Evaluating Association Between Two Event Times with Observations Subject to Informative Censoring

This article is concerned with evaluating the association between two event times without specifying the joint distribution parametrically. This is particularly challenging when the observations on the event times are subject to informative censoring due to a terminating event such as death. There are few methods suitable for assessing covariate effects on association in this context. We link the joint distribution of the two event times and the informative censoring time using a nested copula function. We use flexible functional forms to specify the covariate effects on both the marginal and joint distributions. In a semiparametric model for the bivariate event time, we estimate simultaneously the association parameters, the marginal survival functions, and the covariate effects. A byproduct of the approach is a consistent estimator for the induced marginal survival function of each event time conditional on the covariates. We develop an easy-to-implement pseudolikelihood-based inference procedure, derive the asymptotic properties of the estimators, and conduct simulation studies to examine the finite-sample performance of the proposed approach. For illustration, we apply our method to analyze data from the breast cancer survivorship study that motivated this research. Supplementary materials for this article are available online.

本文旨在无需参数化指定联合分布的前提下，评估两类事件时间之间的关联关系。当事件时间的观测值因死亡这类终止事件而受到信息删失（informative censoring）时，此类任务尤具挑战性。现有针对该场景下关联关系的协变量效应评估方法较为匮乏。我们采用嵌套Copula（copula function）函数，将两类事件时间的联合分布与信息删失时间相联结。我们使用灵活的函数形式，对边缘分布与联合分布上的协变量效应进行设定。在双变量事件时间的半参数模型中，我们同时估计关联参数、边缘生存函数以及协变量效应。该方法的一项附带成果是，可得到给定协变量条件下各事件时间的诱导边缘生存函数的一致估计量。我们开发了一种易于实现的基于伪似然（pseudolikelihood）的推断流程，推导了估计量的渐近性质，并开展仿真研究以检验所提方法的有限样本表现。为便于说明，我们将所提方法应用于一项启发本研究的乳腺癌生存研究的数据分析中。本文的补充材料可在线获取。