On the distinguished role of the multivariate exponential distribution in Bayesian estimation in competing risks problems

Abstract

In a companion paper, Neath and Samaniego (1996) derive the limiting posterior estimate of the multiple decrement function (MDP), relative to a Dirichlet process prior. It is noted there that, due to the nonidentifiability of the MDF in competing risks problems, the limiting posterior estimate can be inferior to the estimate of the MDF based on the prior distribution alone. This leads, among other things, to the search for distinguished parameter values, or models, for which Bayesian updating necessarily improves upon one's prior estimate. In this article, it is shown that when the true multiple decrement function is bivariate exponential and the parameter measures of the Dirichlet process prior is also bivariate exponential, the posterior estimates of marginal survival functions are uniformly better than the prior estimates; thus, Bayesian updating is uniformly efficacious under these latter conditions.