A Two-Stage Approach for Bayesian Parametric Joint Modelling of Longitudinal and Weibull Accelerated Failure Time Data

Abstract

Since longitudinal and survival data are often obtained together in applications, studies on joint modeling that reveal the relationship between these two data have increased considerably in recent years. These models are generally defined by a linear mixed-effects model for longitudinal data and  Cox regression model for survival data, which are connected by a shared random effect. However, in order to use the Cox regression model in the analysis of survival data, the proportional hazards assumption must be satisfied. In cases where the proportional hazards assumption is not satisfied and survival data have a certain distribution, parametric joint models should be used to obtain more unbiased parameter estimates in the analysis of the relationship between two data. In this paper, we propose a two-stage approach in a Bayesian framework to obtain parameter estimates in parametric joint modeling. To examine the performance of the proposed method, we perform a simulation study in scenarios with different censoring and sample sizes and compare the method with classical approaches. In addition, to demonstrate the applicability of the proposed method, we perform an application on the aortic valve replacement surgery data, which is frequently used in the literature, and test the methods on real data. Simulation studies from different scenarios show that in all cases our approach in the joint modeling which consists of a binary longitudinal measurement and of survival data that does not provide the assumption of proportional hazards, gives more unbiased estimates compared to the other two classical approaches. To demonstrate the applicability of the simulation findings, we performed an application on the real data set and obtained results consistent with the simulation results.