### Abstract

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 language | English |
---|---|

Pages (from-to) | 186-190 |

Number of pages | 5 |

Journal | Pharmaceutical Research |

Volume | 16 |

Issue number | 2 |

Publication status | Published - 1999 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Chemistry(all)
- Pharmaceutical Science
- Pharmacology

### Cite this

*Pharmaceutical Research*,

*16*(2), 186-190.

**Subject-by-formulation interaction in determinations of individual bioequivalence : Bias and prevalence.** / Endrenyi, Laszlo; Tóthfalusi, L.

Research output: Contribution to journal › Article

*Pharmaceutical Research*, vol. 16, no. 2, pp. 186-190.

}

TY - JOUR

T1 - Subject-by-formulation interaction in determinations of individual bioequivalence

T2 - Bias and prevalence

AU - Endrenyi, Laszlo

AU - Tóthfalusi, L.

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

KW - Crossover design

KW - Individual bioequivalence

KW - Intra-subject variation

KW - Maximum likelihood

KW - Regulatory criterion

KW - Subject-by-formulation interaction

UR - http://www.scopus.com/inward/record.url?scp=0033013237&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033013237&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 186

EP - 190

JO - Pharmaceutical Research

JF - Pharmaceutical Research

SN - 0724-8741

IS - 2

ER -