Bonferroni-based correction factor for multiple, correlated endpoints

Multiple testing and its impact on the type I and type II error rates are frequently discussed in the statistical and biomedical literature. The Bonferroni adjustment is one of the most widely used approaches, yet it suffers from poor statistical performance when there are correlated test statistics. For example, it is criticized to be too conservative. Nonetheless, part of the strong appeal of the Bonferroni approach is the straightforward implementation and relatively intuitive explanation. In this manuscript, a novel adaptation to the traditional Bonferroni approach that accounts for correlated data is proposed. A simple correction factor based on intraclass correlation is applied to the standard Bonferroni method to overcome the shortcomings of the standard Bonferroni adjustment yet maintains its advantages. The method is motivated by an early phase clinical trial examining the effect of a study medication on marijuana craving, which is commonly quantified into four correlated constructs. A detailed simulation study demonstrated that the proposed approach is statistically sound and appropriate for a wide range of common settings.