Joint Modeling of Longitudinal and Survival Outcomes

Abstract

Joint modeling of longitudinal and survival data is becoming increasingly essential in most cancer and AIDS clinical trials. We propose a likelihood approach to extend both longitudinal and survival components to be multidimensional. A multivariate mixed effects model is presented to explicitly capture two different sources of dependence among longitudinal measures over time as well as dependence between different variables. For the survival component of the joint model, we introduce a shared frailty, which is assumed to have a positive stable distribution, to induce correlation between failure times. Given the common frailty, all failure time random variables are assumed to be independent. The proposed marginal univariate survival model, which accommodates both zero and nonzero cure fractions for the time-to-event, is then applied to each marginal survival function. The proposed multivariate survival model has a proportional hazards structure for the population hazard, conditionally as well as marginally, when the baseline covariates are specified through a specific mechanism. In addition, the model is capable of dealing with survival functions with different cure rate structures. With the complexity of the joint likelihood, we adopt a Bayesian paradigm and develop an efficient Gibbs sampling scheme for the posterior distributions. Extensive simulations have been carried out to examine the property of the proposed multivariate survival model, and to investigate the performance of our joint model. The methodology is specifically applied to the International Breast Cancer Study Group (IBCSG) trial to investigate the relationship between quality of life, disease-free survival and overall survival.