Marginal Regression Models for Multivariate Failure Time Data
提出一种Cox型回归模型处理多元失效时间数据，允许不同失效类型有不同基准风险函数，并给出参数估计的渐近性质及推断方法，适用于医学等领域的生存数据分析。
Abstract In this article we propose a general Cox-type regression model to formulate the marginal distributions of multivariate failure time data. This model has a nested structure in that it allows different baseline hazard functions among distinct failure types and imposes a common baseline hazard function on the failure times of the same type. We prove that the maximum “quasi-partial-likelihood” estimator for the vector of regression parameters under the independence working assumption is consistent and asymptotically normal with a covariance matrix for which a consistent estimator is provided. Furthermore, we establish the uniform consistency and joint weak convergence of the Aalen-Breslow type estimators for the cumulative baseline hazard functions, and develop a resampling technique to approximate the joint distribution of these processes, which enables one to make simultaneous inference about the survival functions over the time axis and across failure types. Finally, we assess the small-sample properties of the proposed methods through Monte Carlo simulation, and present an application to a real dental study.