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

Pharmaceutical Research volume 33, pages2805–2814(2016)Cite this article

Abstract

Purpose

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.

Methods

Monte-Carlo simulations of three different replicate designs covering a wide range of sample sizes and intra-subject variabilities were performed.

Results

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.

Conclusions

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.

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Abbreviations

(A)BE:

(Average) bioequivalence

ABEL:

Average bioequivalence with expanding limits

AUC :

Area under the curve

CI:

Confidence interval

C max :

Maximum observed concentration

CV wR :

Within-subject coefficient of variation of the reference treatment

EMA:

European Medicines Agency

FDA:

(United States) Food and Drug Administration

GMR :

Geometric means ratio

HVD(P):

Highly variable drug (product)

k :

Regulatory constant

L :

Lower expanded acceptance limit for bioequivalence

N :

Sample size

n 1,2 :

Number of subjects in sequence 1, 2

R:

Reference product

RSABE:

Reference-scaled average bioequivalence

T:

Test product

TIE:

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

U :

Upper expanded acceptance limit for bioequivalence

α :

Nominal level of the statistical test

α adj :

Adjusted α

θ :

True T/R ratio

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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.

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  1. Cooperative Clinical Drug Research and Development AG, 15366, Neuenhagen, Germany

    Detlew Labes

  2. BEBAC – Consultancy Services for Bioequivalence and Bioavailability Studies, 1070, Vienna, Austria

    Helmut Schütz

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  1. Detlew Labes
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Correspondence to Helmut Schütz.

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Labes, D., Schütz, H. Inflation of Type I Error in the Evaluation of Scaled Average Bioequivalence, and a Method for its Control. Pharm Res 33, 2805–2814 (2016). https://doi.org/10.1007/s11095-016-2006-1

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KEY WORDS

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