Liu Yanyan, Wu Yuanshan, Zhou Haibo
School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, P. R. China.
J Multivar Anal. 2010 Mar 1;101(3):679-691. doi: 10.1016/j.jmva.2009.09.008.
How to take advantage of the available auxiliary covariate information when the primary covariate of interest is not measured is a frequently encountered question in biomedical study. In this paper, we consider the multivariate failure times regression analysis in which the primary covariate is assessed only in a validation set but a continuous auxiliary covariate for it is available for all subjects in the study cohort. Under the frame of marginal hazard model, we propose to estimate the induced relative risk function in the nonvalidation set through kernel smoothing method and then obtain an estimated pseudo-partial likelihood function. The proposed estimated pseudo-partial likelihood estimator is shown to be consistent and asymptotically normal. We also give an estimator of the marginal cumulative baseline hazard function. Simulations are conducted to evaluate the finite sample performance of our proposed estimator. The proposed method is illustrated by analyzing a heart disease data from Studies of Left Ventricular Dysfunction (SOLVD).
当感兴趣的主要协变量未被测量时，如何利用可用的辅助协变量信息是生物医学研究中经常遇到的问题。在本文中，我们考虑多变量失效时间回归分析，其中主要协变量仅在验证集中进行评估，但针对该协变量的连续辅助协变量可用于研究队列中的所有受试者。在边际风险模型的框架下，我们建议通过核平滑方法估计非验证集中的诱导相对风险函数，然后获得估计的伪偏似然函数。所提出的估计伪偏似然估计量被证明是一致的且渐近正态的。我们还给出了边际累积基线风险函数的估计量。进行了模拟以评估我们提出的估计量的有限样本性能。通过分析来自左心室功能障碍研究（SOLVD）的心脏病数据来说明所提出的方法。
