three-arm non inferiority trial - SAMPLE SIZE

[ashar ata]

I was reaching out to get some advice on sample size for a study. The goal is to show non-inferiority of (E) compared to (R) . But we also wanted to include a placebo. So the study will basically be a three armed non-inferiority placebo controlled clinical trial. It will therefore have two hypotheses-
a) superiority of Experimental (E) over placebo (P) and
b) non-inferiority of experimental (E) compared to reference (R)

Three arms are Experimental, Placebo and Reference

• Outcome is a continuous variable (O).
• Standard Deviation (SD) of outcome in E and R groups is known and is similar.
• Delta for meaningful difference for the superiority trial is D_s and is half of SD
• Delta for the non-inferiority between E and R is D_ni and is half of D_s

The question I have is how should we assess the sample size based on these two hypothesis. Based on the literature I have reviewed sample size estimations for three-armed non-inferiority trial have been discussed and some methods have been proposed. The attached paper by Zhou and Kundu suggests a two stage estimation. They also provide the R code for it and I am trying to figure it out.
Is there and alternative method to approach this sample size estimation? I explored STATA’s ssi, fpower , power command packages and none of them provide solution to account for a three arm non-inferiority trial.

Any suggestions or recommendations?
Thanks
Ashar

[Joseph Coveney]

I don't know what Zhou et al. say, but why not compute the sample size required for each and then take the greater of the two?

If you're having trouble analytically computing the sample size for the noninferiority part, then express it in terms of a confidence bound and use simulation.

[Tomasz Stryjewski]

I have an unrelated question regarding design of non-inferiority studies. We are looking to show inferiority of CONTROL X in comparison to TREATMENT Y.

I have been using ssi but it only results in balanced sample size groups.

Ideally, I would like to have 2 treatment for every 1 control. Does anyone know how to do this?

[ashar ata]

Tomasz
I suggest that you post this as new topic under the general forum as you also mentioned this is an unrelated question. . Also your question is not clear.
If you are "looking to show inferiority of CONTROL X in comparison to TREATMENT Y" you can simply use STATA's sampsi command with the ratio option. But please post your question or a follow up to this answer as well as new topic.
Thanks

[ashar ata]

I don't know what Zhou et al. say, but why not compute the sample size required for each and then take the greater of the two?

If you're having trouble analytically computing the sample size for the noninferiority part, then express it in terms of a confidence bound and use simulation.

I am taking the first approach - computing the sample size for each and taking the greater of the two.

However - how would i use simulation for a difference in means non-inferiority comparison and confidence bounds would be based on the standard deviation?