Joint modeling is a useful approach to dynamic prediction of clinical outcomes using longitudinally measured predictors. When the outcomes are competing risk events, fitting the conventional shared random effects joint model often involves intensive computation, especially when multiple longitudinal biomarkers are be used as predictors, as is often desired in prediction problems. Motivated by a longitudinal cohort study of chronic kidney disease, this paper proposes a new joint model for the dynamic prediction of end-stage renal disease with the competing risk of death. The model factorizes the likelihood into the distribution of the competing risks data and the distribution of longitudinal data given the competing risks data. The estimation with the EM algorithm is efficient, stable and fast, with a one-dimensional integral in the E-step and convex optimization for most parameters in the M-step, regardless of the number of longitudinal predictors. The model also comes with a consistent albeit less efficient estimation method that can be quickly implemented with standard software, ideal for model building and diagnotics. This model enables the prediction of future longitudinal data trajectories conditional on being at risk at a future time, a practically significant problem that has not been studied in the statistical literature. We study the properties of the proposed method using simulations and a real dataset and compare its performance with the shared random effects joint model.

翻译：联合建模是利用纵向测量指标对临床结局进行动态预测的有效方法。当结局为竞争风险事件时，传统共享随机效应联合模型的拟合通常涉及密集计算，尤其在预测问题中常需使用多个纵向生物标志物作为预测因子时更为突出。受一项慢性肾脏病纵向队列研究的启发，本文提出一种新的联合模型，用于在死亡竞争风险存在的情况下动态预测终末期肾病。该模型将似然函数分解为竞争风险数据的分布以及给定竞争风险数据下纵向数据的分布。基于EM算法的估计过程高效、稳定且快速，其E步涉及一维积分，M步中大多数参数可通过凸优化求解，且与纵向预测因子数量无关。该模型还提供了一种虽效率稍低但具有一致性的估计方法，可通过标准软件快速实现，适用于模型构建与诊断。该模型能够实现条件于未来风险状态下的纵向数据轨迹预测——这一实践中的重要问题在统计文献中尚未被研究。我们通过模拟与真实数据集研究了所提方法的性质，并将其与共享随机效应联合模型的性能进行了比较。