Signature
GMR = exp(d); GMR_L = exp(d - t_crit * SE); GMR_U = exp(d + t_crit * SE)
| Inputs | Definition | Unit |
|---|---|---|
d | Estimated difference in means of the natural log of AUC or Cmax, test minus reference, from the study model | natural log units |
t_crit | 95th percentile of the t distribution with the residual degrees of freedom of the model, n minus 2 for a two-period crossover | dimensionless |
SE | Standard error of d from the study model | natural log units |
GMR | Point estimate of the ratio of geometric means of the pharmacokinetic measure | ratio |
|---|---|---|
GMR_L | Lower limit of the 90% confidence interval for the ratio | ratio (multiply by 100 for per cent) |
GMR_U | Upper limit of the 90% confidence interval for the ratio | ratio (multiply by 100 for per cent) |
Function
Average bioequivalence and generic price function
For an ANDA, bioequivalence to the reference listed drug is shown when the 90% confidence interval for the ratio of geometric means of a pharmacokinetic measure, such as AUC or Cmax, lies within 80.00% to 125.00% after rounding. The interval is computed on the log scale and exponentiated. For economic models, the approval of generic competitors is then translated into a post-entry price.
Implementations
Excel
90 per cent interval for the ratio
With the mean log difference in MeanLogDiff, its standard error in SELogDiff and the residual degrees of freedom in DF, the formulas return the ratio and its 90% limits.
=EXP(MeanLogDiff); =EXP(MeanLogDiff-T.INV(0.95,DF)*SELogDiff); =EXP(MeanLogDiff+T.INV(0.95,DF)*SELogDiff)
Assumptions
Log-normal pharmacokinetic measures
AUC and Cmax are analysed after log transformation, as the FDA guidance recommends; normality of the residuals is not tested and is not a reason to analyse on the original scale.
Equal-tails interval and two one-sided tests
Each limit of the 90% interval is by itself a 95% one-sided bound, so the interval test is equivalent to two one-sided tests at the 5% level.
Standard limits for most drugs
The 80.00% to 125.00% limits apply for a broad range of drugs. Narrow therapeutic index drugs, highly variable drugs and some product-specific guidances use scaled or tighter criteria.
Worked examples
Generic that meets the limits
A two-period crossover in 24 subjects gives a mean log difference of minus 0.051293, a ratio of 0.95, with a standard error of 0.06. With 22 degrees of freedom the t quantile is 1.717144, so the 90% interval is 85.70% to 105.31%, inside the limits. The figures are illustrative.
d = -0.051293; SE = 0.06; t_crit = 1.717144; GMR = 0.9500; GMR_L = 0.8570; GMR_U = 1.0531
Generic that fails the lower limit
A ratio of 0.88, a mean log difference of minus 0.127833, with a standard error of 0.07 gives an interval of 78.03% to 99.24%. The point estimate is inside the limits but the lower confidence limit is not, so bioequivalence is not shown.
d = -0.127833; SE = 0.07; t_crit = 1.717144; GMR = 0.8800; GMR_L = 0.7803; GMR_U = 0.9924
Common errors
Testing the point estimate instead of the interval
A ratio of 0.88 lies within 0.80 to 1.25, but its lower confidence limit of 78.03% does not. The criterion applies to the whole 90% interval.
Reading the limits as allowing 20 per cent less drug
The limits apply to the confidence interval for the ratio of exposure measures, not to the drug content of the dose. A product whose true ratio sat near 0.80 would usually fail, because its interval would extend below the limit.
Using a 95 per cent two-sided interval
A 95% two-sided interval corresponds to one-sided tests at 2.5% and is wider than the interval the guidance specifies for average bioequivalence of AUC and Cmax.
Sources
FDA statistical guidance on average bioequivalence
US Food and Drug Administration, Center for Drug Evaluation and Research. Statistical Approaches to Establishing Bioequivalence: Guidance for Industry. Silver Spring, MD: FDA; May 2026. Section I.B (average bioequivalence: 90% confidence interval for the ratio of population geometric means within a limit usually 80.00% to 125.00%; footnote 6, rounded interval at least 80.00% and not more than 125.00%), section II.C.1 (log transformation of AUC and Cmax), section II.D.1.a (two one-sided tests and equal-tails intervals) and Appendix B (rationale for log transformation).
Regulatory definition of bioequivalence
Code of Federal Regulations, Title 21, section 314.3. Definitions (bioequivalence). Accessed 29 September 2026. Bioequivalence: the absence of a significant difference in the rate and extent to which the active ingredient becomes available at the site of drug action when administered at the same molar dose under similar conditions in an appropriately designed study.
Canonical Identity
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