A simple sample size formula for analysis of covariance in randomized clinical trials

J Clin Epidemiol. 2007 Dec;60(12):1234-8. doi: 10.1016/j.jclinepi.2007.02.006. Epub 2007 Jun 6.


Objective: Randomized clinical trials that compare two treatments on a continuous outcome can be analyzed using analysis of covariance (ANCOVA) or a t-test approach. We present a method for the sample size calculation when ANCOVA is used.

Study design and setting: We derived an approximate sample size formula. Simulations were used to verify the accuracy of the formula and to improve the approximation for small trials. The sample size calculations are illustrated in a clinical trial in rheumatoid arthritis.

Results: If the correlation between the outcome measured at baseline and at follow-up is rho, ANCOVA comparing groups of (1-rho(2))n subjects has the same power as t-test comparing groups of n subjects. When on the same data, ANCOVA is used instead of t-test, the precision of the treatment estimate is increased, and the length of the confidence interval is reduced by a factor 1-rho(2).

Conclusion: ANCOVA may considerably reduce the number of patients required for a trial.

MeSH terms

  • Analysis of Variance
  • Antirheumatic Agents / therapeutic use
  • Arthritis, Rheumatoid / drug therapy
  • Drug Therapy, Combination
  • Humans
  • Isoxazoles / therapeutic use
  • Leflunomide
  • Randomized Controlled Trials as Topic / methods*
  • Research Design
  • Sample Size*
  • Sulfasalazine / therapeutic use
  • Treatment Outcome


  • Antirheumatic Agents
  • Isoxazoles
  • Sulfasalazine
  • Leflunomide