A generalized linear mixed model for longitudinal binary data with a marginal logit link function.
A generalized linear mixed model for longitudinal binary data with a marginal logit link function.
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DOI：
10.1214/10-aoas390
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Ibrahim JG
中科院分区：
文献类型：
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作者：
Parzen M;Ghosh S;Lipsitz S;Sinha D;Fitzmaurice GM;Mallick BK;Ibrahim JG
对二元结果的纵向研究在健康、社会和行为科学中很常见。一般来说，纵向二元数据的随机效应逻辑回归模型的一个特征是，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，在聚类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。他们的模型的一个公认的局限性是它只允许单个随机效应因簇而异。在本文中，我们提出对其模型进行修改以处理纵向数据，允许在每个测量场合进行单独但相关的随机截距。所提出的模型允许随机截距之间的灵活相关结构，其中相关性可以用 Kendall τ 来解释。例如，重复的二元结果之间的边际相关性可能会随着时间间隔的增加而下降，而模型保留了具有匹配条件和边际 Logit 链接函数的属性。最后，所提出的方法用于分析一项纵向研究的数据，该研究旨在监测艾滋病毒感染妇女所生儿童的心脏异常。
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, 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.