Bayesian Analysis of Survival Data with Semi-competing Risks and Treatment Switching

Abstract

Treatment switching is common in clinical trials due to ethical and practical reasons. When the outcome of interest is time to death and patients were switched at the time of intermediate nonterminal event, semi-competing risk issue intertwines with the challenge of treatment switching. In this chapter, we develop a Bayesian conditional model for survival data with semi-competing risks in the presence of partial treatment switching. Properties of the conditional model are examined and an efficient Gibbs sampling algorithm is developed to sample from the posterior distribution. A Bayesian procedure to estimate the marginal survival functions and to assess the treatment effect is also derived. The Deviance Information Criterion with an appropriate deviance function and Logarithm of the Pseudo-marginal Likelihood are constructed for model comparison. The proposed method is examined empirically through a simulation study and is further applied to analyze data from a colorectal cancer study.