  A practical limitation of cluster randomized controlled trials (cRCTs) is
that the number of available clusters may be small, resulting in an increased
risk of baseline imbalance under simple randomization. Constrained
randomization overcomes this issue by restricting the allocation to a subset of
randomization schemes where sufficient overall covariate balance across
comparison arms is achieved. However, for multi-arm cRCTs, several design and
analysis issues pertaining to constrained randomization have not been fully
investigated. Motivated by an ongoing multi-arm cRCT, we elaborate the method
of constrained randomization and provide a comprehensive evaluation of the
statistical properties of model-based and randomization-based tests under both
simple and constrained randomization designs in multi-arm cRCTs, with varying
combinations of design and analysis-based covariate adjustment strategies. In
particular, as randomization-based tests have not been extensively studied in
multi-arm cRCTs, we additionally develop most-powerful randomization tests
under the linear mixed model framework for our comparisons. Our results
indicate that under constrained randomization, both model-based and
randomization-based analyses could gain power while preserving nominal type I
error rate, given proper analysis-based adjustment for the baseline covariates.
Randomization-based analyses, however, are more robust against violations of
distributional assumptions. The choice of balance metrics and candidate set
sizes and their implications on the testing of the pairwise and global
hypotheses are also discussed. Finally, we caution against the design and
analysis of multi-arm cRCTs with an extremely small number of clusters, due to
insufficient degrees of freedom and the tendency to obtain an overly restricted
randomization space.
