Abstract
Testing for the bioequivalence alternative H 1: |θ| ≤ Δ in a normal univariate setting is usually performed with the well-known ”two-one-sidedt-tests procedure”, which is an intersection-union test. Based on the intersection-union principle recently tests for the multivariate rectangular alternative H d : max i = 1,..., d |θ i | ≤ Δ have been constructed. In this paper we show that rectangular hypotheses are not always a suitable generalization of H 1 to the multivariate setting. In order to overcome the drawbacks encountered with rectangular hypotheses we suggest ellipsoids as alternatives. Finally, an asymptotic test for the new hypotheses is suggested and compared with existing methods.
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References
Anderson, T.W. (1984): An Introduction to Multivariate Statistical Analysis. John Wiley & Sons, second edition, New York.
BERGER, R.L. and HSU, J.C. (1996): Bioequivalence Trials, Intersection-Union Tests, and Equivalence Confidence Sets (with discussion). Statistical Science, 11, 283–319.
BROWN, L.D., CASELLA, G. and HWANG, J.T.G. (1995): Optimal Confidence Sets, Bioequivalence, and the Limaçon of Pascal. Journal of the American Statistical Association, 90, 880–889.
BROWN, L.D., HWANG, J.T.G. and MUNK, A. (1998): An Unbiased Test for the Bioequivalence Problem. The Annals of Statistics, 25, 2345–2367.
CHINCHILLI, V.M. and ELSWICK, R.K.jr. (1997): The Multivariate Assessment of Bioequivalence. Journal of Biopharmaceutical Statistics (1), 113–123.
CHOW, S.-C. and LIU, J.-P. (1992): Design and Analysis of Bioavailability and Bioequivalence Studies. Marcel Dekker, New York.
EC-GCP (1993): Biostatistical Methodology in Clinical Trials in Applications for Marketing Authorization for Medical Products. CPMP Working Party on Efficacy of Medical Products, Commision of the European Communities, Brussels, Draft Guideline edition.
ENDRENYI, L., FRITSCH, S. and YAN, W. (1991): Cmax/AUC is a Clearer Measure than Cmax for Absorbtion Rates in Investigation of Bioequivalence. International Journal of Clinical Pharmacology, Therapy and Toxicology 29, p. 394–399.
FDA (United States Food and Drug Administration) (1992): Bioavailability and bioequivalence requirements. U.S. Government Printing Office, U.S. Code of Federal Regulations, volume 21, chapter 320.
HSU, H.C., LU, H.L. and CHAN, K.K.H.(1995): A Novel Multivariate Approach for Estimating the Degree of Similarity in Bioavailability Between Two Pharmaceutical Products. Journal of Biopharmaceutical Statistics, 768–772.
MATHAI, A.M. and PROVOST, S.B. (1992): Quadratic Forms in Random Variables. Marcel Dekker, New York.
MUNK, A. and PFLÜGER, R. (1998): 1–α Confidence Rules for Convex Sets are 3-Level Tests - with Applications to the Multivariate Assessment of Bioequivalence. Preprint Ruhr-Universität Bochum.
PFLÜGER, R. (1997): Bioäquivalenztests für die multivariate Normalverteilung bei unbekannter Kovarianzstruktur. Master Thesis, Institut für Stochastik der Universität Göttingen, Göttingen.
SERFLING, R.J. (1980): Approximation Theorems of Mathematical Statistics. John Wiley & Sons, New York.
SCHALL, R., GROENEWALD, P.C.N., POTGIETER, L.A. and LUUS, H.G. (1996): Multivariate Assessment of Bioequivalence. Technical Report, University of the Orange Free State.
STEINIJANS, V., SAUTER, R., HAUSCHKE, D. and ELZE, M. (1995): Metrics to Characterize Concentration-Time Profiles in Single-and Multiple Dose Bioequivalence Studies. Drug Information Journal 29, 981–987.
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© 1999 Springer-Verlag Berlin · Heidelberg
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Pflüger, R., Munk, A. (1999). New Hypotheses and Tests for the Multivariate Bioequivalence Problem. In: Gaul, W., Locarek-Junge, H. (eds) Classification in the Information Age. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60187-3_63
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DOI: https://doi.org/10.1007/978-3-642-60187-3_63
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