Design and analysis of three-arm parallel cluster randomized trials with small numbers of clusters

In this article, we review and evaluate a number of methods used in the design and analysis of small three-arm parallel cluster randomized trials. We conduct a simulation-based study to evaluate restricted randomization methods including covariate-constrained randomization and a novel method for matched-group cluster randomization. We also evaluate the appropriate modelling of the data and small sample inferential methods for a variety of treatment effects relevant to three-arm trials. Our results indicate that small-sample corrections are required for high (0.05) but not low (0.001) values of the intraclass correlation coefficient and their performance can depend on trial design, number of clusters, and the nature of the hypothesis being tested. The Satterthwaite correction generally performed best at an ICC of 0.05 with a nominal type I error rate for single-period trials, and in trials with repeated measures type I error rates were between 0.04 and 0.06. Restricted randomization methods produce little benefit in trials with repeated measures but in trials with single post-intervention design can provide relatively large gains in power when compared to the most unbalanced possible allocations. Matched-group randomization improves power but is not as effective as covariate-constrained randomization. For model-based analysis, adjusting for fewer covariates than were used in a restricted randomization process under any design can produce non-nominal type I error rates and reductions in power. Where comparisons to two-arm cluster trials are possible, the performance of the methods is qualitatively very similar.