Bioequivalence and Bioavailability Forum

To whom it may concern,

❝ Ehhm, do I get this completely wrong or does Fig.4, lower half in Wonnemann, 2014 tell a different story? Just asking...

Figure 4 (both parts) is misleading. Let’s concentrate on the lower part. The sample sizes (× N_total) are for an expected GMR of 1 and 80% power (see Table II below). These sample sizes were taken from the paper of the two Lászlós. Their table is a little bit unfortunate because sometimes sample sizes are imbalanced (e.g., 25 mod 3 ≠ 0). The filled circles give the chance to pass BE with a GMR of 1.25, which – as Alfredo correctly noted – is irrelevant if scaling is applied. Therefore, the label­ing of the y-axis is not unfortunate. If the Null is modified, the relevant value for the GMR would be one of he scaled limits.
Example for the partial replicate design GMR 1, ≥80% power (10⁵ simulations for the sample size and 10⁶ sim’s for the type I error):





Maximum inflation of the TIE 0.0684 (at CV 30.1%). If one designs the study for higher power, the TIE would further increase. In studies with ≥90% power the maximum TIE would be 0.0697.

As Alfredo also noted (and mentioned by the Lászlós as well) we could expect higher inflation of the TIE if the GMR moves away from 1. This time 0.9 (recommended for HVDs):





Maximum inflation of the TIE 0.0716 (or 0.0727 if designed for ≥90% power).

Generally slightly higher inflation is seen in fully replicated designs. Overview:

design  GMR  % power  TIEmax
2×3×3   1.0     80    0.0684
        0.9     80    0.0716
        1.0     90    0.0697
        0.9     90    0.0727
2×2×4   1.0     80    0.0782
        0.9     80    0.0817
        1.0     90    0.0795
        0.9     90    0.0824
2×2×3   1.0     80    0.0835
        0.9     80    0.0878
        1.0     90    0.0845
        0.9     90    0.0891


2×3×3: TRR|RRT|RTR, 2×2×4: TRTR|RTRT, 2×2×3: TRT|RTR.

In the last case we are already close to the TIE of 1–(1–0.05)²=0.0975 expected for two simul­ta­ne­ous tests at α 0.05.

@Alfredo: Since the inflation of the TIE not only depends on the observed CV_wR but also – though to a minor degree – on the sample size (dropouts…) it is difficult to counteract the inflation by a pre-­spe­cified adjusted α. I’m not sure yet whether even Bonferroni’s 0.025 could maintain the TIE at 5% in all cases.* However, generally less adjustment will be required (especially for a higher CV_wR). “Iteratively ad­justed α” is a procedure to find a suitable value (given the study’s CV_wR and n) which would keep the pa­tient’s risk for the modified Null (i.e., at the scaled limits) at 5%. Only the procedure could be stated in the protocol. Hence, since the CI will be wider than the GL’s 90% CI I think that – as a con­ser­va­tive approach – it should be acceptable for regulators.

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• Extreme example: Design TRT|RTR, GMR 0.85, power ≥99%, n 506. At CV 0.301 TIE 0.0927. With Bonferroni’s α_adj 0.025 the TIE is still 0.0532 (significantly >0.05; binomial test).