Parzen Michael, Ghosh Souparno, Lipsitz Stuart, Sinha Debajyoti, Fitzmaurice Garrett M, Mallick Bani K, Ibrahim Joseph G
Goizueta Business School, Emory University.
Ann Appl Stat. 2011;5(1):449-467. doi: 10.1214/10-AOAS390.
Longitudinal studies of a binary outcome are common in the health, social, and behavioral sciences. In general, a feature of random effects logistic regression models for longitudinal binary data is that the marginal functional form, when integrated over the distribution of the random effects, is no longer of logistic form. Recently, Wang and Louis (2003) proposed a random intercept model in the clustered binary data setting where the marginal model has a logistic form. An acknowledged limitation of their model is that it allows only a single random effect that varies from cluster to cluster. In this paper, we propose a modification of their model to handle longitudinal data, allowing separate, but correlated, random intercepts at each measurement occasion. The proposed model allows for a flexible correlation structure among the random intercepts, where the correlations can be interpreted in terms of Kendall's τ. For example, the marginal correlations among the repeated binary outcomes can decline with increasing time separation, while the model retains the property of having matching conditional and marginal logit link functions. Finally, the proposed method is used to analyze data from a longitudinal study designed to monitor cardiac abnormalities in children born to HIV-infected women.
对二元结局的纵向研究在健康、社会和行为科学中很常见。一般来说，用于纵向二元数据的随机效应逻辑回归模型的一个特点是，当对随机效应的分布进行积分时，边际函数形式不再是逻辑形式。最近，Wang和Louis（2003年）在聚类二元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。他们模型的一个公认局限性是，它只允许一个从聚类到聚类变化的单一随机效应。在本文中，我们提出对他们的模型进行修改以处理纵向数据，允许在每个测量时刻有单独但相关的随机截距。所提出的模型允许随机截距之间有灵活的相关结构，其中相关性可以用肯德尔τ来解释。例如，重复二元结局之间的边际相关性可以随着时间间隔的增加而下降，而该模型保留了具有匹配的条件和边际对数似然链接函数的性质。最后，所提出的方法被用于分析一项纵向研究的数据，该研究旨在监测感染艾滋病毒妇女所生孩子的心脏异常情况。
