Survival parametricmodel

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ParametricModel

Which of lifelines' parametric univariate models ParametricSurvival fits.

public enum ParametricModel { Exponential, Weibull, LogNormal, LogLogistic, PiecewiseExponential, GeneralizedGamma }

Members — each with its parameters in ParametricFit.ParameterNames' order:

• Exponential, H(t) = t / λ: lambda_. lifelines' ExponentialFitter.
• Weibull, H(t) = (t / λ)^ρ: lambda_, rho_. WeibullFitter.
• LogNormal, log T normal with mean μ and deviation σ: mu_, sigma_. LogNormalFitter.
• LogLogistic, S(t) = 1 / (1 + (t / α)^β): alpha_, beta_. LogLogisticFitter.
• PiecewiseExponential, a constant hazard 1 / λᵢ between consecutive breakpoints: lambda_0_, lambda_1_ and so on, one more than there are breakpoints. PiecewiseExponentialFitter.
• GeneralizedGamma, in (μ, log σ, λ): mu_, ln_sigma_, lambda_. GeneralizedGammaFitter.

Example — the same ten patients under three models, by AIC.

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];

double exponential = Math.Round(ParametricSurvival.Fit(ParametricModel.Exponential, months, died).Aic, 4);   // => 53.6435
double weibull = Math.Round(ParametricSurvival.Fit(ParametricModel.Weibull, months, died).Aic, 4);           // => 53.4005
double logNormal = Math.Round(ParametricSurvival.Fit(ParametricModel.LogNormal, months, died).Aic, 4);       // => 52.3648

Remarks — the exponential is a Weibull with ρ = 1, and both are generalized gammas, as the log-normal is at λ = 0: the generalized gamma nests them, and its fit is the check that a simpler one is not forcing its shape on the data. A difference of one in AIC, as above, is no evidence either way on ten subjects.

The piecewise exponential needs its breakpoints in ParametricOptions.Breakpoints, and is refused without them.

Applies to — net10.0, netstandard2.0.

See also — ParametricSurvival, AftModel.