Chan Kwun Chuen Gary, Wang Mei-Cheng
Department of Biostatistics and Department of Health Services, University of Washington, Seattle, Washington 98105, U.S.A.
Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland 21205, U.S.A.
J Am Stat Assoc. 2017;112(517):351-362. doi: 10.1080/01621459.2016.1140051. Epub 2017 May 3.
Recurrent event processes with marker measurements are mostly and largely studied with forward time models starting from an initial event. Interestingly, the processes could exhibit important terminal behavior during a time period before occurrence of the failure event. A natural and direct way to study recurrent events prior to a failure event is to align the processes using the failure event as the time origin and to examine the terminal behavior by a backward time model. This paper studies regression models for backward recurrent marker processes by counting time backward from the failure event. A three-level semiparametric regression model is proposed for jointly modeling the time to a failure event, the backward recurrent event process, and the marker observed at the time of each backward recurrent event. The first level is a proportional hazards model for the failure time, the second level is a proportional rate model for the recurrent events occurring before the failure event, and the third level is a proportional mean model for the marker given the occurrence of a recurrent event backward in time. By jointly modeling the three components, estimating equations can be constructed for marked counting processes to estimate the target parameters in the three-level regression models. Large sample properties of the proposed estimators are studied and established. The proposed models and methods are illustrated by a community-based AIDS clinical trial to examine the terminal behavior of frequencies and severities of opportunistic infections among HIV infected individuals in the last six months of life.
带有标记测量的复发事件过程大多是从初始事件开始，主要通过向前时间模型进行研究。有趣的是，这些过程在失效事件发生前的一段时间内可能会表现出重要的终末行为。在失效事件之前研究复发事件的一种自然且直接的方法是，以失效事件为时间原点来对齐这些过程，并通过向后时间模型来检查终末行为。本文通过从失效事件开始倒推时间来研究向后复发标记过程的回归模型。提出了一个三级半参数回归模型，用于联合建模失效事件的时间、向后复发事件过程以及在每次向后复发事件发生时观察到的标记。第一级是失效时间的比例风险模型，第二级是失效事件之前发生的复发事件的比例率模型，第三级是给定向后时间复发事件发生时标记的比例均值模型。通过联合对这三个部分进行建模，可以为标记计数过程构建估计方程，以估计三级回归模型中的目标参数。研究并建立了所提出估计量的大样本性质。通过一项基于社区的艾滋病临床试验来说明所提出的模型和方法，以研究艾滋病毒感染者在生命最后六个月中机会性感染的频率和严重程度的终末行为。
