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Compares the survival of several groups at once: lifelines' multivariate_logrank_test.

public static LogRankResult MultiGroup(ReadOnlySpan<double> durations, ReadOnlySpan<int> groups, ReadOnlySpan<bool> eventObserved, LogRankOptions options = null)

public static LogRankResult MultiGroup(ReadOnlySpan<double> durations, ReadOnlySpan<int> groups, ReadOnlySpan<bool> eventObserved, ReadOnlySpan<double> weights, LogRankOptions options = null)

The second overload weighs each subject, lifelines' weights=.

Parameters — durations holds one non-negative duration per subject and eventObserved its flag. groups holds one label per subject, any integers, at least two distinct. weights is one positive, finite weight per subject, or empty for ones. options chooses the weighting, its exponents and the truncation; null runs the log-rank test.

Returns — a LogRankResult on one degree of freedom fewer than the groups.

Exceptions — ArgumentException when the spans differ in length, the sample is empty, a duration is negative or NaN, fewer than two groups appear, weights is neither empty nor one positive, finite value per subject, or the distinct durations or the groups times the groups are more cells than one array holds. ArgumentOutOfRangeException when options names no weighting, or holds a negative or non-finite exponent, or a negative or NaN truncation.

Example — three groups that do not differ.

using Lodestar.Survival;

double[] durations = [5, 8, 12, 3, 9, 15, 4, 6, 20, 11, 7, 14];
int[] groups = [1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 2, 3];
bool[] observed = [true, true, false, true, true, true, true, true, false, true, false, true];

LogRankResult result = LogRank.MultiGroup(durations, groups, observed);

double statistic = Math.Round(result.Statistic, 6);   // => 0.159352
double p = Math.Round(result.PValue, 6);              // => 0.923415
int df = result.DegreesOfFreedom;                     // => 2

Remarks — at each distinct duration every group's observed events are set against the share of the pooled events its risk set would carry, and the statistic is that difference vector over its hypergeometric covariance, for every group but the last. The covariance is read through a pseudo-inverse, as lifelines reads it through numpy.linalg.pinv, so a group nobody is at risk in by the first event leaves the others' comparison standing rather than failing. Which group is left out does not change the statistic.

A weight of two is the subject written twice, in every risk set and every event count — except in the pooled curve Fleming-Harrington weighs by, which lifelines builds from the subjects unweighted, and so does this. A time whose pooled risk set has fallen below one, possible only with fractional weights, adds nothing to the covariance, as in lifelines.

Reference behaviour is lifelines.statistics.multivariate_logrank_test 0.30.3, matched with and without weights under every weighting.

Applies to — net10.0, netstandard2.0.

See also — LogRank.Pairwise, LogRank.Test, LogRankOptions.