The benefit of stratification in clinical trials revisited

Stratification is common in clinical trials because it can reduce the variance of the estimated treatment effect. The traditional demonstration of variance reduction relies on the assumption of stratum sizes being fixed quantities. However, in practice, to speed up enrollment, and to obtain a study population with a similar distribution as the overall population, the stratum sizes are allowed to vary. Under the condition that the total sample size is fixed and that the stratum sizes have a multinomial distribution, the criterion changes for achieving a reduction in variance. The relationship between the stratified and unstratified variances is established and shown to be approximately the same for prestratified and post-stratified trials. It is demonstrated why stratification may actually increase the variance compared with no stratification even when the mean square error is reduced on account of stratification. Data from a real clinical trial will be used for illustration. The benefit attributed to stratification needs to be re-examined in light of the findings presented, particularly given its widespread use.