Regression Analysis of Multivariate Incomplete Failure Time Data by Modeling Marginal Distributions
本文提出一种对多元失效时间数据进行回归分析的方法，每个失效时间的边际分布用Cox模型建模，不假设失效间的依赖结构，通过最大化部分似然估计参数，并允许时变协变量和缺失数据。
Abstract Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time observations. Each marginal distribution of the failure times is formulated by a Cox proportional hazards model. No specific structure of dependence among the distinct failure times on each subject is imposed. The regression parameters in the Cox models are estimated by maximizing the failure-specific partial likelihoods. The resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated. Simultaneous inferential procedures are then proposed. Extensive Monte Carlo studies indicate that the normal approximation is adequate for practical use. The new methods allow time-dependent covariates, missing observations, and arbitrary patterns of censorship. They are illustrated with two real-life examples. For recurrent failure time data, various regression methods have been proposed in the literature. These methods, however, generally assume stringent structures of dependence among the recurrences of each subject. Moreover, as shown in the present article, they are rather sensitive to model misspecification.