Lin D Y
Department of Biostatistics, University of Washington, Seattle 98195.
Stat Med. 1994 Nov 15;13(21):2233-47. doi: 10.1002/sim.4780132105.
Multivariate failure time data are commonly encountered in scientific investigations because each study subject may experience multiple events or because there exists clustering of subjects such that failure times within the same cluster are correlated. In this paper, I present a general methodology for analysing such data, which is analogous to that of Liang and Zeger for longitudinal data analysis. This approach formulates the marginal distributions of multivariate failure times with the familiar Cox proportional hazards models while leaving the nature of dependence among related failure times completely unspecified. The baseline hazard functions for the marginal models may be identical or different. Simple estimating equations for the regression parameters are developed which yield consistent and asymptotically normal estimators, and robust variance-covariance estimators are constructed to account for the intra-class correlation. Simulation results demonstrate that the large-sample approximations are adequate for practical use and that ignoring the intra-class correlation could yield rather misleading variance estimators. The proposed methodology has been fully implemented in a simple computer program which also incorporates several alternative approaches. Detailed illustrations with data from four clinical or epidemiologic studies are provided.
在科学研究中，多变量失效时间数据很常见，这是因为每个研究对象可能经历多个事件，或者因为存在对象聚类，使得同一聚类内的失效时间具有相关性。在本文中，我提出了一种分析此类数据的通用方法，该方法类似于Liang和Zeger用于纵向数据分析的方法。这种方法用熟悉的Cox比例风险模型来制定多变量失效时间的边际分布，同时完全不明确相关失效时间之间的依赖性质。边际模型的基线风险函数可以相同也可以不同。开发了用于回归参数的简单估计方程，这些方程产生一致且渐近正态的估计量，并构建了稳健的方差 - 协方差估计量以考虑组内相关性。模拟结果表明，大样本近似在实际应用中是足够的，并且忽略组内相关性可能会产生相当误导性的方差估计量。所提出的方法已在一个简单的计算机程序中完全实现，该程序还包含几种替代方法。提供了来自四项临床或流行病学研究数据的详细示例。
