A joint model of the individual mean and within-subject variability of a longitudinal outcome with a competing risks time-to-event outcome

Motivated by recent findings that within-subject (WS) visit-to-visit variabilities of longitudinal biomarkers can be strong risk factors for health outcomes, this paper introduces and examines a new joint model of a longitudinal biomarker with heterogeneous WS variability and competing risks time-to-event outcome. Specifically, our joint model consists of a linear mixed-effects multiple location-scale submodel for the individual mean trajectory and WS variability of the longitudinal biomarker and a semiparametric cause-specific Cox proportional hazards submodel for the competing risks survival outcome. The submodels are linked together via shared random effects. We derive an expectation-maximization algorithm for semiparametric maximum likelihood estimation and a profile-likelihood method for standard error estimation. We implement efficient computational algorithms that scales to biobank-scale data with tens of thousands of subjects. Our simulation results demonstrate that, in the presence of heterogeneous WS variability, the proposed method has superior performance for estimation, inference, and prediction, over the classical joint model with homogeneous WS variability. An application of our method to a Multi-Ethnic Study of Atherosclerosis (MESA) data reveals that there is substantial heterogeneity in systolic blood pressure (SBP) WS variability across MESA individuals and that SBP WS variability is an important predictor for heart failure and death, (independent of, or in addition to) the individual SBP mean level. Furthermore, by accounting for both the mean trajectory and WS variability of SBP, our method leads to a more accurate dynamic prediction model for heart failure or death. A user-friendly R package \textbf{JMH} is developed and publicly available at \url{https://github.com/shanpengli/JMH}.