A Bayesian inference for the penalized spline joint models of longitudinal and time-to-event data: A prior sensitivity analysis

Abstract

Bayesian approaches have been used in the literature to estimate the parameters for joint models of longitudinal and time-to-event data. The main aim of this paper is to analyze the impact of prior distributions on estimating parameters in a proposed fully Bayesian analysis setting for the penalized spline joint models. To achieve this aim, the joint posterior distribution of parameters in survival and longitudinal submodels is presented. The Markov chain Monte Carlo (MCMC) algorithm is then proposed, which consists of the Gibbs sampler (GS) and Metropolis Hastings (MH) algorithms to sample for the target conditional posterior distributions. The prior sensitivity analysis for the baseline hazard rate and association parameters is performed through simulation studies and a case study.