Bioequivalence and Bioavailability Forum

Hi BEQool,

❝ 1. If we dont pass BE in the first stage, why do we have to assume a fixed GMR (i.e. 95% - same as before the 1st stage) when doing sample size estimation for the 2nd stage?

Because the methods (not only Potvin’s) were only validated for a fixed GMR. No own simulations needed.
BTW, I once saw a deficiency letter form a European assessor stating the Potvin’s grid (Method B!) was not narrow enough and an inflated type I error ‘might be observed between the tabulated values’. Bullshit. Excuse my French.

❝ Why dont we just use the observed GMR from the 1st stage? Because TIE would increase?

In this case you have to (a) perform own simulations covering a wide range of n₁ and CV with a reasonably narrow grid in order to find a suitable \(\alpha_\text{adj}\) and (b) convince regulators that this adjustment is justified, i.e., controls the type I error. If you want to give it a try, set usePE = TRUE in the power-functions of the package Power2Stage. Don’t forget to assess also power and the distribution of expected total sample sizes. Might go through the ceiling. You can consider the alternative functions *.fC(), allowing to specify a futility on the sample size, the PE or its CI. Its a hit and miss.

❝ Has anyone ever gone into the 2nd stage with sample size estimation based on observed GMR from the 1st stage and the agency accepted it without any objections?

Not me.

❝ Additionally, if we use fixed GMR for both stages, can we also use GMR for example 92% from the beginning (not exactly GMR=95%)?

If you performed own simulations before (see above), yes.

❝ 2. I understand the difference between Group Sequential Designs and Adaptive Two-Stage Sequential Designs, but I have troubles understanding what exactly are Add-On Designs. Here Add-On Designs are defined as "Sample sizes of both groups have a lower limit." Could anyone please explain what this exactly means?

In a classical GSD you assume a ‘worst case’ CV. Based on that you design the study for N subjects. According to Pocock’s approach you perform one interim analysis at exactly n/2 with an adjusted \(\alpha_\text{adj}\). If you pass BE, you stop. Otherwise, you continue with the second group of n/2 subject and perform an analysis of pooled data at the end with the same \(\alpha_\text{adj}\). Drawback: Even if you fail by a small margin in the first group, you have to go full throttle. Ethically and economically questionable, IMHO.
Note that Potvin’s \(\alpha_\text{adj}=0.0294\) in their TSD with sample size re-estimation (not a GSD!) was a lucky punch. That’s for a superiority testing in a parallel design and known variances. For equivalence \(\alpha_\text{adj}=0.0304\)… Known variance? Gimme a break.
Apart from Mexico (?) Add-On designs are history. Japan recommended them for ages but without adjusting the level of the tests, which lead to a massive inflation of the type I error.

❝ 3. And the last question, according to this slide there are currently no Two Stage Sequential methods for replicate designs and designs with 2 formulations.

Correct. A manuscript was submitted last year to the AAPS Journal but not accepted. The authors failed to demonstrate control of the type I error. I was not surprised (see below).

❝ a) why cant we use Two-Stage Sequential design for replicate designs (for example 2x2x3)? I assume you have to use the same design in both stages (in 1st and 2nd), but other than that, why cant we use it (using adjusted alpha of course)?

I guess you are thinking about scaled average bioequvalence (ABEL or RSABE)? How would you find a suitable one? For the type I error you need 10⁶ simulations. Doable in a 2×2×2 and parallel design because there is an exact formula for power. Multiply that with the number of grid points. Takes some time, but OK. On the contrary in SABE there is no analytical solution for power and we need 10⁵ simulations for the sample size re-estimation of every grid point. See this article. Good luck!

❝ b) regarding 2 formulations, so there is no way to go into the study with 2 test formulations and then choose the best one to go into the 2nd stage if we dont pass the BE in the 1st stage? Of course alpha should be adjusted both for 2 test formulations and one interim analysis - so I would say Bonferroni (most conservative) alpha correction with alpha 1.667% (3 hypotheses) or alpha 1.25% (4 hypotheses) should be used?

If you are adventurous… I did it once, but stopped in the interim for success. Was accepted but there is no guarantee.

Hi BEQool,

❝ 1. If we dont pass BE in the first stage, why do we have to assume a fixed GMR (i.e. 95% - same as before the 1st stage) when doing sample size estimation for the 2nd stage? Why dont we just use the observed GMR from the 1st stage? Because TIE would increase?

❝ Has anyone ever gone into the 2nd stage with sample size estimation based on observed GMR from the 1st stage and the agency accepted it without any objections?

My views differ perhaps a bit from Helmut's. I think everybody who played around with TSD's tried it and found out it did not work.
The reason is very simple:
After the first stage you will very, very often (painfully often!) end up in a scenario where it is impossible to achieve 80% power or whatever you are aiming for. Often course it depends on the simulated CV and GMR but this is a very concrete and practical drawback that completely kills all practical use of the observed GMR for planning of stage 2.
Remember: Power is the same as alpha when you are on the acceptance border. So, at GMR=0.8 your power can never exceed alpha. Which means that even well within acceptance borders there are areas of GMR where you cannot achieve 80% power regardless of your sample size. It completely does not work.
I played around with all sorts of ways to circumvent it. Didn't come up with anything of practical use. For example, trying to halve the distance from the observed GMR to 1 and plugging this into sample size calc. I.e. if we get a GMR of 1.28 then we do GMR'=1.00+(1.28-1.00)/2 = 1.14 and plug it into the sample size calc. Tried many other variants of such a principle. Nothing that I tried works well.

❝ b) regarding 2 formulations, so there is no way to go into the study with 2 test formulations and then choose the best one to go into the 2nd stage if we dont pass the BE in the 1st stage? Of course alpha should be adjusted both for 2 test formulations and one interim analysis - so I would say Bonferroni (most conservative) alpha correction with alpha 1.667% (3 hypotheses) or alpha 1.25% (4 hypotheses) should be used?

There is a paper about running a stage 1 with two test formulations. Then picking the best one and doing stage 2 with it. I think it was some Danish weirdo who published it. That wasn't a replicate design, though.