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Motivated by recent findings that within-subject (WS) visit-to-visitvariabilities of longitudinal biomarkers can be strong risk factors for healthoutcomes, this paper introduces and examines a new joint model of alongitudinal biomarker with heterogeneous WS variability and competing riskstime-to-event outcome. Specifically, our joint model consists of a linearmixed-effects multiple location-scale submodel for the individual meantrajectory and WS variability of the longitudinal biomarker and asemiparametric cause-specific Cox proportional hazards submodel for thecompeting risks survival outcome. The submodels are linked together via sharedrandom effects. We derive an expectation-maximization algorithm forsemiparametric maximum likelihood estimation and a profile-likelihood methodfor standard error estimation. We implement efficient computational algorithmsthat scales to biobank-scale data with tens of thousands of subjects. Oursimulation results demonstrate that, in the presence of heterogeneous WSvariability, the proposed method has superior performance for estimation,inference, and prediction, over the classical joint model with homogeneous WSvariability. An application of our method to a Multi-Ethnic Study ofAtherosclerosis (MESA) data reveals that there is substantial heterogeneity insystolic blood pressure (SBP) WS variability across MESA individuals and thatSBP 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, ourmethod leads to a more accurate dynamic prediction model for heart failure ordeath. A user-friendly R package \textbf{JMH} is developed and publiclyavailable at \url{https://github.com/shanpengli/JMH}.

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