Tests for Equivalence or Noninferiority Between Two Proportions
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TESTS FOR EQUIVALENCE OR NONINFERIORITY BETWEEN TWO PROPORTIONS* JAMES J. CHEN Division of Biometry and Risk Assessment, National Center for Toxicological Research, United States Food and Drug Administration, Jefferson, Arkansas
YI TSONG Quantitative Methods & Research Staff, Office of Biostatistics, Center for Drug Evaluation and Research, United States Food and Drug Administration, Rockville, Maryland
SEUNG-HOKANG Division of Biometry and Risk Assessment, National Center for Toxicological Research, United States Food and Drug Administration, Jefferson, Arkansas
Bioequivalence between two treatments or two drugs is ofren assessed by comparing the two proportions (success rate or eradication rate) of binomial outcomes when the conventional pharmacokinetic parameters are inadequate for the assessment. Setting the equivalence limits can be based on one of the three measures: difference, ratio, or odds ratio between the two binomial probabilities. This paper reviews the existing asymptotic test statistics for comparing two independent binomial probabilities in terms of the three measures in the context of equivalence or noninferiority testing. The actual type I error and power of the asymptotic tests are evaluated by enumerating the exact probabilities in the rejection region. The results show that to establish an equivalence between two treatments with an equivalence limit of 20% in difference, a sample size of at least 50 per treatment is needed. When the sample size is sufficient, the actual type I error rate is close to the nominal level (slightly above the nominal level in several cases)for a test in terms of difference for equivalence limits, and it tends to exceed the nominal level for tests in terms of ratio or odds ratio. Key Words: Asymptotic test; Bioequivalence; Binomial; Conditional exact test; Difference; Odds ratio; Ratio
INTRODUCTION THE ASSESSMENT OF equivalence between two treatments, two drugs, or two formulations of the same drug occurs in various types of clinical trials. The bioequivalence assessment of a new formulation to a stan-
dard formulation of the exactly same active compounds has been extensively discussed in the literature (1). For approval of generic drug products (ie, products of a new formulation of an innovative drug with an expired patent), the United States Food and Drug Administration (FDA) (2,3) usually requires
Reprint address: Dr. James I. Chen, Division of Biometry and Risk Assessment, NCIWFDNHFT-20, Jefferson. AR 72079. E-mail [email protected]. *The views presented in this paper are those of authors and do not necessary represent those of the United States Food and Drug Administration.
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James J. Chen, Yi Tsong, and Seung-Ho Kang
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the generic drug companies to demonstrate (bio)equivalence between the generic drug and the innovator products. Bioequivalence studies are usually designed as crossover experiments wit
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