Joint Analysis of Longitudinal Data and Zero-Inflated Recurrent Events

Longitudinal data together with recurrent events are commonly encountered in clinical trials. In many applications, these two processes are highly correlated. When there exist a large portion of subjects not experiencing recurrent events of interest, it is possible that some of these subjects are unsusceptible to the events. Therefore, we assume the underlying population is composed of two subpopulations: one subpopulation susceptible to the recurrent events, and the other unsusceptible. In this article, we propose a joint model of longitudinal outcomes and zero-inflated recurrent event data. Our model consists of three submodels: (1) a generalized linear mixed model for the longitudinal process; (2) a proportional intensities model for the recurrent event process in the susceptible subpopulation; and (3) a logistic regression model for the probability such that a subject belongs to the unsusceptible subpopulation. We consider associations (1) between longitudinal outcomes and the zero-inflation rate; and (2) between longitudinal outcomes and the intensity rate of recurrent events in the susceptible subpopulation. Estimation is carried out by maximizing the log-likelihood function using Gaussian quadrature techniques, which can be conveniently implemented in SAS Proc NLMIXED. Simulation studies demonstrate that the proposed method performs well. We apply the method to a clinical trial.

纵向数据与复发事件在临床试验中颇为常见。在多数实际应用场景中，这两类数据生成过程存在较强相关性。当大量受试者未出现所关注的复发事件时，其中部分受试者可能对该事件不存在易感性。据此，我们假定目标总体由两个亚人群组成：一类为对复发事件具有易感性的亚群，另一类为不易感亚群。本文针对纵向结局与零膨胀（zero-inflated）复发事件数据，提出一种联合模型。该模型包含三个子模型：(1) 用于刻画纵向数据生成过程的广义线性混合模型（generalized linear mixed model）；(2) 用于易感性亚群内复发事件过程的比例强度模型（proportional intensities model）；(3) 用于预测受试者归属不易感亚群概率的logistic回归模型（logistic regression model）。本模型考量两类关联关系：(1) 纵向结局与零膨胀率之间的关联；(2) 纵向结局与易感性亚群内复发事件强度率之间的关联。模型参数估计通过最大化对数似然函数完成，采用高斯求积（Gaussian quadrature）技术，该方法可便捷地通过SAS Proc NLMIXED实现。仿真研究结果表明，所提方法性能优异。最后，我们将该方法应用于一项临床试验。