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The delta-method interval of the survival function: lifelines' confidence_interval_survival_function_.

public (double[] Lower, double[] Upper) SurvivalBounds(ReadOnlySpan<double> times)

Parameters — times are the positive times to read at.

Returns — the lower and upper bounds at ConfidenceLevel, one of each per time, not clipped to [0, 1].

Example — inside the data the interval is a probability; far past it, it is not.

using Lodestar.Survival;

double[] months = [5, 8, 12, 3, 15, 9, 20, 6, 11, 14];
bool[] died = [true, true, false, true, true, true, false, true, true, false];

ParametricFit fit = ParametricSurvival.Fit(ParametricModel.Weibull, months, died);

(double[] lower, double[] upper) = fit.SurvivalBounds([10.0, 40.0]);
double atTen = Math.Round(lower[0], 6);         // => 0.297678
double pastTheData = Math.Round(lower[1], 6);   // => -0.015345

Remarks — the interval is symmetric about the estimate on the survival scale, S ± z·σ, with σ² the gradient of S in the parameters through their covariance. That is lifelines' reading, and it is why a bound can leave [0, 1], as the one at forty months does; lifelines does not clip it, and neither does this. CumulativeHazardBounds is the same interval on the hazard.

Applies to — net10.0, netstandard2.0.

See also — ParametricFit, ParametricFit.Survival.