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

from arxiv, This manuscript needs to be withdrawn. The conclusions we've made in Section 4 (read data application) has outstanding errors as the statistical methods and conclusions are not scientifically reasonable, and thus need to be reconsidered

Motivated by recent findings that within-subject (WS) variability of longitudinal biomarkers is a risk factor for many health outcomes, this paper introduces and studies 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 (EM) algorithm for semiparametric maximum likelihood estimation and a profile-likelihood method for standard error estimation. We implement scalable computational algorithms that can scale to biobank-scale data with tens of thousands of subjects. Our simulation results demonstrate that the proposed method has superior performance and that classical joint models with homogeneous WS variability can suffer from estimation bias, invalid inference, and poor prediction accuracy in the presence of heterogeneous WS variability. An application of the developed method to the large Multi-Ethnic Study of Atherosclerosis (MESA) data not only revealed that subject-specific WS variability in systolic blood pressure (SBP) is highly predictive of heart failure and death, but also yielded more accurate dynamic prediction of heart failure or death by accounting for both the mean trajectory and WS variability of SBP. Our user-friendly R package \textbf{JMH} is publicly available at \url{https://github.com/shanpengli/JMH}.

翻译：受近期发现纵向生物标志物的个体内变异性是多种健康结局危险因素的启发，本文提出并研究了一种新的联合模型，该模型整合了具有异质性个体内变异性的纵向生物标志物与竞争风险生存结局。具体而言，我们的联合模型包含两个子模型：一是针对纵向生物标志物的个体均值轨迹和个体内变异性的线性混合效应多重位置-尺度子模型，二是针对竞争风险生存结局的半参数因果特定Cox比例风险子模型。子模型之间通过共享随机效应相联结。我们推导了用于半参数最大似然估计的期望最大化算法，并采用轮廓似然法进行标准误估计。我们实现了可扩展的计算算法，能处理数万样本规模的生物银行级数据。模拟结果表明，所提方法具有优越性能，而传统假设同质性个体内变异性的联合模型在存在异质性个体内变异性时，会出现估计偏差、推断无效及预测精度下降问题。将该方法应用于大型多种族动脉粥样硬化研究数据，不仅揭示了收缩压个体特异性个体内变异性对心力衰竭和死亡具有高度预测性，还通过同时考虑收缩压的均值轨迹和个体内变异性，获得了更准确的心力衰竭或死亡动态预测。我们开发的易用R软件包JMH已公开于https://github.com/shanpengli/JMH。