## Tricky question, lengthy answer [Power / Sample Size]

Hi Olivbood,

» […] bioequivalence study which would aim at assessing drug effect and food effect at the same time (in order to bridge the clinical formulation with the market formulation) with a 3-Treatment Williams Design (3x6x3).
»
» A = the clinical formulation (reference) under fasting status,
» B = the market formulation (test 1) under fasting status,
» C = the market formulation (test 2) under fed status
»
» The goal of the study is to asses the FE on the market formulation in addition to BE between the market and clinical formulations, so that we would test C vs B and A vs B.
»
» Primary Pk parameters for the study would be AUC0-inf, AUC0-t, and Cmax, for which I have CV intra estimates from a previous single sequence study where subjects took the clinical formulation in a single dose for the first period, and then took repeated doses of the clinical formulation in the second period.

Some obstacles. That was a paired design. Not unusual but you have to assume no period effect. This comparison makes only sense for AUC0–τ (steady state) vs. AUC0–∞ (SD), i.e., if you were within some pre-specified limits you demonstrated linear PK. Since CVintra of AUC0–∞ generally is larger than the one of AUC0–t, no worries. On the other hand what you got from this study is pooled from AUC0–∞ and AUC0–τ, where quite often the variability is steady state is lower than the one after a SD. Hence, allow for a safety margin.
The most important CV is the one of Cmax. Here I would allow for an even larger safety margin (in steady state its variability might be substantially lower than after a SD). In other words, the lower CV in steady state dampens the pooled CV and the one you will observe after a SD likely will be higher.
In the crossover you will have one degree of freedom less than in the paired design (the CI will be wider). Given, peanuts.
Now it gets nasty. In many cases the variability in fed state is (much) higher than in fasted state. I have seen too many studies of generics (sorry) where the fasting study passed (“We perform it first because that’s standard.”) – only to face a failed one in fed state. Oops! Hence, I always recommend to perform the fed study first. For you that’s tricky since you have only data of fasted state. What about a pilot or a two-stage design? I prefer the latter because with the former you throw away information. In a TSD you can stop the arms which are already BE in the first stage (likely the fasting part) and continue the others to the second stage.

» My first question would be, do I need to power the study to get average bioequivalence on each of the PK param or just one is sufficient?
»
» The FDA guidance "Food-Effect Bioavailability and Fed Bioequivalence Studies" notes that:
»
» "For an NDA, an absence of food effect on BA is not established if the 90 percent CI for the ratio of population geometric means between fed and fasted treatments, based on log-transformed data, is not contained in the equivalence limits of 80-125 percent for either AUC0-inf (AUC0-t when appropriate) or Cmax".
• EMA
• B vs. A
AUC0–t and Cmax. If modified release additionally AUC0–∞ (once you cross flip-flop PK with ka ≤ ke the late part of the profile represents absorption).
• C vs. B
As above.
• FDA
• B vs. A
AUC0–t, AUC0–∞, and Cmax.
• C vs. B
Tricky. I prefer always AUC0–t over AUC0–∞ due to its intrinsic lower variability. I never understood why the FDA asks for AUC0–∞ at all. There are a couple of papers (one even by authors of the FDA…) showing that once absorption is essentially complete (for IR 2×tmax), the PE is stable and only its variability increases. I would initiate a controlled correspondence arguing in this direction (what does “when appropriate mean”?).
“Or Cmax is strange. I can only speculate that the FDA prefers Cmax for MR formulations (where dose-dumping is more likely than for IR). But what about efficacy? Why not AUC and Cmax? I’m afraid that you have to clarify that with the FDA as well. For the sample size estimation it’s not relevant since you have to power the study for the BE-part anyhow.
BTW, you were referring to the FDA’s guidance of Dec 2002 (page 7). The current draft guidance for INDs/NDAs of Feb 2019 (page 9) states “… and Cmax”.
If you are not BE (B vs. A), bad luck.
If you are not within the limits (C vs. B) the food effect goes into the SmPC (EMA) or the label (FDA).

» If I had to compute power to get bioequivalence for all the PK parameters, how should I proceed ? If possible using the package Power.TOST.

You only have to observe the one with the highest variability / largest deviation form unity. Yep, doable in Power.TOST.

» Then, since I am interested in the comparisons C vs B and A vs B, how should I proceed to get power estimates, likewise using the package Power.TOST?

Although you plan for a 3×6×3 Williams’ design, the two parts will be evaluated as incomplete block designs (IBD), having the same degrees of freedom as the conventional 2×2×2 crossover. Hence, in sampleN.TOST() use the argument design="2x2x2" and not design="3x6x3". You will get a small reward:

library(PowerTOST) sampleN.TOST(CV=0.3, design="2x2x2", targetpower=0.9,              print=FALSE)[["Sample size"]] [1] 52 sampleN.TOST(CV=0.3, design="3x6x3", targetpower=0.9,              print=FALSE)[["Sample size"]] [1] 54

» If I remember correctly the EMA advises to analyse the comparisons one at a time,…

» … so should I perform a multiplicity adjustment? Since only the marketed formulation would then be prescribed to the patients I would not use multiplicity correction, but since I plan to interpret both comparisons independently I'm not sure...

Yep, that’s fine.

Dif-tor heh smusma 🖖
Helmut Schütz

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