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Means: Correlated, Paired, and Cross-Over Designs

Individual Bioequivalence Calculator

Computes the FDA individual bioequivalence (IBE) aggregate criterion and the corresponding linearized criterion on the log scale. The calculation accounts for the Test–Reference mean difference, subject-by-formulation interaction variance, and within-subject variances.

IBE Population Parameters

Enter variance components on the natural-log scale. For a fully replicated 2×4 crossover design, these are the population quantities used by the IBE criterion.

Results

The FDA aggregate criterion is compared with the specified IBE limit. The linearized criterion is shown as the equivalent quantity whose target boundary is zero.
Enter the population parameters and click Calculate IBE Criterion.

Methodology

The FDA individual bioequivalence criterion compares the squared Test–Reference mean difference, subject-by-formulation interaction variance, and the difference between Test and Reference within-subject variances. The denominator uses the larger of the Reference within-subject variance and the specified constant variance.

η = [(μT − μR)2 + σ2D + σ2WT − σ2WR] / max(σ2W0, σ2WR)

Under the FDA formulation described in the literature, individual bioequivalence corresponds to the alternative η < θI. The 2001 FDA guidance used θI = 2.4948 with σ2W0 = 0.04.

Linearized Criterion

For the 2×4 replicated crossover design, the linearized criterion is obtained by subtracting the IBE limit multiplied by the scaling denominator:

g = δ2 + σ20.5,0.5 + 0.5σ2WT − 1.5σ2WR − θI max(σ2W0, σ2WR)

σ20.5,0.5 = σ2D + 0.5(σ2WT + σ2WR)

Thus, g < 0 is algebraically equivalent to η < θI at the population-parameter level. When σ2WR ≤ σ2W0, the criterion is constant-scaled; when σ2WR > σ2W0, it is reference-scaled.

Important: This calculator evaluates the population IBE criterion. It does not replace the modified-large-sample (MLS) upper-confidence-bound procedure used for an inferential IBE analysis of observed replicated-crossover data. A regulatory analysis requires estimation of the variance components and construction of the appropriate upper confidence bound.

References

Chiang, C., Hsiao, C.-F., & Liu, J.-P. (2014). Sample Size Determination for Individual Bioequivalence Inference. PLoS ONE, 9(10), e109746. The paper defines the IBE criterion, the linearized criterion, and the MLS approach for replicated 2×4 crossover designs.

Schall, R., & Williams, R. L., for the FDA Individual Bioequivalence Working Group (1996). Towards a practical strategy for assessing individual bioequivalence. Journal of Pharmacokinetics and Biopharmaceutics, 24(1), 133–149.

U.S. Food and Drug Administration (2001). Guidance for Industry: Statistical Approaches to Establishing Bioequivalence. The guidance describes the replicated-crossover framework and the FDA IBE criterion.

For current PASS documentation and procedure listings, see the PASS documentation.