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have a three armed clinical trial with two treatments and one placebo. I am to compare the Restricted Mean Survival Time among the three.

I need to find the sample sizes for each arms (equal allocation)

I know that R software has survRM2 package for calculating sample sizes for a RMST of two armed trial. The code as used is:

library(SSRMST) ssrmst(ac_rate=ac_rate, ac_period=ac_period, tot_time=tot_time, tau=tau, shape0=shape0, scale0=scale0, shape1=shape1, scale1=scale1, margin=margin, seed=seed)

So, my question is, how do I use this package to calculate sample size for a three armed trial (with equal allocation). How will the above code modify?

Any guidance will be very helpful.

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    $\begingroup$ Do you want to compare the treatment arms to each other? Or do you just want to compare each treatment arm to the control? $\endgroup$
    – num_39
    Commented Feb 23, 2022 at 19:59
  • $\begingroup$ Would like to compare the treatement arms to each other. $\endgroup$
    – OJS
    Commented Feb 23, 2022 at 20:14
  • $\begingroup$ @num_39 Was consulting the internet regarding this question and found that the case you are mentioning as in if we compare each treatement with control only, we might lower the p value and use the same formula for sample size. Is this theory valid ? $\endgroup$
    – OJS
    Commented Feb 23, 2022 at 23:30

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You can think about a trial with multiple treatment arms as multiple trials. I'm not familiar with the function you've referenced above, but I don't see why you can't use it to separately estimate the required sample size for each of your trials and then to take the largest required sample for each group, $treatment_1$, $treatment_2$, and $control$, as the required sample size.

Presuming that you expect the difference between $treatment_1$ and $treatment_2$ will be much smaller than the difference between either treatment arm and control, this comparison between treatment arms will require you to dramatically increase your sample size. For other approaches to a multi-armed trial, see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4843088/ and for a discussion related to a three arm "non-inferiority" approach see this paper by Stucke and Kieser.

Now as you note, instead of doing one test (between treatment and control), you'll now be doing three tests. If you want to adjust for making multiple comparisons, then you will indeed need to increase your sample size further by decreasing the alpha you're using for the power calculation. Whether you need to adjust for multiple comparisons is debated. See this article for an overview: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4177585/

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