Xu Jian-Lun, Prorok Philip C
Biometry Research Group, National Cancer Institute, Executive Plaza North, Suite 3131, 6130 Executive Blvd, MSC 7354, Bethesda, MD 20892-7354, USA.
Stat Med. 2003 Aug 15;22(15):2401-16. doi: 10.1002/sim.1527.
Correlated binary data occur very frequently in cluster sample surveys, dependent repeated cancer screening, teratological experiments, ophthalmologic and otolaryngologic studies, and other clinical trials. The standard methods to analyse these data include the use of beta-binomial models and generalized estimating equations with third and fourth moments specified by 'working matrices'. However, in many applications it is reasonable to assume that the data from the same cluster are exchangeable. When all sampled clusters have equal sizes, Bowman and George introduced maximum likelihood estimates (MLEs) of the population parameters such as the marginal means, moments, and correlations of order two and higher. They also extended their approach to sampled clusters with unequal sizes. It seems that their extension has a gap. This paper points out the source of this gap and shows that estimates introduced by Bowman and George are not the MLEs of the parameters which are used to identify the joint distribution of correlated binary data. We show that the MLEs of the population parameters have no closed form in general and should be calculated by numerical methods. We apply our results and a generalized estimating equation procedure to a data set from a double-blind randomized clinical trial comparing two antibiotics, cefaclor and amoxicillin, used for the treatment of acute otitis media. To see the performance of the MLEs with small or moderate sample sizes, several simulation studies are also conducted.
相关二元数据在整群抽样调查、相关重复癌症筛查、致畸实验、眼科和耳鼻喉科研究以及其他临床试验中非常常见。分析这些数据的标准方法包括使用贝塔二项式模型和广义估计方程，其中三阶和四阶矩由“工作矩阵”指定。然而，在许多应用中，假设来自同一群的数据是可交换的是合理的。当所有抽样群的大小相等时，鲍曼和乔治引入了总体参数的最大似然估计（MLE），如边际均值、矩以及二阶及更高阶的相关性。他们还将其方法扩展到了大小不等的抽样群。他们的扩展似乎存在一个缺陷。本文指出了这个缺陷的来源，并表明鲍曼和乔治引入的估计不是用于识别相关二元数据联合分布的参数的MLE。我们表明，总体参数的MLE一般没有封闭形式，应该通过数值方法计算。我们将我们的结果和一个广义估计方程程序应用于一个双盲随机临床试验的数据集，该试验比较了用于治疗急性中耳炎的两种抗生素，头孢克洛和阿莫西林。为了观察小样本或中等样本量时MLE的性能，还进行了几项模拟研究。
