Bioequivalence

The ICH M13 series

M13 is the first globally harmonised bioequivalence guidance, replacing a patchwork of regional requirements.

Until M13C is adopted, reference-scaled approaches remain regional and mutually incompatible. That is the single most important practical fact about scaled BE: FDA and EMA do not accept each other's method, and a study must be designed for the criterion of the agency it is going to.

Average bioequivalence

The default criterion everywhere:

The 90% confidence interval for the geometric mean ratio (test/reference) of AUC and Cmax must lie entirely within 80.00% to 125.00%.

Computed on log-transformed data — the interval is symmetric on the log scale and asymmetric back-transformed, which is why the limits are 0.80 and 1.25 rather than ±20%.

Narrow therapeutic index drugs are tightened to 90.00-111.11% in several regions, and the FDA additionally requires a comparison of within-subject variability between test and reference.

Designs

A crossover removes between-subject variability, which is why it needs far fewer subjects than a parallel design. It requires an adequate washout — at least 5 terminal half-lives — and pre-dose concentrations in later periods should be below 5% of Cmax, or the subject is excluded.

Reference-scaled approaches for highly variable drugs

A highly variable drug is one with CVwR > 30%. Both approaches require a replicate design; neither can be applied to a 2×2 study however high the observed variability, because without repeated reference administrations there is no CVwR to scale to.

EMA: average bioequivalence with expanding limits (ABEL)

limits = exp(± 0.760 * swR)      capped at CVwR = 50%  ->  69.84% - 143.19%

Conditions: replicate design; the widening must be pre-specified in the protocol with clinical justification; the point estimate must still fall within 80.00-125.00%; and widening is applied to Cmax (and for some products AUC, though EMA generally does not permit AUC widening).

FDA: reference-scaled average bioequivalence (RSABE)

Not an interval criterion at all. The criterion is

(mu_T - mu_R)^2 - theta^2 * s2wR  <=  0        with theta = ln(1.25)/0.25 = 0.8926

evaluated as a 95% upper confidence bound using Hyslop's linearised method:

E  = (Ybar_T - Ybar_R)^2                    Eh = (|Ybar_T - Ybar_R| + t(0.95,df)*SE)^2
H  = -theta^2 * s2wR                        Hh = -theta^2 * s2wR * df / chi2(0.05, df)
upper bound = E + H + sqrt((Eh-E)^2 + (Hh-H)^2)

Pass requires the upper bound ≤ 0 and the point estimate within 80-125%. Applied when CVwR ≥ 30%; below that, unscaled ABE applies. bioequivalence.py --scaling rsabe implements this.

The two criteria can disagree on the same dataset. Which applies is a regulatory fact, not a statistical choice, and must be pre-specified.

Sample size

Driven by three things, in order of influence: the assumed true GMR, the within-subject CV, and the target power.

Published values for a 2×2 crossover, GMR 0.95, 80% power, 80-125% limits — reproduced exactly by bioequivalence.py --power:

Assuming a GMR of 1.00 rather than 0.95 roughly halves the calculated N, and is the most common reason a bioequivalence study comes in underpowered. A GMR of exactly 1.00 is not a realistic planning assumption for two different formulations.

Power must be computed by integrating over the sampling distribution of the estimated standard deviation (equivalently, Owen's Q). Treating the standard error as known overstates power at these sample sizes.

Common errors

1. Using a t test. "p > 0.05, therefore the formulations are equivalent" inverts the hypothesis. Failing to detect a difference is not evidence of equivalence, and on a small BE dataset that outcome is nearly guaranteed. The 90% CI (equivalently, two one-sided tests at α = 0.05) is the test.
2. Analysing untransformed data. AUC and Cmax are log-normal; the criterion is defined on the log scale.
3. Scaling from a 2×2 design. Refused by bioequivalence.py, and by regulators.
4. Post hoc scaling. Deciding to widen limits after seeing high variability is not pre-specification.
5. Dropping subjects after unblinding for reasons not defined in the protocol.
6. Reporting only AUC. Cmax must meet the criterion too, and it is the more variable of the two.
7. Ignoring the period effect by analysing as a paired comparison. bioequivalence.py labels this explicitly when the sequence column is missing.

Endogenous compounds and other special cases

• Endogenous substances (potassium, iron, hormones) require baseline correction, and the baseline-correction method changes the answer. Pre-specify it.
• Long half-life drugs: AUC(0-72h) is accepted in place of AUC(0-inf) under M13A for immediate release products, avoiding a very long sampling schedule.
• Highly variable Cmax with acceptable AUC is the usual pattern that pushes a programme towards a replicate design.
• Fed versus fasted: both usually required; the food effect study is separate from BE.