Longitudinal studies of a binary outcome are common in the health, social,and behavioral sciences. In general, a feature of random effects logisticregression models for longitudinal binary data is that the marginal functionalform, when integrated over the distribution of the random effects, is no longerof logistic form. Recently, Wang and Louis [Biometrika 90 (2003) 765--775]proposed a random intercept model in the clustered binary data setting wherethe marginal model has a logistic form. An acknowledged limitation of theirmodel is that it allows only a single random effect that varies from cluster tocluster. In this paper we propose a modification of their model to handlelongitudinal data, allowing separate, but correlated, random intercepts at eachmeasurement occasion. The proposed model allows for a flexible correlationstructure among the random intercepts, where the correlations can beinterpreted in terms of Kendall's $\tau$. For example, the marginalcorrelations among the repeated binary outcomes can decline with increasingtime separation, while the model retains the property of having matchingconditional and marginal logit link functions. Finally, the proposed method isused to analyze data from a longitudinal study designed to monitor cardiacabnormalities in children born to HIV-infected women.
展开▼
机译：在健康，社会和行为科学中，对二元结果进行纵向研究是很普遍的。通常，用于纵向二进制数据的随机效应逻辑回归模型的一个特征是，边际函数形式当在随机效应的分布上进行积分时，不再是逻辑形式。最近，Wang和Louis [Biometrika 90（2003）765--775]在聚类的二进制数据设置中提出了一种随机截距模型，其中边际模型具有逻辑形式。他们的模型公认的局限性在于，它仅允许一个随机效果，该效果随群集的不同而不同。在本文中，我们提出了对他们的模型的修改，以处理纵向数据，允许在每个测量时机使用独立但相关的随机截距。所提出的模型允许在随机截距之间具有灵活的相关性结构，其中相关性可以根据肯德尔的$ \ tau $来解释。例如，重复的二元结果之间的边际相关性会随着时间间隔的增加而下降，而模型保留了具有条件和边际对数链接函数匹配的属性。最后，该提议的方法用于分析一项纵向研究的数据，该研究旨在监测HIV感染妇女所生孩子的心脏异常。
展开▼
