EFFICIENCY AND POWER OF TESTS FOR MULTIPLE BINARY OUTCOMES

Global tests provide a useful tool for comparing two or more groups wi th respect to multiple correlated outcomes. We adapt and compare the p erformance of tests that have been suggested for use with multiple con tinuous outcomes to the case of multiple binary outcomes. Comparisons and guidelines are based on asymptotic relative efficiencies (ARE's) a nd simulations. These results are illustrated using an application fro m teratology. We extend the work of Lefkopoulou and Ryan to include ge neral 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 multivariat e polar coordinates. Our findings indicate that the common outcome eff ect 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 commo n 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( max imal and minimal z tests), a rank-sum test, a generalized least square s test, and a test based on collapsing multiple endpoints to a single binary outcome. Besides the common outcome effect tests, the resamplin g tests and the rank-sum test are found to perform very well for the c ases under consideration.