel.Weibull, dose, months, died, featureCount: 2);
    refusal = "fitted";
}
catch (ArgumentException error)
{
    refusal = error.ParamName!;
}

string parameter = refusal;  // => design

Remarks — the coefficients come in lifelines' order: the primary parameter's covariates, then its intercept, then the ancillary block — its intercept alone by default, or its covariates and then its intercept under AftOptions.Ancillary. AftSummary.ParameterNames and CovariateIndices say which is which.

Newton's method on exact derivatives, from the univariate fit lifelines starts from, each parameter the intercept of its block; that univariate fit is also the null model of the likelihood-ratio test. lifelines' own optimiser stops short of the maximum this reaches, so a default lifelines fit differs in about the sixth significant figure.

A design that does not identify the coefficients is refused — a covariate that does not vary is collinear with the intercept, and the observed information is then singular.

Applies to — net10.0, netstandard2.0.

See also — AcceleratedFailureTime, AftSummary, AftOptions.