Pooling 2 Times 2 Tables: Asymptotic Moments of Estimators
研究了合并多个独立2×2列联表数据时，共同关联度量（如比值比）的合并估计量的渐近性质，发现比值比估计量有偏而比率和差值估计量无偏，并提出了同质性检验。
SUMMARY Consider J independent pairs of mutually independent binomial variates which can be considered as 72 times 2 tables. We assume a common measure of association, such as the odds ratio, between the tables. This paper studies the asymptotic moments of the ‘pooled' estimators, i.e. those constructed from the data summed over all the tables. For balanced designs, or proportional subclass numbers, it is shown that the pooled estimator of the common odds ratio is asymptotically biased towards 1, while those of the common ratio and difference are asymptotically unbiased. The asymptotic variances are also compared. A simple test for complete homogeneity is suggested. The various results are illustrated in numerical examples.