Bioequivalence and Bioavailability Forum

Dear all,

I want to share with you a recent example. Endogenous drug, baseline with circadian rhythm. Borderline highly variable, both for C_max and AUC. Previous studies contradictory; CV reported with ~20–40%. Since for an European submission scaling AUC is not possible and the CV was unclear we considered various TSDs (“type 1”: T/R 0.95, target power 80% with optimized adjusted α for n₁ 16–66, CV 15–60%). We were also exploring the impact of various futility rules. Left panels empiric Type I error, right panels % power (lower surface in the first stage and upper one overall).

I.    α 0.0302 (93.96% CI), no futility criterion



II.    α 0.0306 (93.88% CI), futility criterion ]0.8000–1.2500[



III.    α 0.0313 (93.74% CI), futility criterion ]0.8250–1.2121[



IV.    α 0.0327 (93.46% CI), futility criterion ]0.8500–1.1765[

TIE_max-values are 0.05003 (I), 0.04995 (II), 0.05000 (III), and 0.05005 (IV).

TIE-surfaces show the shape common to “type 1” TSDs. With futility rules the methods become in­creas­ingly conservative at the extreme combinations of n₁/CV.
Trivial observation: Increasingly restrictive futility rules prevent more studies from proceeding to the second stage. Therefore, we need less adjustment of α.
Hey, wider CIs! Are we more likely too pass and/or pay a smaller sample size penalty? On the contrary. Anders¹ already showed last year that futility rules on the total sample size may substantially deteriorate power. For an example of the full adaptive methods proposed by Karalis/Macheras see the recent review.² We get a similar effect for the GMR here. In the right panels white lines show the intersection with the plane of 80% power. With increasingly restrictive futility rules only small changes in the first stage’s power but overall the surface is lower and tilted down.

1. Without a futility rule overall power is generally ≥80% – unless the first stage was small and one will be hit by a high CV. The 80%-border runs almost linear from n₁ 16 / CV 33% to n₁ 46 / CV 60%. However, even for n₁ 16 and CV 60% power is still 75.2%. For such a stupidly low n₁ one deserves it to be punished by an average total sample size of 159… Don’t go there.
   
2. A futility of ]0.8–1.25[ (as proposed by Peter Armitage) is still suitable – if the sample size is not too small for the “best guess” CV.
   
3. With ]0.8250–1.2121[ we enter a slippery field. For moderate sample sizes it may be difficult to maintain the desired power.
   
4. A futility of ]0.8500–1.1765[ (proposed by Charles Bon) makes only sense if one is willing to start in a relatively large sample size and is confident that the CV will not be too high…

We must not forget that in my example we had to deal with a borderline HVD, Assuming a T/R of 0.95 is nice, but who knows? Remember that the two Lászlós recommend a T/R of 0.90 for RSABE. Our final design was (based on a “best guess” CV of 30%) a sample size of 46 and an FC of ]0.8250–1.2121[. We expect for this CV a power in the first stage of 80.9% and 67.2% for a CV of 35%. Chances to proceed to the second stage are 10.1% and 28.2%. Overall-power is expected with 85.3% and 83.2%. We will have still 80% power for a CV up to 46% (very unlikely, anyhow). In this extreme case the average total sample size will be 79. Let’s see.

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1. Fuglsang A. Futility rules in bioequivalence trials with sequential designs. AAPS J. 2014;16(1):79–82. doi:10.1208/s12248-013-9540-0
   
2. Schütz H. Two-stage designs in bioequivalence trials. Eur J Clin Pharmacol. 2015;71(3):271-81. doi:10.1007/s00228-015-1806-2