Bayesian Life Table Analysis

Summary The moments of the posterior p.d.f. of the probability of surviving to time t, P(t), are obtained, assuming a time-dependent Poisson process for failures and i.i.d. gamma prior densities for the hazard function. For improper densities the results reduce to the Kaplan–Meier estimate of p(t) and to the Cox result for the comparison of two survival curves, which, because of the use of improper priors, may be inadmissible with respect to mean square error loss. A way of estimating the priors from the data, and hence of obtaining estimates that may be uniformly superior to those of Kaplan–Meier and Cox, is given. The use of a class of more realistic, but still non-parametric, priors is discussed.