A Simulation Study of the Analysis of Sets of 2 × 2 Contingency Tables under Cluster Sampling: Estimation of a Common Odds Ratio
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聚类抽样下多组二乘二列联表共同优势比估计的模拟研究
- 研究问题
- 多个二乘二列联表存在簇内相关时，共同优势比及簇内相关系数的估计偏差、方差和方差调整效果如何变化？
- 方法与思路
- 作者用 beta-binomial 分布描述簇内相关，模拟比较两种最大似然估计与 Mantel–Haenszel 估计，并评估相关系数估计及调整。
- 材料陈述的贡献
- 摘要称相关增强通常增大优势比估计的方差和正偏差；簇膨胀调整常高估 Mantel–Haenszel 方差，未调整公式在多数模拟情形较保守。
- 阅读关注点
- 应核对共同优势比假设、簇大小与成功概率设置，以及方差调整失效和不同估计量排序发生变化的具体参数范围。
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原文摘要
This article presents the results of a simulation study of the estimation of a common odds ratio in multiple-contingency tables when the data are correlated within clusters. The correlation is modeled by the beta-binomial distribution. The three objectives of the study were to determine (a) the variances, biases, and relative efficiencies of the beta-binomial maximum likelihood estimator (MLE), the binomial MLE, and the Mantel-Haenszel estimator of the common odds ratio; (b) the variances and biases of two estimators of the intracluster correlation coefficient, ρ; and (c) the effectiveness of adjusting variance estimates of the binomial and Mantel-Haenszel estimators using the two estimators of ρ. The simulation shows that increasing the size of the intracluster correlation coefficient increases the variance and the positive bias of all three estimators of the odds ratio. The Mantel-Haenszel estimator displays less variance and bias than the MLE except for large values of Ψ and ρ. An unexpected but important observation, however, is that applying a cluster-inflation factor to the formula for the large-sample variance of the Mantel-Haenszel estimator often results in an overestimate of the variance. The only circumstances in which the unadjusted variance is an underestimate of the observed variance occur when the clustering is high and the odds ratio is unity or when the contingency tables represent a wide band of success probabilities. This observation, coupled with the fact that the Mantel-Haenszel estimator is expressed as a closed formula, leads to the recommendation of the large-sample variance formula as a conservative estimator in most cases. A comparison of the moment and analysis of variance (ANOVA) estimators of intracluster correlation coefficient ρ shows that the ANOVA estimator is consistently positively biased, but that both its bias and variance are less than those of the moment estimator, especially when ρ is small. The moment estimator is extremely positively biased when the correlation is low, and negatively biased when it is high.