School of Medicine, Health Policy and Practice, University of East Anglia, U.K.
Stat Med. 2010 Jan 30;29(2):199-209. doi: 10.1002/sim.3747.
Bayesian approaches to inference in cluster randomized trials have been investigated for normally distributed and binary outcome measures. However, relatively little attention has been paid to outcome measures which are counts of events. We discuss an extension of previously published Bayesian hierarchical models to count data, which usually can be assumed to be distributed according to a Poisson distribution. We develop two models, one based on the traditional rate ratio, and one based on the rate difference which may often be more intuitively interpreted for clinical trials, and is needed for economic evaluation of interventions. We examine the relationship between the intracluster correlation coefficient (ICC) and the between-cluster variance for each of these two models. In practice, this allows one to use the previously published evidence on ICCs to derive an informative prior distribution which can then be used to increase the precision of the posterior distribution of the ICC. We demonstrate our models using a previously published trial assessing the effectiveness of an educational intervention and a prior distribution previously derived. We assess the robustness of the posterior distribution for effectiveness to departures from a normal distribution of the random effects.
贝叶斯方法已被用于研究群组随机试验中正态分布和二分类结局指标的推断。然而，对于计数资料这种结局指标，关注相对较少。我们讨论了先前发表的贝叶斯层次模型在计数资料中的扩展，计数资料通常假定服从泊松分布。我们建立了两种模型，一种基于传统的率比，另一种基于率差，对于临床试验，后者可能更直观，对于干预措施的经济评价是必需的。我们研究了这两种模型中每个模型的组内相关系数（ICC）和组间方差之间的关系。在实践中，这允许使用先前发表的关于 ICC 的证据来推导出一个信息丰富的先验分布，然后可以使用该分布来提高 ICC 的后验分布的精度。我们使用先前发表的评估教育干预措施效果的试验和先前推导的先验分布来演示我们的模型。我们评估了后验分布的稳健性，以检验随机效应正态分布的偏离情况。
