Bayesian inference of survival probabilities, under stochastic ordering constraints

In the statistical analysis of survival data arising from two populations, 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 separately from the corresponding samples, may not be consistent with this prior assumption, because of inherent statistical variability in the observations. This problem has been considered in a number of papers during the past decade, by adopting a (generalized) maximum likelihood approach. Our approach is Bayesian and, in essence, nonparametric. The a priori assumption regarding stochastic ordering is formulated naturally in terms of a joint prior distribution defined for pairs of survival functions. Nonparametric specification of the model, based on hazard rates and using a few hyperparameters, allows for sufficient flexibility in practical applications. The numerical computations are based on a coupled version of the Metropolis-Hastings algorithm. The results from a statistical analysis are summarized nicely by a pair of predictive survival functions that are consistent with the assumed stochastic ordering.