Inefficiency of randomization methods that balance on stratum margins and improvements with permuted blocks and a sequential method

Stratified permuted blocks randomization is commonly applied in clinical trials, but other randomization methods that attempt to balance treatment counts marginally for the stratification variables are able to accommodate more stratification variables. When the analysis stratifies on the cells formed by crossing the stratification variables, these other randomization methods yield treatment effect estimates with larger variance than does stratified permuted blocks. When it is truly necessary to balance the randomization on many stratification variables, it is shown how this inefficiency can be improved by using a sequential randomization method where the first level balances on the crossing of the strata used in the analysis and further stratification variables fall lower in the sequential hierarchy.