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}.

翻译：受近期关于纵向生物标志物的受试者内（WS）访视间变异性可成为健康结局强风险因素的研究发现启发，本文提出并探讨了一种新的联合模型，该模型整合了存在异质性WS变异性的纵向生物标志物与竞争风险时间至事件结局。具体而言，该联合模型包含两部分：一部分是用于纵向生物标志物个体均值轨迹及WS变异性的线性混合效应多重位置-尺度子模型，另一部分是用于竞争风险生存结局的半参数原因特异性Cox比例风险子模型。这两个子模型通过共享随机效应相互关联。我们推导了用于半参数极大似然估计的期望最大化算法，以及用于标准误估计的轮廓似然方法。我们实现了高效的计算算法，可扩展至包含数万名受试者的生物库规模数据。模拟结果表明，在存在异质性WS变异性的情况下，相较于采用同质性WS变异性的经典联合模型，所提方法在估计、推断和预测方面均表现出更优性能。将该方法应用于动脉粥样硬化多种族研究（MESA）数据后发现，MESA个体间收缩压（SBP）WS变异性存在显著异质性，且SBP WS变异性是心力衰竭和死亡的重要预测因子（独立于或附加于个体SBP均值水平）。此外，通过联合考虑SBP的均值轨迹与WS变异性，该方法构建了更精确的心力衰竭或死亡动态预测模型。我们开发了用户友好的R语言软件包\textbf{JMH}，并公开于网址\url{https://github.com/shanpengli/JMH}。