The relationship among design parameters for statistical power between continuous and binomial outcomes in cluster randomized trials.

While research on statistical power for designs with continuous outcomes is extensive, the literature on power for designs with binary outcomes is notably more limited. Because statistical power for continuous outcomes is well known, a natural question is whether power may be estimated in a similar way for the case of binary outcomes. This question involves establishing the appropriate analogy between design parameters in the continuous and binary outcome cases, which consists of an analogy in effect sizes and an analogy in the intraclass correlation coefficient (ICC). This article proposes two possible analogies for the ICC and discusses the challenges in establishing a valid and useful analogy for statistical power in designs with binary outcomes. Using the results from two simulation studies, we compare the power estimates and Type I error rates under two analytic models for binary outcomes and the corresponding values under the ICC analogies. We use the simulation results to assess the implications for power and statistical inference when no useful analogy in ICCs exists for a given study. We provide a discussion on how researchers might think of the analogies using an empirical example on a preschool intervention in Ghana. We conclude with final thoughts on the limitations in establishing an analogy in design parameters and ideas for future research. (PsycINFO Database Record (c) 2019 APA, all rights reserved)