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Suppose there's a study where an interim analysis was performed to evaluate efficacy with the intention of stopping the study. However, since the predefined success criterion wasn't achieved, the study continued until completion. In this scenario, should the final analysis account for multiplicity, considering that no type-1 error occurred during the interim analysis?

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Yes you would still need to make some correction to control the probability of a Type 1 error from your experimental procedure as a whole.

If you reset alpha to (say) 0.05 whenever the interim analysis doesn't suggest an effect, then overall your experiment has a probability greater than 0.05 of a type 1 error (so long as the interim analysis had a non-zero type 1 error probability).

That your particular instance of the experiment didn't stop early is not relevant, it's the long run probability of a type 1 error from the procedure as a whole that is important.

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