Inflation of Type I Error in the Evaluation of Scaled Average Bioequivalence, and a Method for its Control
- 425 Downloads
To verify previously reported findings for the European Medicines Agency’s method for Average Bioequivalence with Expanding Limits (ABEL) for assessing highly variable drugs and to extend the assessment for other replicate designs in a wide range of sample sizes and CVs. To explore the properties of a new modified method which maintains the consumer risk ≤0.05 in all cases.
Monte-Carlo simulations of three different replicate designs covering a wide range of sample sizes and intra-subject variabilities were performed.
At the switching variability of CV wR 30% the consumer risk is substantially inflated to up to 9.2%, which translates into a relative increase of up to 84%. The critical region of inflated type I errors ranges approximately from CV wR 25 up to 45%. The proposed method of iteratively adjusting α maintains the consumer risk at the desired level of ≤5% independent from design, variability, and sample size.
Applying the European Medicines Agency’s ABEL method at the nominal level of 0.05 inflates the type I error to an unacceptable degree, especially close to a CV wR of 30%. To control the type I error nominal levels ≤0.05 should be employed. Iteratively adjusting α is suggested to find optimal levels of the test.
KEY WORDSbioequivalence European Medicines Agency highly variable drugs Monte-Carlo simulation reference-scaling
Average bioequivalence with expanding limits
Area under the curve
Maximum observed concentration
Within-subject coefficient of variation of the reference treatment
European Medicines Agency
(United States) Food and Drug Administration
Geometric means ratio
Highly variable drug (product)
Lower expanded acceptance limit for bioequivalence
Number of subjects in sequence 1, 2
Reference-scaled average bioequivalence
Empiric type I error (probability of α, consumer risk)
Upper expanded acceptance limit for bioequivalence
Nominal level of the statistical test
True T/R ratio
ACKNOWLEDGMENTS AND DISCLOSURES
We would like to thank László Endrényi and Anders Fuglsang for useful comments on an earlier draft of this article. Their comments and challenges directly improved the quality of this article.
- 1.European Medicines Agency, Committee for Medicinal Products for Human Use (2010) Guideline on the Investigation of Bioequivalence. London; 2010 Jan 20. Available from: http://www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/2010/01/WC500070039.pdf.
- 3.Blume HH, KK Midha, editors. Bio-International. bioavailability, bioequivalence and pharmacokinetics. Stuttgart: medpharm Scientific Publishers; 1993.Google Scholar
- 7.Tóthfalusi L, Endrényi L. Sample sizes for bioequivalence studies for highly variable drugs. J Pharm Pharmaceut Sci. 2012;15(1):73–84.Google Scholar
- 9.European Medicines Agency, Committee for Human Medicinal Products. Questions & Answers: positions on specific questions addressed to the Pharmacokinetics Working Party (PKWP). London; 2015 Nov 19. Available from: http://www.ema.europa.eu/docs/en_GB/document_library/Scientific_guideline/2009/09/WC500002963.pdf.
- 13.Chow S-C, J-p L. Design and analysis of bioavailability and bioequivalence studies. Boca Raton: Chapman & Hall/CRC Press; 2009. p. 596–8.Google Scholar
- 14.d_labes (Berlin, DE). RSABE/ABEL: ‘alpha’ of scaled ABE? In: Bioequivalence and Bioavailability Forum [Internet]. Vienna: BEBAC; 2013 Mar 15. Available from: http://forum.bebac.at/mix_entry.php?id=10202.
- 19.Labes D, Schütz H, Lang B. PowerTOST: power and sample size based on Two One-Sided t-Tests (TOST) for (Bio)Equivalence Studies. R package version 1.3–5. 2016. Available from: https://cran.r-project.org/package=PowerTOST.
- 20.R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna; 2016. Available from: https://www.r-project.org/.
- 22.Brent RP. Algorithms for minimization without derivatives. Mineola: Dover Publications; 2003.Google Scholar
- 23.European Generic Medicines Association. Revised EMA Bioequivalence Guideline. Questions & Answers. Summary of the discussions held at the 3rd EGA Symposium on Bioequivalence. London: 2010 Jun. Available from: http://www.medicinesforeurope.com/wp-content/uploads/2016/03/EGA_BEQ_QA_WEB_QA_1_32.pdf.
- 24.Blume H, Kübel-Thiel K, Reutter B, Siewert M, Stenzhorn G. [Nifedipin: Monographie zur Prüfung der Bioverfügbarkeit/Bioäquivalenz von schnell-freisetzenden Zubereitungen]. Pharm Ztg. 1988;133:389–93. German.Google Scholar
- 25.Commission of the European Communities, CPMP Working Party on the Efficacy of Medicinal Products. Investigation of Bioavailability and Bioequivalence. Note for Guidance III/54/89-EN, 9th Draft. Brussels: 1991.Google Scholar
- 26.Health Canada, Therapeutic Products Directorate. Guidance Document. Comparative Bioavailability Standards: Formulations Used for Systemic Effects. Ottawa:2012 May 22. Available from: http://www.hc-sc.gc.ca/dhp-mps/alt_formats/pdf/prodpharma/applic-demande/guide-ld/bio/gd_standards_ld_normes-eng.pdf.
- 27.European Medicines Agency, Committee for Medicinal Products for Human Use. Concept paper for an addendum to the note for guidance on the investigation of bioavailability and bioequivalence: evaluation of bioequivalence of highly variable drugs and drug products. London; 2006 Apr 27. Available from: http://bebac.at/downloads/14723106en.pdf.
- 33.ClinicalTrial.gov. A service of the U.S. National Institutes of Health [Internet]. Bethesda (MD): U.S. National Library of Medicine  – Identifier NCT01290757 [last updated 2014 May 8]. Available from: https://clinicaltrials.gov/ct2/show/NCT01290757.
- 34.U.S. Department of Health and Human Services, Food and Drug Administration, Center for Drug Evaluation and Research. Guidance for Industry. Statistical Approaches to Establishing Bioequivalence. Rockville (MD): 2001 Jan. Available from: http://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/ucm070244.pdf.
- 35.International Council for Harmonisation. ICH Harmonised Tripartite Guideline: Statistical Principles for Clinical Trials. 1998 Feb 5. Available from: http://www.ich.org/fileadmin/Public_Web_Site/ICH_Products/Guidelines/Efficacy/E9/Step4/E9_Guideline.pdf.
- 36.Commission of the European Communities. Investigation of Bioavailability and Bioequivalence. Note for Guidance III/54/89-EN. Brussels: 1991 Dec. Available from: http://www.clindesc.com/Guidelines_online/3%20Clinical/3.1%20General/3_1_2.pdf.
- 43.World Health Organization. Multisource (generic) pharmaceutical products: guidelines on registration requirements to establish interchangeability. Geneva: 2015 May 20. Available from: http://apps.who.int/medicinedocs/documents/s21898en/s21898en.pdf.