Generalized linear mixed-effects joint model for longitudinal and bivariate survival data

Joint modeling of longitudinal and survival data (JMLS) has been widely utilized to investigate the relationship between longitudinal outcomes and two survival times in clinical trials. Existing methods for analyzing JMLS focus mainly on the assumptions that two time-to-event endpoints are uncorrelated and longitudinal outcomes are continuous. However, in many cancer clinical trials, bivariate survival times and discrete longitudinal outcomes are routinely encountered. To this end, this paper proposes a novel generalized linear mixed-effects JMLS by introducing a copula function to account for the correlation between two survival times and incorporating an exponential family distribution to accommodate for either continuous or discrete longitudinal outcomes. Further, the developed JMLS offers flexibility allowing covariates to be time-dependent and random-effects to be shared. A nonparametric maximum likelihood estimation procedure via the expectation-maximization (EM) algorithm is developed to estimate parameters and nonparametric functions in JMLS. Specifically, a two-stage procedure is designed to implement the M-step. Under some regularity conditions, the consistency and asymptotic normality of parameter and nonparametric function estimators are established. The proposed model and method are illustrated through simulation studies and a real example from the IBCSG clinical study. A R package, JM2survClayton, has been developed to implement the proposed method and is made publicly available to support reproducibility.