An unbiased test for the bioequivalence problem. (English) Zbl 0905.62107

Brown, Lawrence D.; Hwang, J. T. Gene; Munk, Axel

Ann. Stat. 25, No. 6, 2345-2367 (1997).

The authors treat the problem demonstrating bioequivalence of treatments. The standard two one-sided tests procedure for bioequivalence is biased, so they construct an unbiased \(\alpha\)-level test. Since, in the construction, the rejection region of the unbiased test contains that of the two one-sided tests procedure, it is seen that the unbiased test is uniformly more powerful than the \(\alpha\)-level two-sided test procedure. The construction is numerically complemented and also the critical region is illustrated.

Reviewer: M.Akahira (Ibaraki)

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
62F03	Parametric hypothesis testing

Keywords:

uniformly most powerful; pharmacokinetic parameters; two one-sided tests procedure; unbiased \(\alpha\)-level test

References:

[1]	Anderson, S. and Hauck, W. W. (1983). A new procedure for testing equivalence in comparative bioavailability and other clinical trials. Comm. Statist. Theory Methods 12 2263-2692. · Zbl 0553.62097
[2]	Berger, R. (1982). Multiparameter hy pothesis testing and acceptance sampling. Technometrics 24 295-300. JSTOR: · Zbl 0497.62091
[3]	Berger, R. and Hsu, J. (1996). Bioequivalence trials, intersection-union tests and equivalence confidence sets (with discussion). Statist. Sci. 11 283-319. · Zbl 0955.62555
[4]	Diletti, E., Hauschke, D. and Steinijans, V. W. (1991). Sample size determination for bioequivalence assessment by means of confidence intervals. International Journal of Clinical Pharmacology, Therapy and Toxicology 29 1-8.
[5]	EC-GCP (1993). Biostatistical methodology in clinical trials in applications for marketing authorization for medical products. CPMP Working Party on Efficacy of Medical Products, Commission of the European Communities, Brussels.
[6]	FDA (1992). Draft recommendation on statistical procedures for bioequivalence studies using the standard two-treatment crossover design. Center for Drug Evaluation and Research, Food and Drug Administration, Rockville, MD.
[7]	Frick, H. (1987). On level and power of Anderson and Hauck’s procedure for testing equivalence in comparative bioavailability. Comm. Statist. Theory Methods 16 2771-2778. · Zbl 0639.62013
[8]	Hauck, W. W. and Anderson, S. (1984). A new statistical procedure for testing equivalence in two-group comparative bioavailability trials. J. Pharmacokinetics and Biopharmaceutics 12 83-91.
[9]	Hauck, W. W. and Anderson, S. (1996). Comments on ”Bioequivalence trials, intersection-union · Zbl 0988.35147
[10]	tests and equivalence confidence sets” by R. Berger and J. Hsu (1996). Statist. Sci. 11 303.
[11]	Hodges, J. L. and Lehmann, E. L. (1954). Testing the approximate validity of statistical hy pothesis. J. Roy. Statist. Soc. Ser. B 16 261-268. JSTOR: · Zbl 0057.35403
[12]	Hsu, J., Hwang, J. T. G., Liu, H. K. and Ruberg, S. J. (1994). Confidence intervals associated with tests for bioequivalence. Biometrika 81 103-114. JSTOR: · Zbl 0803.62094
[13]	Hwang, J. T. G. and Liu, H. K. (1992). Confidence intervals associated with tests for bioequivalence. Cornell Statistical Center Technical Report. · Zbl 0803.62094
[14]	Lehmann, E. L. (1986). Testing Statistical Hy potheses, 2nd ed. Wiley, New York.
[15]	Munk, A. (1992). Aquivalenz und Intervalltests in exponentiellen Familien. Ph.D. dissertation, Institut f ür Mathematische Stochastik, Univ. Göttingen.
[16]	Munk, A. (1993). An improvement on commonly used tests in bioequivalence assessment. Biometrics 49 1225-1230 [see also correspondence in Biometrics 50 884-886 (1994)]. · Zbl 0825.62752
[17]	Rocke, D. M. (1984). On testing for bioequivalence. Biometrics 40 225-230 [see also correspondence in Biometrics 41 561-563 (1985)]. JSTOR: · Zbl 0533.62090
[18]	Schuirmann, D. J. (1987). A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of coverage bioavailability. J. Pharmacokinetics and Biopharmaceutics 15 657-680.
[19]	Schuirmann, D. J. (1996). Comments on ”Bioequivalence trials, intersection-union tests and equivalence confidence sets” by R. Berger and J. Hsu (1996). Statist. Sci. 11 312-313.
[20]	Westlake, W. J. (1974). The use of balanced incomplete block designs in comparative bioavailability trials. Biometrics 30 319-327. · Zbl 0285.92009
[21]	Westlake, W. J. (1976). Sy mmetrical confidence intervals for bioequivalence trials. Biometrics 32 741-744. · Zbl 0337.62025