Odds Ratio Inference With Dependent Data
当数据以一系列2×2表格呈现且二项分布假设不成立时，研究了共同优势比的推断问题，推导了Mantel-Haenszel估计量的一致性和渐近正态性，并提出了两个一致的检验统计量。
When data can be presented as a series of k 2×2 tables with cell counts (xi ,ni−xi, yi, mi−yi), it is often assumed that xi and yi are binomially distributed. This paper deals with inference for the common odds ratio Ψ when the binomial assumption is invalid. When k increases, the consistency and asymptotic normality of the Mantel & Haenszel (1959) estimator is derived. The conditional maximum likelihood estimator is shown to be inconsistent and the asymptotic bias is computed when either the first-order Markov chain or beta-binomial model is assumed. The Mantel-Haenszel test for testing iΨ = 1 is also shown to be inappropriate through some simulation studies. Two consistent test statistics are proposed and shown to be comparable to each other in terms of size and efficiency. Some possible further work is described.