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AftSummary

What an accelerated failure time fit reports, at lifelines parity, and the predictions it makes.

public sealed class AftSummary

Properties — the per-coefficient lists are parallel and in lifelines' order: the primary parameter's covariates, then its intercept, then the ancillary parameter's block.

• ParameterNames says which parameter each coefficient belongs to: lambda_ and rho_ for the Weibull, mu_ and sigma_ for the log-normal, alpha_ and beta_ for the log-logistic.
• CovariateIndices says which design column it multiplies, -1 for an intercept.
• Coefficients are the estimates: the log of the parameter is the sum of each times its covariate.
• StandardErrors are the square roots of the covariance's diagonal: the inverse observed information, or the sandwich when Robust.
• ZStatistics is each coefficient over its standard error, and PValues are two-sided, from the normal tail.
• ConfidenceLower and ConfidenceUpper are each coefficient's interval at ConfidenceLevel.
• ExpCoefficients, ExpConfidenceLower and ExpConfidenceUpper are the exponentials of the three above: how much a unit of the covariate multiplies the parameter.

For the model:

• Model is the AftModel fitted, and FeatureCount the number of covariates a design row holds.
• LogLikelihood is the log-likelihood at the fit, less the penalty on its summed scale: lifelines' log_likelihood_. NullLogLikelihood is the univariate model's, with no covariate at all.
• LikelihoodRatioStatistic is twice their difference, and LikelihoodRatioPValue its chi-squared tail on LikelihoodRatioDegreesOfFreedom degrees, the coefficients past the univariate model's two; NaN when there are none.
• Aic is −2 · LogLikelihood + 2k over the k coefficients.
• ConcordanceIndex is Harrell's C between the durations and the predicted medians; NaN for an interval-censored fit.
• ConfidenceLevel is the level the intervals were built at, and Robust says whether the standard errors, and everything built on them, are the Huber sandwich.

Example — the fit of the AcceleratedFailureTime page: the dose, the Weibull scale's intercept, and its shape.

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];

AftSummary fit = AcceleratedFailureTime.Fit(AftModel.Weibull, dose, months, died, featureCount: 1);

string intercept = fit.ParameterNames[1];              // => lambda_
int column = fit.CovariateIndices[1];                  // => -1
string shape = fit.ParameterNames[2];                  // => rho_
double statistic = Math.Round(fit.LikelihoodRatioStatistic, 6);   // => 15.822317
double modelP = fit.LikelihoodRatioPValue;             // => 6.9577…
int degrees = fit.LikelihoodRatioDegreesOfFreedom;     // => 1

Remarks — every z statistic is measured from zero, a coefficient that does not move its parameter. ParametricFit's are measured from lifelines' comparison values instead, because its parameters are not on the log scale.

An exponentiated coefficient multiplies the parameter, not the hazard. For the Weibull, lambda_ is the time scale, so 0.577 per unit of dose means every percentile comes 0.577 times as soon; a Cox hazard ratio would say how much more often the event happens. The two agree only through the shape: for the Weibull, a hazard ratio is the time ratio to the power −ρ.

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 — AcceleratedFailureTime.Fit, AftOptions.

Members

Member	What it does
AftSummary.PredictCumulativeHazard	Each subject's cumulative hazard at given times.
AftSummary.PredictExpectation	Each subject's expected survival time.
AftSummary.PredictMedian	Each subject's median survival time.
AftSummary.PredictPercentile	The time each subject's survival falls to a level.
AftSummary.PredictSurvivalFunction	Each subject's survival at given times.