Subject-by-formulation interaction in determinations of individual bioequivalence: Bias and prevalence

Laszlo Endrenyi, Laszlo Tothfalusi

Research output: Contribution to journalArticle

19 Citations (Scopus)


Purpose. 1. To determine properties of the estimated variance component for the subject-by-formulation interaction (σ(D)/2) in investigations of individual bioequivalence (IBE), and 2. to evaluate the prevalence of interactions in replicate-design studies published by FDA. Methods. Four- period crossover studies evaluating IBE were simulated repeatedly. Generally, the true bioequivalence of the two formulations, including σ(D)/2 = 0, was assumed. σ(D)/2 was then estimated in a linear mixed-effect model by restricted maximum likelihood (REML). The same method was applied for estimating σ(D)/2 for the data sets of FDA. Results. 1. σ(D) estimated by REML was positively biased. The bias and dispersion of the estimated σ(D) increased approximately linearly with the estimated within-subject standard deviation for the reference formulation (σ(WR)). Only a small proportion of the estimated σ(D) exceeded the estimated σ(WR). 2. Distributions of the estimated σ(D) were evaluated. At σ(WR) = 0.30, a level of estimated σ(D) = 0.15 was exceeded, by random chance, with a probability of about 25%. 3. Importantly, the behaviour of the σ(D)/2 values estimated from the FDA data sets was similar to that exhibited by the simulated estimates of σ(D)/2 which were generated under the conditions of true bioequivalence. Conclusions. 1. σ(D) estimated by REML is biased; the bias increases proportionately with the estimated σ(WR). Consequently, exceeding a fixed level of σ(D) (e.g., 0.15) does not indicate substantial interaction. 2. The data sets of FDA are compatible with the hypothesis of σ(D)/2 = 0. Consequently, they do not demonstrate the prevalence of subject-by- formulation interaction. Therefore, it could be sufficient and reasonable to evaluate bioequivalence from 2-period crossover studies.

Original languageEnglish
Pages (from-to)186-190
Number of pages5
JournalPharmaceutical Research
Issue number2
Publication statusPublished - Jan 1 1999


  • Crossover design
  • Individual bioequivalence
  • Intra-subject variation
  • Maximum likelihood
  • Regulatory criterion
  • Subject-by-formulation interaction

ASJC Scopus subject areas

  • Biotechnology
  • Molecular Medicine
  • Pharmacology
  • Pharmaceutical Science
  • Organic Chemistry
  • Pharmacology (medical)

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