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Abstract:
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When there are multiple endpoints, a key issue is whether one should set the unknown correlations at their least favorable configurations, or can sample estimates of correlation be incorporated. Taking supremum over the unknown correlations does control the rate of incorrect (regulatory) decisions over infinitely many studies, so this has generally been the practice. One might expect, however, to be able to take correlation into account when the endpoints correspond to efficacies in subgroups and their mixtures. Surprisingly, taking correlation into account correctly for binary and time-to-event outcomes require delicate derivations quite different from the continuous outcome case. We will use the binary outcome case to demonstrate how different the correct and naïve (common but incorrect) calculations of correlation may be. Going forward, we will also introduce a new - conditional error rate -concept.
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