Bayesian Copula-Based Analysis of Multiple Longitudinal Measures and Multiple Recurrent Events

Abstract

Estimating parameters of a joint model for longitudinal measurement and recurrent event data have been developed and further research is still ongoing. In some longitudinal studies we observe multiple repeated measures processes and multiple recurrent events that maybe correlated within a subject. For example, lower CD4 cell counts and higher viral loads are associated with higher risk of recurrent antiretroviral (ARV) regimen changes and opportunistic disease infections. A simple statistical procedure jointly models a single longitudinal measurement and recurrent event data, both of which are modified to include a random effect term which captures the dependence of the data within a subject. A more realistic technique needs to jointly model all the correlated processes, which may be achieved by using shared-random effects components for all the processes and process-specific random components. We show how the outcome-specific covariate effects and the correlation structure can be estimated by Bayesian estimation using copulas. The estimation method is applied to the ARV Pharmacovigilance Study data set from South Africa. Results are compared to those obtained using Gaussian quadrature based maximum-likelihood techniques.