MCMC Bayesian Estimation Of A Simple Progressive Multi-state Model

The data we obtained about the time to the event of interest during survival analysis has a common characteristic that the results of surveying are either censored or truncated, and especially call it interval-censored when we only know the event within a interval. Hitherto, the research of interval-censored data mainly focus on the estimation of survival function about this kind data, by contrast, there are less research on parametric estimation,therefore few methods on hand. Progression-related endpoints (such as time to progression or progression-free survival) and time to death are common endpoints in cancer clinical trials. It is of interest to study the link between progression-related endpoints and time to death (e.g. to evaluate the degree of surrogacy). There are various methods to estimate the parameters in the proposed joint model of progression and death through a frailty term. In this paper, we propose a conceptually simple and computationally feasible Bayesian MCMC estimation method to estimate the parameters. We also argue that interval-censoring needs to be taken into account to more closely match the latent disease evolution. We conduct simulation studies to confirm the theoretical results and provide a real data set to illustrate our proposed method.