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Fits a parametric model to interval-censored times: lifelines' fit_interval_censoring.

public static ParametricFit FitIntervalCensored(ParametricModel model, ReadOnlySpan<double> lower, ReadOnlySpan<double> upper, ParametricOptions options = null)

public static ParametricFit FitIntervalCensored(ParametricModel model, ReadOnlySpan<double> lower, ReadOnlySpan<double> upper, ReadOnlySpan<double> weights, ReadOnlySpan<double> entries, ParametricOptions options = null)

The second overload takes lifelines' weights and entry.

Parameters — model is the ParametricModel to fit. lower and upper bound each subject's event: lower non-negative, upper at least lower, infinite for a subject still event-free at lower. Equal bounds are an event observed exactly. weights holds one positive, finite weight per subject, or is empty for ones; entries each subject's entry time, non-negative, or is empty for none. options sets the interval level, the iteration budget and the piecewise breakpoints; null takes the defaults.

Returns — a ParametricFit, as Fit returns.

Exceptions — ArgumentException when the spans differ in length or are empty, a bound is NaN or negative, an upper bound is below its lower one, a weight or entry span is neither empty nor one valid value per subject, or the piecewise model is given no breakpoint. ArgumentOutOfRangeException when model names no model. InvalidOperationException when the fit does not converge, or its parameters are not identified.

Example — ten subjects examined at visits: one seen at the event, two still event-free at their last visit.

using Lodestar.Survival;

double[] lastClear = [2, 4, 0, 6, 3, 8, 5, 1, 7, 10];
double[] firstSeen = [4, 6, 3, 9, 3, double.PositiveInfinity, 7, 4, 10, double.PositiveInfinity];

ParametricFit fit = ParametricSurvival.FitIntervalCensored(ParametricModel.LogNormal, lastClear, firstSeen);

double mu = Math.Round(fit.Parameters[0], 6);        // => 1.64757
double z = Math.Round(fit.ZStatistics[1], 6);        // => -1.581959

Remarks — a subject contributes S(lower) − S(upper), the probability the event fell between its two visits, and an infinite upper makes that S(lower), a right-censoring. The one design where this is not a choice is a disease found only when looked for: dating the event at the visit that found it biases every estimate late.

The z statistic above measures sigma_ from one, not zero: ParametricFit has why. Turnbull's non-parametric estimate for interval-censored data is not here.

Applies to — net10.0, netstandard2.0.

See also — ParametricSurvival, ParametricSurvival.Fit, AcceleratedFailureTime.FitIntervalCensored.