Pharmaceutical Research

, Volume 33, Issue 11, pp 2805–2814 | Cite as

Inflation of Type I Error in the Evaluation of Scaled Average Bioequivalence, and a Method for its Control

  • Detlew Labes
  • Helmut Schütz
Research Paper



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.


bioequivalence European Medicines Agency highly variable drugs Monte-Carlo simulation reference-scaling 



(Average) bioequivalence


Average bioequivalence with expanding limits


Area under the curve


Confidence interval


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)


Regulatory constant


Lower expanded acceptance limit for bioequivalence


Sample size


Number of subjects in sequence 1, 2


Reference product


Reference-scaled average bioequivalence


Test product


Empiric type I error (probability of α, consumer risk)


Upper expanded acceptance limit for bioequivalence


Nominal level of the statistical test


Adjusted α


True T/R ratio



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.

Supplementary material

11095_2016_2006_MOESM1_ESM.doc (994 kb)
ESM 1 (DOC 994 kb)
11095_2016_2006_MOESM2_ESM.xls (203 kb)
ESM 2 (XLS 203 kb)


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Cooperative Clinical Drug Research and Development AGNeuenhagenGermany
  2. 2.BEBAC – Consultancy Services for Bioequivalence and Bioavailability StudiesViennaAustria

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