A note on stratifying versus complete random assignment in clinical trials
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TL;DR
This analysis shows that in small samples relying on post-randomization stratification can lead to significant loss in efficiency when compared to prerandomization Stratification, even though the two design strategies should have similar variances.
Abstract
The efficiency of stratifying on a risk factor before randomization as opposed to complete randomization and adjustment for the risk factor by post-randomization analysis is examined by calculating the variance of the estimated difference between two treatment means for the two design strategies. This analysis shows that in small samples relying on post-randomization stratification can lead to significant loss in efficiency when compared to prerandomization stratification. In moderate and large samples the two design strategies should have similar variances.