Bayesian Joint Models for Longitudinal and Multi-state Survival Data

Abstract

Joint models for longitudinal and time to event data are frequently used in many observational studies such as clinical trials with the aim of investigating how biomarkers which are recorded repeatedly in time are associated with time to an event of interest. In most cases, these joint models only consider a univariate time to event process. However, many clinical trials of patients with cancer, involve multiple recurrences of a single event together with a single terminal event experienced by patients over time. Therefore, this article proposes joint modelling approachs for longitudinal and multi-state data. The approach considers two sub-models that are linked by a common latent random variable. The first sub-model is linear mixed effect model that defines the longitudinal process and the second sub-model is a proportional intensity function for the multi-state process. Furthermore, on the proportional intensity model, two different formulations are used to define dependence structure between longitudinal and multi-state processes. In this article, a semi-Markov process that consider the time spent in the current state is defined for the transitions between states. Moreover, the time spent in each transient state is assumed to have Gompertz distribution. A Bayesian method using Markov Chain Monte Carlo (MCMC) is developed for parameter estimation and inferences. The deviance information criterion (DIC) is also derived for Bayesian model selection and comparison. Finally, our proposed joint modeling approach is evaluated through a simulation study and is applied to real datasets (colorectal and colorectal.Longi) which present a random selection of 150 patients from a multi-center randomized phase III clinical trial FFCD 2000-05 of patients diagnosed with metastatic colorectal cancer.