Efficiency and power of tests for multiple binary outcomes

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Journal Article
Journal of the American Statistical Association, 1995, 90 (430), pp. 680 - 693
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Global tests provide a useful tool for comparing two or more groups with respect to multiple correlated outcomes. We adapt and compare the performance of tests that have been suggested for use with multiple continuous outcomes to the case of multiple binary outcomes. Comparisons and guidelines are based on asymptotic relative efficiencies (ARE’s) and simulations. These results are illustrated using an application from teratology. We extend the work of Lefkopoulou and Ryan to include general M-group comparisons alternatives where group effects may differ for each outcome. A concise form for this general class of score tests is derived. To compute the ARE’s for this class of tests, we devise a useful characterization of the alternative space based on multivariate polar coordinates. Our findings indicate that the common outcome effect tests are efficient for a remarkably large range of circumstances. A simple formula applies to compute the maximum number of unaffected outcomes that can be included in a set of outcomes for which the common outcome effect tests remain more efficient than those derived under multidimensional alternatives. For comparison, other global tests are also considered in the simulations: two tests based on resampling (maximal and minimal z tests), a rank-sum test, a generalized least squares test, and a test based on collapsing multiple endpoints to a single binary outcome. Besides the common outcome effect tests, the resampling tests and the rank-sum test are found to perform very well for the cases under consideration. © 1995 Taylor & Francis Group, LLC.
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