Statistical power of multiplicity adjustment strategies for correlated binary endpoints

There are numerous alternatives to the so-called Bonferroni adjustment to control for familywise Type I error among multiple tests. Yet, for the most part, these approaches disregard the correlation among endpoints. This can prove to be a conservative hypothesis testing strategy if the null hypothesis is false. The James procedure was proposed to account for the correlation structure among multiple continuous endpoints. Here, a simulation study evaluates the statistical power of the Hochberg and James adjustment strategies relative to that of the Bonferroni approach when used for multiple correlated binary variables. The simulations demonstrate that relative to the Bonferroni approach, neither alternative sacrifices power. The Hochberg approach has more statistical power for ρ<0.50; whereas the James procedure provides more statistical power with higher ρ, the common correlation among the multiple outcomes. A study of gender differences in New York City homicides is used to illustrate the approaches.