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AalenSummary

What an Aalen additive fit reports, at lifelines parity, and the predictions it makes.

public sealed class AalenSummary

Properties — the per-time lists are row-major, one row per event time and one column per coefficient: the covariates in the design's order, then the intercept.

• EventTimes are the distinct event times the coefficients step at, ascending: lifelines' index, cut where the fit stopped.
• CovariateIndices says which design column each coefficient multiplies, -1 for the intercept.
• Hazards are each coefficient's increment at each event time, lifelines' hazards_.
• CumulativeHazards are the increments summed, lifelines' cumulative_hazards_.
• CumulativeVariance is their variance, lifelines' cumulative_variance_.
• ConfidenceLower and ConfidenceUpper are each cumulative coefficient's normal interval at ConfidenceLevel.

For the model, one value per coefficient or one in all:

• Slopes are each cumulative coefficient's slope through the origin, weighted by the number at risk, lifelines' summary["slope(coef)"], and SlopeStandardErrors their standard errors.
• ConcordanceIndex is Harrell's C, lifelines' concordance_index_.
• ConfidenceLevel is the level the intervals were built at, FeatureCount the number of covariates a design row holds, and FitIntercept whether the fit carries an intercept, the last coefficient.

Example — the fit of the AalenAdditive page: the treatment, then the intercept, over ten event times.

using Lodestar.Survival;

double[] treated = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1];
double[] months = [3, 10, 5, 4, 8, 18, 12, 6, 9, 20, 7, 15];
bool[] died = [true, true, true, false, true, true, true, true, true, false, true, true];

AalenSummary fit = AalenAdditive.Fit(treated, months, died, featureCount: 1);

int times = fit.EventTimes.Count;                          // => 10
int intercept = fit.CovariateIndices[1];                   // => -1
double treatment = Math.Round(fit.CumulativeHazards[18], 6);   // => -2.083333
double lower = Math.Round(fit.ConfidenceLower[18], 6);     // => -3.851921
double slopeError = fit.SlopeStandardErrors[0];            // => 0.113183…

Remarks — a cumulative coefficient is read by its slope, not its level. Its value at a time is the effect summed up to then; where it runs straight the covariate adds a constant amount to the hazard, where it bends the effect changed. Slopes sums that up in one number, and SmoothedHazards gives the slope time by time.

lifelines' readings are kept on purpose, so the numbers are lifelines':

• CumulativeVariance is rescaled by the covariate's deviation, not its square. The fit runs on covariates scaled to unit deviation, and lifelines divides the variance back by the deviation once, as it does the coefficients; the bounds are built on it.
• ConcordanceIndex pairs the durations sorted by lifelines with the predictions in the design's order. lifelines scores the training subjects that way, so the index is not Harrell's C of the fit unless the design came sorted by duration. With tied durations, lifelines' own pairing follows numpy's unstable sort, which varies with the CPU; this one sorts stably.

A class rather than a record, as CoxSummary is: it carries the fitted model its predictions evaluate.

Applies to — net10.0, netstandard2.0.

See also — AalenAdditive.Fit, AalenOptions.

Members

Member	What it does
AalenSummary.PredictCumulativeHazard	Each subject's cumulative hazard at every event time.
AalenSummary.PredictExpectation	Each subject's expected lifetime, over the event times.
AalenSummary.PredictMedian	Each subject's median survival time.
AalenSummary.PredictPercentile	The event time at which each subject's survival reaches a level.
AalenSummary.PredictSurvivalFunction	Each subject's survival at every event time.
AalenSummary.SmoothedHazards	The increments smoothed by an Epanechnikov kernel.