Su Li, Hogan Joseph W
Medical Research Council, Biostatistics Unit, Robinson Way, Cambridge CB2 0SR, UK.
Stat Med. 2008 Jul 30;27(17):3247-68. doi: 10.1002/sim.3265.
Longitudinal studies with binary repeated measures are widespread in biomedical research. Marginal regression approaches for balanced binary data are well developed, whereas for binary process data, where measurement times are irregular and may differ by individuals, likelihood-based methods for marginal regression analysis are less well developed. In this article, we develop a Bayesian regression model for analyzing longitudinal binary process data, with emphasis on dealing with missingness. We focus on the settings where data are missing at random (MAR), which require a correctly specified joint distribution for the repeated measures in order to draw valid likelihood-based inference about the marginal mean. To provide maximum flexibility, the proposed model specifies both the marginal mean and serial dependence structures using nonparametric smooth functions. Serial dependence is allowed to depend on the time lag between adjacent outcomes as well as other relevant covariates. Inference is fully Bayesian. Using simulations, we show that adequate modeling of the serial dependence structure is necessary for valid inference of the marginal mean when the binary process data are MAR. Longitudinal viral load data from the HIV Epidemiology Research Study are analyzed for illustration.
具有二元重复测量的纵向研究在生物医学研究中广泛存在。针对平衡二元数据的边际回归方法已经得到了很好的发展，而对于二元过程数据，其中测量时间不规则且个体之间可能不同，基于似然的边际回归分析方法则发展得不太完善。在本文中，我们开发了一种贝叶斯回归模型来分析纵向二元过程数据，重点是处理缺失值。我们关注数据随机缺失（MAR）的情况，这需要为重复测量正确指定联合分布，以便对边际均值进行有效的基于似然的推断。为了提供最大的灵活性，所提出的模型使用非参数平滑函数指定边际均值和序列依赖性结构。允许序列依赖性取决于相邻结果之间的时间滞后以及其他相关协变量。推断是完全贝叶斯的。通过模拟，我们表明当二元过程数据为MAR时，对序列依赖性结构进行充分建模对于边际均值的有效推断是必要的。为了说明，我们分析了来自HIV流行病学研究的纵向病毒载量数据。
