Equivalence tests for ratio of means in bioequivalence studies under crossover design

Abstract

There are several problems concerning the statistical definition of average bioequivalence provided by the U.S. Food and Drug Administration. We proposed a ratio of means based on the original bioavailability measure as the definition for average bioequivalence. Under the log-normal distribution assumption, we proposed a hypothesis testing-based method and a confidence interval-based method to answer the question of whether the ratio of means falls into a predetermined interval. For the hypothesis testing-based method, we decomposed the null two-sided hypothesis of the ratio of means into two one-sided hypotheses. With the intersection–union theorem for asymptotic tests, we constructed two asymptotic size- $α$ tests for the original null hypothesis. The method of variance estimation recovery was adopted to develop the confidence interval-based method. Simulation studies showed that the proposed methods can maintain the empirical type I error rate closely at the nominal level and is as powerful as the two one-sided $t$ -test for testing the ratio of means under different settings. The application of the proposed methods was illustrated through six datasets in real-world examples.

Keywords

Equivalence test bioequivalence two one-sided test geometric mean ratio ratio of means

Get full access to this article

View all access options for this article.

References

FDA. Guidance for industry: bioequivalence studies submitted in NDAs or INDs – general considerations. Rockville, MD, 2014.

Metzler

. Bioavailability—a problem in equivalence. Biometrics 1974; 30: 309–317.

Hauck

Hyslop

Anderson

et al. Statistical and regulatory considerations for multiple measures in bioequivalence testing. Clin Res Regul Aff 1995; 12: 249–265.

Ghosh

Gönen

. Bayesian modeling of multivariate average bioequivalence. Stat Med 2008; 27: 2402–2419.

de Souza

Achcar

Martinez

. Use of Bayesian methods for multivariate bioequivalence measures. J Biopharm Stat 2009; 19: 42–66.

Pallmann

Jaki

. Simultaneous confidence regions for multivariate bioequivalence. Stat Med 2017; 36: 4585–4603.

Westlake

. Bioavailability and bioequivalence of pharmaceutical formulations. In: Peace KE (ed.) Biopharmaceutical Statistics for Drug Development. Marcel Dekker, Inc., New York, 1988, pp. 329–352.

Liu

Weng

. Estimation of direct formulation effect under log-normal distribution in bioavailability/bioequivalence studies. Stat Med 1992; 11: 881–896.

FDA. Guidance on statistical procedures for bioequivalence studies using a standard two-treatment crossover design. Informal communication by the Division of Bioequivalence, Office of Generic Drugs, Rockville, MD, 1992.

10.

FDA. Guidance for industry: statistical approaches to establishing bioequivalence. Rockville, MD: Center for Drug Evaluation and Research, Food and Drug Administration, 2001.

11.

Feng

Wang

. Geometric mean of nonnegative random variable. Commun Stat-Theory Meth 2013; 42: 2714–2717.

12.

Feng

Wang

Zhang

et al. Generalized definition of the geometric mean of a non negative random variable. Commun Stat-Theory Meth 2017; 46: 3614–3620.

13.

Chow

Tse

. A related problem in bioavailability/bioequivalence studies–estimation of the intrasubject variability with a common cv. Biom J 1990; 32: 597–607.

14.

United States. Drug Bioequivalence Study Panel. Drug bioequivalence: a report of the office of technology assessment, The Office, 1974.

15.

Locke

. An exact confidence interval from untransformed data for the ratio of two formulation means. J Pharmacokinet Biopharm 1984; 12: 649–655.

16.

Vuorinen

Tuominen

. Fieller’s confidence intervals for the ratio of two means in the assessment of average bioequivalence from crossover data. Stat Med 1994; 13: 2531–2545.

17.

Schuirmann

. Confidence intervals for the ratio of two means from a crossover study. In: Proceedings of the biopharmaceutical section of the American Statistical Association. Washington, DC: American Statistical Association, 1989, pp. 121–126.

