## TSD, GSD, Add-Ons, etc. [Two-Stage / GS Designs]

❝ 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?

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?

*n*

_{1}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?

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

❝ 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?

*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.

❝ 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)?

^{6}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 10

^{5}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?

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!

_{}

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

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### Complete thread:

- Two-Stage Sequential Potvin Designs BEQool 2024-03-04 08:45 [Two-Stage / GS Designs]
- TSD, GSD, Add-Ons, etc.Helmut 2024-03-05 13:56
- Two-Stage Sequential Potvin Designs ElMaestro 2024-03-05 20:51
- Two-Stage Sequential Potvin Designs BEQool 2024-03-10 10:11
- Two-Stage Sequential Potvin Designs ElMaestro 2024-03-10 20:18
- Too coarse grid? Helmut 2024-03-10 20:49
- Too coarse grid? ElMaestro 2024-03-10 21:06
- Balance… Helmut 2024-03-12 11:40

- Too coarse grid? ElMaestro 2024-03-10 21:06
- Two-Stage Sequential Potvin Designs BEQool 2024-03-11 20:45

- Too coarse grid? Helmut 2024-03-10 20:49

- Two-Stage Sequential Potvin Designs ElMaestro 2024-03-10 20:18

- Two-Stage Sequential Potvin Designs BEQool 2024-03-10 10:11