Klingenberg Bernhard, Agresti Alan
Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267, USA.
Biometrics. 2006 Sep;62(3):921-8. doi: 10.1111/j.1541-0420.2006.00525.x.
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 and show that it is a generalized score test under a generalized estimating equations (GEE) approach. Univariate features such as the relationship between the Wald and score tests and the dropout of pairs with the same response carry over to the multivariate case and the test does not depend on the working correlation assumption among the components of the multivariate response. For sparse or imbalanced 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 bootstrap, and if this is computationally too complex, a permutation distribution. We apply the test to safety data for a drug, in which two doses are evaluated by comparing multiple responses by the same subjects to each one of them.
本文基于来自两个相关多变量二元样本的数据，考虑了二项概率配对向量之间差异的全局检验。差异被定义为边际分布中的不均匀性或联合分布中的不对称性。为了检测第一种类型的差异，我们提出了McNemar检验的多变量扩展，并表明它是广义估计方程（GEE）方法下的广义得分检验。单变量特征，如Wald检验和得分检验之间的关系以及具有相同响应的配对的缺失，在多变量情况下仍然适用，并且该检验不依赖于多变量响应分量之间的工作相关性假设。对于稀疏或不平衡数据，例如当变量数量很大或比例接近零时出现的数据，最好使用自助法来实施该检验，如果计算过于复杂，则使用置换分布。我们将该检验应用于一种药物的安全性数据，其中通过比较同一受试者对两种剂量各自的多个反应来评估这两种剂量。
