Improper analysis of trials randomised using stratified blocks or minimisation

Abstract

Many clinical trials restrict randomisation using stratified blocks or minimisation to balance prognostic factors across treatment groups. It is widely acknowledged in the statistical literature that the subsequent analysis should reflect the design of the study, and any stratification or minimisation variables should be adjusted for in the analysis. However, a review of recent general medical literature showed only 14 of 41 eligible studies reported adjusting their primary analysis for stratification or minimisation variables. We show that balancing treatment groups using stratification leads to correlation between the treatment groups. If this correlation is ignored and an unadjusted analysis is performed, standard errors for the treatment effect will be biased upwards, resulting in 95% confidence intervals that are too wide, type I error rates that are too low and a reduction in power. Conversely, an adjusted analysis will give valid inference. We explore the extent of this issue using simulation for continuous, binary and time-to-event outcomes where treatment is allocated using stratified block randomisation or minimisation.