Markov processes in survival analysis

Abstract

This chapter presents some discrete and continuous Markov processes that have shown to be useful in survival analysis and other biostatistics applications. Both discrete and continuous time processes are used to define Bayesian nonparametric prior distributions. The discrete time processes are constructed via latent variables in a hierarchical fashion, whereas the continuous time processes are based on Léevy increasing additive processes. To avoid discreteness of the implied random distributions, these latter processes are further used as mixing measures of the parameters in a particular kernel, which lead to the so-called Léevy-driven processes. We present the use of these models in the context of survival analysis. We include univariate and multivariate settings, regression models and cure rate models.