Liu Yanyan, Yuan Zhongshang, Cai Jianwen, Zhou Haibo
School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China.
Lifetime Data Anal. 2012 Jan;18(1):116-38. doi: 10.1007/s10985-011-9209-x. Epub 2011 Nov 18.
In many biomedical studies, it is common that due to budget constraints, the primary covariate is only collected in a randomly selected subset from the full study cohort. Often, there is an inexpensive auxiliary covariate for the primary exposure variable that is readily available for all the cohort subjects. Valid statistical methods that make use of the auxiliary information to improve study efficiency need to be developed. To this end, we develop an estimated partial likelihood approach for correlated failure time data with auxiliary information. We assume a marginal hazard model with common baseline hazard function. The asymptotic properties for the proposed estimators are developed. The proof of the asymptotic results for the proposed estimators is nontrivial since the moments used in estimating equation are not martingale-based and the classical martingale theory is not sufficient. Instead, our proofs rely on modern empirical process theory. The proposed estimator is evaluated through simulation studies and is shown to have increased efficiency compared to existing methods. The proposed method is illustrated with a data set from the Framingham study.
在许多生物医学研究中，由于预算限制，主要协变量通常仅在从完整研究队列中随机选择的子集中收集，这是很常见的。通常，对于主要暴露变量存在一种廉价的辅助协变量，所有队列受试者都可轻易获取。需要开发利用辅助信息来提高研究效率的有效统计方法。为此，我们针对具有辅助信息的相关失效时间数据开发了一种估计部分似然方法。我们假设具有共同基线风险函数的边际风险模型。推导了所提出估计量的渐近性质。由于估计方程中使用的矩不是基于鞅的，且经典鞅理论并不充分，因此所提出估计量的渐近结果的证明并不简单。相反，我们的证明依赖于现代经验过程理论。通过模拟研究对所提出的估计量进行了评估，结果表明与现有方法相比，其效率有所提高。用弗明汉姆研究的一个数据集对所提出的方法进行了说明。
