Bioequivalence trials, intersectio–union tests and equivalence confidence sets

Roger L. Berger, Jason C. Hsu

Research output: Contribution to journalArticlepeer-review

449 Scopus citations


The bioequivalence problem is of practical importance because the approval of most generic drugs in the United States and the European Community (EC) requires the establishment of bioequivalence between the brand-name drug and the proposed generic version. The problem is theoretically interesting because it has been recognized as one for which the desired inference, instead of the usual significant difference, is practical equivalence. The concept of intersection(union tests will be shown to clarify, simplify and unify bioequivalence testing. A test more powerful than the one currently specified by the FDA and EC guidelines will be derived. The claim that the bioequivalence problem defined in terms of the ratio of parameters is more difficult than the problem defined in terms of the difference of parameters will be refuted. The misconception that size-α bioequivalence tests generally correspond to 100(1-2α)% confidence sets will be shown to lead to incorrect statistical practices, and should be abandoned. Techniques for constructing 100(1-α)% confidence sets that correspond to size-α bioequivalence tests will be described. Finally, multiparameter bioequivalence problems will be discussed.

Original languageEnglish (US)
Pages (from-to)283-302
Number of pages20
JournalStatistical Science
Issue number4
StatePublished - 1996
Externally publishedYes


  • Bioavailability
  • Bioequivalence
  • Confidence interval
  • Equivalence test
  • Hypothesis test
  • Intersection–union
  • Level
  • Pharmacokinetic
  • Size
  • Unbiased

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty


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