A Multivariate Extension of McNemar's Test

• Activity Number: 230
• Type: Contributed
• Date/Time: Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Bernhard Klingenberg*+ and Alan Agresti
• Companies: Williams College and University of Florida
• Keywords: Multiple binary data ; Drug safety ; Marginal homogeneity ; Matched pairs

Abstract

This article considers global tests of differences between paired vectors of binomial probabilities based on data from two dependent multivariate binary samples. Difference is defined as either an inhomogeneity in the marginal distributions or asymmetry in the joint distribution. For detecting the first type of difference, we propose a multivariate extension of McNemar's test. It is shown that the relationship between the Wald and McNemar statistic for univariate matched categorical responses also holds in the multivariate case. The proposed statistic also can be derived as a generalized score test under a GEE approach. As in the univariate case, it does not depend on the working correlation among the components of the multivariate response or on the pairs for which the responses are identical in each sample. We illustrate the test with a safety trial for a drug, in which two doses of a drug are evaluated by comparing multiple responses by the same subject to each of them. For sparse data, such as occurs when the number of variables is large or the proportions are close to zero, the test is best implemented using a permutation distribution.