Posterior likelihood methods for multivariate survival data

This article deals with the semiparametric analysis of multivariate surviva l data with random block (group) effects. Survival times within the same gr oup are correlated as a consequence of a frailty random block effect. The s tandard approaches assume either a parametric or a completely unknown basel ine hazard function. This paper considers an intermediate solution, that is , a nonparametric function that is reasonably smooth. This is accomplished by a Bayesian model in which the conditional proportional hazards model is used with a correlated prior process for the baseline hazard. The posterior likelihood based on data, as well as the prior process, is similar to the discretized penalized likelihood for the frailty model. The methodology is exemplified with the recurrent kidney infections data of McGilchrist and Ai sbett (1991, Biometrics 47, 461-466), in which the times to infections with in the same patients are expected to be correlated. The reanalysis of the d ata has shown that the estimates of the parameters of interest and the asso ciated standard errors depend on the prior knowledge about the smoothness o f the baseline hazard.