Objective: To develop a simple and robust approach for the test of interaction between community intervention and an individual-level variable suitable for use in typical situations of community randomized trials (CRTs), i.e. small number of communities but large number of subjects per community.
Methods: We propose a method based on taking the difference between summary statistics from groups of individuals with and without an attribute within each community, then applying a two-sample t-test or Wilcoxon test to compare the distribution of within-community differences between trial arms. The method is evaluated using simulations and illustrated using data from a CRT of a health education intervention. Approximate sample size formulas are derived.
Results: Analyses based on the t-test give power very close to expected level in a variety of situations, including when the summary statistics are not symmetrically distributed across communities, the covariate is not distributed as planned, and the number of communities per intervention arm ranges from 8 to 20. Even in the situation with as few as four communities per arm, the power is only slightly lower than expected. Type I error rates always closely follow 5% as required, whether the distributional assumption is correct or not. The application of the Wilcoxon test appears too conservative.
Conclusions: The proposed approach to test for interaction is valid and easy to use. The application of the t-test in this setting is robust.