Improper analysis of trials randomised using stratified blocks or minimisation

Stat Med. 2012 Feb 20;31(4):328-40. doi: 10.1002/sim.4431. Epub 2011 Dec 4.


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.

MeSH terms

  • Antineoplastic Agents / therapeutic use
  • Back Injuries / rehabilitation
  • Back Injuries / surgery
  • Bias
  • Breast Neoplasms / drug therapy
  • Breast Neoplasms / mortality
  • Carcinoma / drug therapy
  • Carcinoma / mortality
  • Computer Simulation / statistics & numerical data
  • Data Interpretation, Statistical*
  • Deoxyribonucleases / therapeutic use
  • Drug Therapy, Combination / statistics & numerical data
  • Female
  • Fibrinolytic Agents / therapeutic use
  • Humans
  • Interferon-alpha / therapeutic use
  • Kidney Neoplasms / drug therapy
  • Kidney Neoplasms / mortality
  • Liver Cirrhosis, Biliary / drug therapy
  • Male
  • Medroxyprogesterone Acetate / therapeutic use
  • Penicillamine / therapeutic use
  • Pleural Effusion / drug therapy
  • Pleural Effusion / mortality
  • Randomized Controlled Trials as Topic / statistics & numerical data*
  • Survival Analysis
  • Tamoxifen / therapeutic use
  • Tissue Plasminogen Activator / therapeutic use
  • Treatment Outcome


  • Antineoplastic Agents
  • Fibrinolytic Agents
  • Interferon-alpha
  • Tamoxifen
  • Medroxyprogesterone Acetate
  • Deoxyribonucleases
  • Tissue Plasminogen Activator
  • Penicillamine