The primary goal of randomized trials is to compare the effects of different interventions on some outcome of interest. In addition to the treatment assignment and outcome, data on baseline covariates, such as demographic characteristics or biomarker measurements, are typically collected. Incorporating such auxiliary covariates in the analysis of randomized trials can increase power, but questions remain about how to preserve type I error when incorporating such covariates in a flexible way, particularly when the number of randomized units is small. Using the Young Citizens study, a cluster-randomized trial of an educational intervention to promote HIV awareness, we compare several methods to evaluate intervention effects when baseline covariates are incorporated adaptively. To ascertain the validity of the methods shown in small samples, extensive simulation studies were conducted. We demonstrate that randomization inference preserves type I error under model selection while tests based on asymptotic theory may yield invalid results. We also demonstrate that covariate adjustment generally increases power, except at extremely small sample sizes using liberal selection procedures. Although shown within the context of HIV prevention research, our conclusions have important implications for maximizing efficiency and robustness in randomized trials with small samples across disciplines.
"Flexible covariate-adjusted exact tests of randomized treatment effects with application to a trial of HIV education." Ann. Appl. Stat. 7 (4) 2106 - 2137, December 2013. https://doi.org/10.1214/13-AOAS679