Bayesian analysis of multivariate survival data using Monte Carlo methods

This paper deals with the analysis of multivariate survival data from a Bayesian perspective using Markov-chain Monte Carlo methods. The Metropolis along with the Gibbs algorithm is used to calculate some of the marginal posterior distributions. A multivariate survival model is proposed, since survival times within the same group are correlated as a consequence of a frailty random block effect. The conditional proportional-hazards model of Clayton and Cuzick is used with a martingale structured prior process (Arjas and Gasbarra) for the discretized baseline hazard. Besides the calculation of the marginal posterior distributions of the parameters of interest, this paper presents some Bayesian EDA diagnostic techniques to detect model adequacy. The methodology is exemplified with kidney infection data where the times to infections within the same patients are expected to be correlated.     

A Weibull Regression Model with Gamma Frailties for Multivariate Survival Data

Frequently in the analysis of survival data, survival times within the same group are correlated due to unobserved co-variates. One way these co-variates can be included in the model is as frailties. These frailty random block effects generate dependency between the survival times of the individuals which are conditionally independent given the frailty. Using a conditional proportional hazards model, in conjunction with the frailty, a whole new family of models is introduced. By considering a gamma frailty model, often the issue is to find an appropriate model for the baseline hazard function. In this paper a flexible baseline hazard model based on a correlated prior process is proposed and is compared with a standard Weibull model. Several model diagnostics methods are developed and model comparison is made using recently developed Bayesian model selection criteria. The above methodologies are applied to the McGilchrist and Aisbett (1991) kidney infection data and the analysis is performed using Markov Chain Monte Carlo methods. This revised version was published online in July 2006 with corrections to the Cover Date.