18.

Hauschke

Kieser

Diletti

et al. Sample size determination for proving equivalence based on the ratio of two means for normally distributed data. Stat Med 1999; 18: 93–105.

19.

Zhou

Gao

Hui

. Methods for comparing the means of two independent log-normal samples. Biometrics 1997; 53: 1129–1135.

20.

Zhou

Gao

et al. Methods for testing equality of means of health care costs in a paired design study. Stat Med 2001; 20: 1703–1720.

21.

Jiang

Wong

et al. Likelihood analysis for the ratio of means of two independent log-normal distributions. Biometrics 2002; 58: 463–469.

22.

Jiang

Rekkas

Wong

et al. Comparing the means of two log-normal distributions: A likelihood approach. J Stat Econ Methods 2014; 3: 137–152.

23.

Krishnamoorthy

Mathew

. Inferences on the means of lognormal distributions using generalized p-values and generalized confidence intervals. J Stat Plan Inference 2003; 115: 103–121.

24.

Bebu

Mathew

. Comparing the means and variances of a bivariate log-normal distribution. Stat Med 2008; 27: 2684–2696.

25.

Abdollahnezhad

Babanezhad

Jafari

. Inference on difference of means of two log-normal distributions; a generalized approach. J Stat Econ Methods 2012; 1: 125–131.

26.

Ozkip

Yazici

Sezer

. Modified generalized p-value and confidence interval by fisher’s fiducial approach. Hacettepe J Math Stat 2017; 46: 1–22.

27.

Gupta

. Statistical inference for the common mean of two log-normal distributions and some applications in reliability. Comput Stat Data Anal 2006; 50: 3141–3164.

28.

Pal

Lim

Ling

. A computational approach to statistical inferences. J Appl Probab Stat 2007; 2: 13–35.

29.

Basu

Mandal

Martín

et al. A robust wald-type test for testing the equality of two means from log-normal samples. Methodol Comput Appl Probab 2019; 21: 85–107.

30.

Schuirmann

. A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. J Pharmacokinet Biopharm 1987; 15: 657–680.

31.

Berger

. Multiparameter hypothesis testing and acceptance sampling. Technometrics 1982; 24: 295–300.

32.

Zou

Donner

. Construction of confidence limits about effect measures: a general approach. Stat Med 2008; 27: 1693–1702.

33.

Berger

Hsu

et al. Bioequivalence trials, intersection-union tests and equivalence confidence sets. Stat Sci 1996; 11: 283–319.

34.

Karalis

Symillides

Macheras

. Bioequivalence of highly variable drugs: A comparison of the newly proposed regulatory approaches by FDA and EMA. Pharm Res 2012; 29: 1066–1077.

35.

Muñoz

Alcaide

Ocaña

. Consumer’s risk in the EMA and FDA regulatory approaches for bioequivalence in highly variable drugs. Stat Med 2016; 35: 1933–1943.

36.

Patterson

Jones

. Bioequivalence and statistics in clinical pharmacology. New York: CRC Press, 2017.

37.

Hauschke

Steinijans

Pigeot

. Bioequivalence studies in drug development: methods and applications. 60. Chichester: John Wiley & Sons, 2007.

38.

Chow

Liu

. Design and analysis of bioavailability and bioequivalence studies. Boca Raton: CRC Press, 2008.

39.

Davit

Chen

Conner

et al. Implementation of a reference-scaled average bioequivalence approach for highly variable generic drug products by the US Food and Drug Administration. Aaps J 2012; 14: 915–924.

40.

Deng

Zhou

. Methods to control the empirical type I error rate in average bioequivalence tests for highly variable drugs. Stat Methods Med Res 2020; 29: 1650–1667.

41.

de Souza

Achcar

Martinez

et al. The use of asymmetric distributions in average bioequivalence. Stat Med 2016; 35: 2525–2542.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.24 MB