Shen Weining, Liu Suyu, Chen Yong, Ning Jing
Department of Statistics, University of California, Irvine.
Department of Biostatistics, The University of Texas MD Anderson Cancer Center.
Scand Stat Theory Appl. 2019 Sep;46(3):831-847. doi: 10.1111/sjos.12373. Epub 2018 Dec 26.
We consider regression analysis of longitudinal data in the presence of outcome-dependent observation times and informative censoring. Existing approaches commonly require correct specification of the joint distribution of the longitudinal measurements, observation time process and informative censoring time under the joint modeling framework, and can be computationally cumbersome due to the complex form of the likelihood function. In view of these issues, we propose a semi-parametric joint regression model and construct a composite likelihood function based on a conditional order statistics argument. As a major feature of our proposed methods, the aforementioned joint distribution is not required to be specified and the random effect in the proposed joint model is treated as a nuisance parameter. Consequently, the derived composite likelihood bypasses the need to integrate over the random effect and offers the advantage of easy computation. We show that the resulting estimators are consistent and asymptotically normal. We use simulation studies to evaluate the finite-sample performance of the proposed method, and apply it to a study of weight loss data that motivated our investigation.
我们考虑在存在依赖于结果的观察时间和信息删失的情况下对纵向数据进行回归分析。现有的方法通常要求在联合建模框架下正确设定纵向测量、观察时间过程和信息删失时间的联合分布，并且由于似然函数的复杂形式，计算可能会很繁琐。鉴于这些问题，我们提出了一种半参数联合回归模型，并基于条件顺序统计量的论证构建了一个复合似然函数。作为我们提出的方法的一个主要特征，不需要指定上述联合分布，并且将所提出的联合模型中的随机效应视为一个干扰参数。因此，导出的复合似然绕过了对随机效应进行积分的需要，并具有计算简便的优点。我们证明了所得估计量是一致的且渐近正态。我们使用模拟研究来评估所提出方法的有限样本性能，并将其应用于一项激发我们研究的减肥数据研究。
