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AftModel

Which of lifelines' accelerated failure time regressions AcceleratedFailureTime fits.

public enum AftModel { Weibull, LogNormal, LogLogistic }

Members — each with its primary and ancillary parameter, as AftSummary.ParameterNames names them:

• Weibull, log λ = Xβ and log ρ an intercept or Xγ: lambda_, rho_. lifelines' WeibullAFTFitter.
• LogNormal, μ = Xβ and log σ an intercept or Xγ: mu_, sigma_. LogNormalAFTFitter.
• LogLogistic, log α = Xβ and log β an intercept or Xγ: alpha_, beta_. LogLogisticAFTFitter.

Example — the dose's coefficient under each model: the time ratio barely depends on the shape assumed.

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];

double weibull = Math.Round(AcceleratedFailureTime.Fit(AftModel.Weibull, dose, months, died, 1).Coefficients[0], 4);           // => -0.5492
double logNormal = Math.Round(AcceleratedFailureTime.Fit(AftModel.LogNormal, dose, months, died, 1).Coefficients[0], 4);       // => -0.5588
double logLogistic = Math.Round(AcceleratedFailureTime.Fit(AftModel.LogLogistic, dose, months, died, 1).Coefficients[0], 4);   // => -0.5525

Remarks — in all three the primary coefficient is a log time ratio: log T is linear in the covariates plus an error whose law the model names — extreme-value for the Weibull, normal for the log-normal, logistic for the log-logistic. The ancillary parameter sets that error's spread.

The Weibull is also a proportional hazards model, so its fit can be read beside a CoxProportionalHazards one; the log-logistic is a proportional odds model, and the log-normal neither.

Applies to — net10.0, netstandard2.0.

See also — AcceleratedFailureTime, ParametricModel.