Parametric Survival Models

Abstract

The nonparametric estimator of S(t) is a very good descriptive statistic for displaying survival data. For many purposes, however, one may want to make more assumptions to allow the data to be modeled in more detail. By specifying a functional form for S(t) and estimating any unknown parameters in this function, one can

• 1. easily compute selected quantiles of the survival distribution;

• 2. estimate (usually by extrapolation) the expected failure time;

• 3. derive a concise equation and smooth function for estimating S(t), Λ(t), and λ(t); and

• 4. estimate S(t) more precisely than S _KM(t) or S _Λ(t) if the parametric form is correctly specified.