In clinical studies incorporating multiple dichotomous outcome measures one is constantly faced with the dilemma of how to avoid large numbers of false positives while maintaining adequate levels of sensitivity of assessing group differences for individual outcomes. One possible method of limiting the number of false positives is to use a Bonferroni correction to the individual comparison alpha levels, say by using alpha* = alpha/k, for k outcome measures. However, this procedure makes it almost impossible to detect group differences unless there is at least one outcome for which the difference is very large. Many modifications of the Bonferroni method have been investigated but they still suffer from the limitations described above, although some improvements can be achieved for specific types of group differences. Alternatively, two general approaches for combining the multiple outcomes have been pursued. The first approach is to create composite summary measures for an individual by creating weighted linear combinations of these outcomes, and then assessing group differences based on this composite summary variable. The second approach creates a global test statistic which is based on a linear combination of the outcome specific test statistics. Here one derives a test statistic for making group comparisons separately for each outcome measure. Then these correlated test statistics are used to form global test statistics, and one statistical test is performed when comparing two groups. Several papers have recently appeared in which various statistical procedures for creating such global tests have been proposed. However, for dichotomous outcome measures little has been done when covariates are present in the model.
