Publication Description
We present methods for the analysis of a K-variate binary measure for two independent groups where some observations may be incomplete, as in the case of K repeated measures in a comparative trial. For the K 2 X 2 tables, let θ = (θ , ..., θ ) be a vector of association parameters where θ is a measure of association that is a continuous function of the probabilities π in each group (i = 1, 2; k = 1, ..., K), such as the log odds ratio or log relative risk. The asymptotic distribution of the estimates θ = ( ) is derived. Under the assumption that θ = θ for all k, we describe the maximally efficient linear estimator θ of the common parameter θ. Tests of contrasts on the θ are presented which provide a test of homogeneity H : θ = θ for all k ≠ l. We then present maximally efficient tests of aggregate as sociation H : θ = θ , where θ is a given value. It is shown that the test of aggregate association H is asymptotically independent of the preliminary test of homogeneity H . These methods generalize the efficient estimators of Gart (1962, Biometrics 18, 601-610), and the Cochran (1954, Biometrics 10, 417-451), Mantel-Haenszel (1959, Journal of the National Cancer Institute 22, 719-748), and Radhakrishna (1965, Biometrics 21, 86-98) tests to nonindependent tables. The methods are illustrated with an analysis of repeated morphologic evaluations of liver biopsies obtained in the National Cooperative Gallstone Study.