May W L, Johnson W D
Department of Preventive Medicine, University of Mississippi Medical Center, Jackson 39216-4505, USA.
Stat Med. 1997 May 30;16(10):1081-96. doi: 10.1002/(sici)1097-0258(19970530)16:10<1081::aid-sim521>3.0.co;2-x.
With measurements taken on subjects over time, on matched pairs of subjects or on clusters of subjects, the data often contain pairs of correlated dichotomous responses. McNemar's test is perhaps the best known test to compare two correlated binomial proportions. The salient feature of McNemar's test is that we compute the variance of the contrast estimator under the restriction that the null hypothesis is true. Wald's test, on the other hand, does not require that restriction. As a consequence, Wald's statistic is always greater in magnitude than McNemar's statistic when the marginal proportions are unequal, but there is a problem with the validity of both McNemar's test and Wald's test with small to moderate samples. There have been various modifications suggested for McNemar's test to improve its performance. We propose a modified Wald's test that is valid in small to moderate samples and maintains good power. We also evaluate the performance of McNemar's test and Wald's test with and without modifications to enhance validity as well as the performance of the large sample likelihood ratio test and an exact test of the equality of correlated binomial proportions. In a smaller study, we compare the behaviour of a test based on the James-Stein estimator of the common odds ratio proposed by Liang and Zeger to McNemar's test and Wald's test.
在对受试者进行长期测量、对配对受试者或受试者集群进行测量时，数据通常包含成对的相关二分反应。麦克内马尔检验可能是比较两个相关二项比例最著名的检验。麦克内马尔检验的显著特点是，我们在原假设为真的限制下计算对比估计量的方差。另一方面， Wald检验不需要该限制。因此，当边际比例不相等时，Wald统计量的绝对值总是大于麦克内马尔统计量，但对于中小样本，麦克内马尔检验和Wald检验的有效性都存在问题。针对麦克内马尔检验提出了各种改进方法以提高其性能。我们提出了一种改进的Wald检验，它在中小样本中有效且保持良好的功效。我们还评估了麦克内马尔检验和Wald检验在有无改进情况下的性能，以提高有效性，以及大样本似然比检验和相关二项比例相等性的精确检验的性能。在一项较小的研究中，我们将基于梁和泽格提出的共同优势比的詹姆斯 - 斯坦估计量的检验行为与麦克内马尔检验和Wald检验进行比较。
