Multiplicative Survival Models based on Counting Processes

Modern survival analysis may be effectively handled within the mathematical framework of counting processes. This theory introduced by Aalen (1972) has been the subject of intense research ever since. In this setting, emphasis is given to construction of the likelihood function due to its importance for both frequentist and Bayesian analysis. Some multiplicative survival models are here presented from a Bayesian perspective, especially frailty models for univariate survival data. A gamma process with independent increments in disjoint intervals is used to model the prior process of the baseline hazard function, and the frailty distribution is assumed to be a gamma distribution. Markov Chain Monte Carlo methods are used to find estimates of several quantities of interest. At last, this approach is illustrated with one example.