Clinical Pharmacokinetics

, Volume 52, Issue 12, pp 1033–1043

Random-Effects Linear Modeling and Sample Size Tables for Two Special Crossover Designs of Average Bioequivalence Studies: The Four-Period, Two-Sequence, Two-Formulation and Six-Period, Three-Sequence, Three-Formulation Designs

  • Francisco J. Diaz
  • Michel J. Berg
  • Ron Krebill
  • Timothy Welty
  • Barry E. Gidal
  • Rita Alloway
  • Michael Privitera
Leading Article


Due to concern and debate in the epilepsy medical community and to the current interest of the US Food and Drug Administration (FDA) in revising approaches to the approval of generic drugs, the FDA is currently supporting ongoing bioequivalence studies of antiepileptic drugs, the EQUIGEN studies. During the design of these crossover studies, the researchers could not find commercial or non-commercial statistical software that quickly allowed computation of sample sizes for their designs, particularly software implementing the FDA requirement of using random-effects linear models for the analyses of bioequivalence studies. This article presents tables for sample-size evaluations of average bioequivalence studies based on the two crossover designs used in the EQUIGEN studies: the four-period, two-sequence, two-formulation design, and the six-period, three-sequence, three-formulation design. Sample-size computations assume that random-effects linear models are used in bioequivalence analyses with crossover designs. Random-effects linear models have been traditionally viewed by many pharmacologists and clinical researchers as just mathematical devices to analyze repeated-measures data. In contrast, a modern view of these models attributes an important mathematical role in theoretical formulations in personalized medicine to them, because these models not only have parameters that represent average patients, but also have parameters that represent individual patients. Moreover, the notation and language of random-effects linear models have evolved over the years. Thus, another goal of this article is to provide a presentation of the statistical modeling of data from bioequivalence studies that highlights the modern view of these models, with special emphasis on power analyses and sample-size computations.

Supplementary material

40262_2013_103_MOESM1_ESM.txt (31 kb)
Supplementary material 1 (TXT 30 kb)


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Francisco J. Diaz
    • 1
  • Michel J. Berg
    • 2
  • Ron Krebill
    • 1
  • Timothy Welty
    • 3
  • Barry E. Gidal
    • 4
  • Rita Alloway
    • 5
  • Michael Privitera
    • 6
  1. 1.Department of BiostatisticsThe University of Kansas Medical CenterKansas CityUSA
  2. 2.Strong Epilepsy CenterUniversity of Rochester Medical CenterRochesterUSA
  3. 3.Department of Clinical Sciences, College of Pharmacy and Health SciencesDrake UniversityDes MoinesUSA
  4. 4.Department of Neurology, School of PharmacyUniversity of WisconsinMadisonUSA
  5. 5.Transplant Section, Division of Nephrology and Hypertension, Department of Internal Medicine, College of MedicineUniversity of CincinnatiCincinnatiUSA
  6. 6.Epilepsy CenterUniversity of Cincinnati Neuroscience InstituteCincinnatiUSA

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