Power calculations for large multi-arm placebo-controlled studies of dichotomous outcomes

Several statistical methods can be used to test for differences in placebo-controlled dichotomous multi-arm studies. These tests include linear and quadratic trends, Dunnett's test, Hochberg's test, and the overall chi-square test. We computed the power of these tests under a wide variety of alternatives. For two arms versus a control, the power was computed exactly. For more than two arms, the power was calculated from 100000 simulations per alternative. Against monotonic alternatives, the linear trend test tended to be superior. Against convex alternatives, the quadratic trend test tended to be superior. Against general alternatives, Dunnett's test, Hochberg's test, and the overall chi-square test were superior and had very similar power curves. The Hochberg test was generally less powerful than Dunnett's test but the difference was offset by its increased power to reject multiple hypotheses. These results remained nearly constant over a wide range of sample sizes, average event rates and average effect sizes.