The separation of timescales in Bayesian survival modeling of the time-varying effect of a time-dependent exposure

In this paper, we apply flexible Bayesian survival analysis methods to investigate the risk of lymphoma associated with kidney transplantation among patients with end-stage renal disease.Of key interest is the potentially time-varying effect of a time-dependent exposure: transplant status.Bayesian modeling of the baseline hazard and the effect of transplant requires consideration of 2 timescales: time since study start and time since transplantation, respectively.Previous related work has not dealt with the separation of multiple timescales.Using a hierarchical model for the hazard function, both timescales are incorporated via conditionally independent stochastic processes; smoothing of each process is specified via intrinsic conditional Gaussian autoregressions.Features of the corresponding posterior distribution are evaluated from draws obtained via a Metropolis.Hastings.Green algorithm.