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Let's say we design a RCT for two different populations and want to test an intervention vs a control. It could be adults and children, male and female, etc.

We have one primary endpoint to be tested in both groups. But for each group we will have an intervention and a control, so two intervention arms and two control arms. E.g. intervention and control for adults and intervention and control for children. So the sample sizes are computed for each group.

We could have 60 adults in intervention arm and 60 in control arm. And 85 children in intervention and 85 in control. Because we assume different effects in each group.

If for the study to be considered a success, it is enough to observe a statistical significant difference in only ONE group, do we need to adjust for multiplicity, as if we had a co-primary endpoint? Is it considered a co-primary endpoint?

I am puzzled. As each group has its own control group. Or can these two analysis be considered as coming from two different studies? I would say we don't need to.

Any thoughts are welcome.

EDIT: Usually it more the other way around. We have one population where patients are randomized to one of the two arms and e.g. 2 endpoints. In this case, one method is to compute sample sizes for each endpoint using e.g. Bonferroni correction and then choose the largest sample size to make sure to preserve the type I error. Here I am unsure, could we combine the two populations? And having a single intervention arm and a single control arm? Using some kind of stratified randomization? And then analyze the data using an interaction term between the intervention and the group? Or is it a kind of subgroup analyses?

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    $\begingroup$ It's up to you to decide what it means for the study to be considered a success. How you think about that would then dictate what / how multiple comparison corrections to use. $\endgroup$ Aug 3, 2022 at 19:46
  • $\begingroup$ Do you want to test if the effects are different between the groups? If you did, & you did not find a significant difference, what would you do? Would you test the interventions in the groups together? Alternatively, do you intend to simple assume they're different & proceed accordingly? $\endgroup$ Aug 3, 2022 at 19:48
  • $\begingroup$ It might help to know what the intervention is (& more about the thinking behind the study generally). $\endgroup$ Aug 3, 2022 at 19:49
  • $\begingroup$ Thanks for the reply. To answer your questions: (1) to be considered a success it is enough to observe only one significant difference. (2) No, we assume a priori the effects are different in both groups $\endgroup$ Aug 3, 2022 at 19:57
  • $\begingroup$ For (3), it is to test the effect of a post-operative procedure for two different kind of surgeries. Here we assume the effect will be different for each kind of surgery. This is why initially two sample sizes were computed. One for each kind of surgery. $\endgroup$ Aug 3, 2022 at 20:01

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Given the conversation in the comments, I gather this is a study to examine if a new procedure will reduce bleeding following hip replacement and knee replacement surgeries. The patients will differ, and it is believed that the efficacy of the procedure will differ between the two kinds of surgeries, but it isn't reasonable to imagine that the null is true for one surgery but not the other. As a result, it is desired to allow the effect to differ between the surgeries, but to get a single test of whether the procedure helps. At the same time, it is of secondary interest to estimate the two levels of efficacy.

I am thinking that I would fit a model with an interaction between surgery (population) and treatment (arm). I would test the full model (controlling for whatever covariates you believe are appropriate a-priori) against a nested model that drops both the interaction and the treatment dummy. That gives you a two degree of freedom test of whether the procedure helps. This is a single test—no correction for multiplicity is needed. Following that, the model will afford two estimates of efficacy for the two surgeries. I would probably use 'least-squares means' to compute these estimates for a constant, idealized population, with special attention paid to confidence intervals for the estimates, not p-values.

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  • $\begingroup$ Thanks, super smart! Give some food for thought on how to tackle a problem! $\endgroup$ Aug 5, 2022 at 16:46
  • $\begingroup$ You're welcome, @user3631369. $\endgroup$ Aug 5, 2022 at 16:49

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