BAYESIAN-INFERENCE OF SURVIVAL PROBABILITIES, UNDER STOCHASTIC ORDERING CONSTRAINTS

In the statistical analysis of survival data arising from two populati ons, it often happens that the analyst knows, a priori, that the life lengths in one population are stochastically shorter than those in the other. Nevertheless, survival probability estimates, if determined se parately from the corresponding samples, may not be consistent with th is prior assumption, because of inherent statistical variability in th e observations. This problem has been considered in a number of papers during the past decade, by adopting a (generalized) maximum likelihoo d approach. Our approach is Bayesian and, in essence, nonparametric. T he a priori assumption regarding stochastic ordering is formulated nat urally in terms of a joint prior distribution defined for pairs of sur vival functions. Nonparametric specification of the model, based on ha zard rates and using a few hyperparameters, allows for sufficient flex ibility in practical applications. The numerical computations are base d on a coupled version of the Metropolis-Hastings algorithm. The resul ts from a statistical analysis are summarized nicely by a pair of pred ictive survival functions that are consistent with the assumed stochas tic ordering.