Hypothesis testing and confidence interval construction in 2 x 2 tables of correlated proportions

The 2 x 2 table is an invaluable tool for displaying bivariate binary data. It is easy to find examples of correlated binary response in biopharmaceutical experiments and clinical research and analysis of these data is a current research topic. The most common hypothesis tested for 2 x 2 tables of correlated proportions is that of homogeneity of the marginal proportions or, equivalently, the hypothesis of table symmetry. The 2 x 2 table of correlated proportions is rich with information and we present a survey of some of the analyses relevant for these data. Using asymptotic theory, we develop estimators of relevant parameters and associated test statistics that are of interest. We discuss interval estimation using arguments proposed by Quesenberry and Hurst (1) and Goodman (2). These interval estimators do not rely on estimation of the covariance matrix and are not necessarily equivalent to those obtained using modified chi-square statistics.