Liu I M, Agresti A
Department of Statistics, National Chung Hsing University, Taipei, Taiwan, R.O.C.
Biometrics. 1996 Dec;52(4):1223-34.
This article proposes a Mantel-Haenszel-type estimator of an assumed common cumulative odds ratio in a proportional odds model for an ordinal response with several 2 x c contingency tables. It is useful, for instance, for comparing two treatments on an ordinal response for data from several centers when the data are highly sparse. The estimator has behavior similar to the Mantel-Haenszel estimator of a common odds ratio for several 2 x 2 tables. It is consistent under the ordinary asymptotic framework in which the number of tables is fixed and, unlike the maximum likelihood (ML) estimator, also under sparse asymptotics in which the number of tables grows with the sample size. Simulations reveal a considerable difference between it and the ML estimator when each table has few observations. Efficiency comparisons suggest that little efficiency loss occurs compared to the ML estimator when the data are not sparse. Tests and estimators are presented for detecting and handling heterogeneity in the odds ratios, and generalizations are available for stratified r x c contingency tables.
本文针对具有多个2×c列联表的有序响应比例优势模型，提出了一种假定的共同累积优势比的Mantel-Haenszel型估计量。例如，当数据非常稀疏时，它对于比较来自多个中心的数据的有序响应上的两种治疗方法很有用。该估计量的行为类似于多个2×2表的共同优势比的Mantel-Haenszel估计量。在表的数量固定的普通渐近框架下它是一致的，并且与最大似然（ML）估计量不同，在表的数量随样本量增长的稀疏渐近情况下它也是一致的。模拟显示，当每个表的观测值很少时，它与ML估计量之间存在相当大的差异。效率比较表明，当数据不稀疏时，与ML估计量相比，效率损失很小。还给出了用于检测和处理优势比异质性的检验和估计量，并且可将其推广到分层的r×c列联表。
