Sample size determination for proving equivalence based on the ratio of two means for normally distributed data

Stat Med. 1999 Jan 15;18(1):93-105. doi: 10.1002/(sici)1097-0258(19990115)18:1<93::aid-sim992>;2-8.


Equivalence trials aim to demonstrate that two treatments do not differ by more than a prespecified clinically irrelevant amount. We consider the problem when equivalence is defined in terms of the ratio of population means and the original (untransformed) data are normally distributed. Application of the intersection-union principle to the test proposed by Sasabuchi results in a two one-sided tests procedure of size alpha. We give the associated 100 (1-2 alpha) per cent confidence interval and derive the exact methods for calculation of power and sample sizes for the parallel group design and the two-period cross-over. We present tables and figures of required sample sizes and achieved power.

MeSH terms

  • Administration, Inhalation
  • Adrenal Cortex Hormones / administration & dosage
  • Adrenal Cortex Hormones / pharmacokinetics
  • Adrenal Cortex Hormones / therapeutic use
  • Asthma / drug therapy
  • Confidence Intervals
  • Cross-Over Studies
  • Humans
  • Normal Distribution*
  • Numerical Analysis, Computer-Assisted
  • Sample Size*
  • Therapeutic Equivalency*


  • Adrenal Cortex Hormones