Salway Ruth, Wakefield Jon
Department of Mathematical Sciences, University of Bath, Bath, UK.
Biostatistics. 2008 Jan;9(1):1-17. doi: 10.1093/biostatistics/kxm022. Epub 2007 Jun 16.
A major drawback of epidemiological ecological studies, in which the association between area-level summaries of risk and exposure is used to make inference about individual risk, is the difficulty in characterizing within-area variability in exposure and confounder variables. To avoid ecological bias, samples of individual exposure/confounder data within each area are required. Unfortunately, these may be difficult or expensive to obtain, particularly if large samples are required. In this paper, we propose a new approach suitable for use with small samples. We combine a Bayesian nonparametric Dirichlet process prior with an estimating functions' approach and show that this model gives a compromise between 2 previously described methods. The method is investigated using simulated data, and a practical illustration is provided through an analysis of lung cancer mortality and residential radon exposure in counties of Minnesota. We conclude that we require good quality prior information about the exposure/confounder distributions and a large between- to within-area variability ratio for an ecological study to be feasible using only small samples of individual data.
流行病学生态研究的一个主要缺点是，利用风险和暴露的区域层面汇总数据之间的关联来推断个体风险时，难以描述区域内暴露和混杂变量的变异性。为避免生态偏倚，需要每个区域内个体暴露/混杂数据的样本。不幸的是，获取这些样本可能困难或昂贵，尤其是在需要大样本的情况下。在本文中，我们提出一种适用于小样本的新方法。我们将贝叶斯非参数狄利克雷过程先验与估计函数方法相结合，表明该模型在之前描述的两种方法之间取得了折衷。使用模拟数据对该方法进行了研究，并通过分析明尼苏达州各县的肺癌死亡率和住宅氡暴露提供了一个实际例证。我们得出结论，对于仅使用个体数据小样本的生态研究而言，要可行的话，我们需要关于暴露/混杂分布的高质量先验信息以及较大的区域间与区域内变异性比率。
