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my study is a randomized controlled clinical trial involving 3 groups in parallel. Sample size was calculated based on blood cholesterol endpoint as 20 participants per group.
However my problem is to calculate the minimal clinically important difference which would be detected with that sample size, I've no idea how to calculate it.

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    $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Aug 29, 2023 at 15:12
  • $\begingroup$ Apolgies, it has been clariefied $\endgroup$ Aug 29, 2023 at 15:49
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    $\begingroup$ The "minimum clinically important difference" has nothing to do with statistics or your sample size or the data, it's a domain knowledge question of what effect sizes you would actually care about. I think you're asking about the minimum the effect size that can reliably deemed significant, but that is totally orthogonal to whether that effect size is clinically important. With lots of data, you can detect arbitrarily small differences of no clinical significance. $\endgroup$ Aug 29, 2023 at 15:54
  • $\begingroup$ Thank you for your kind reply. So as the reviewer asked me to add this in sample size section, maybe it meant the "minimal dectable cange" i could detect with that sampe size? $\endgroup$ Aug 29, 2023 at 15:58
  • $\begingroup$ You should show a snippet of what the data look like, it may help answering you. Also, note that if the sample size is fixed, you can calculate the minimal effect size you'll be able to detect, but this is very different from defining if this effect is clinically or practically important. Clinical importance is defined from domain knowledge, not from a sample size. (e.g. would a difference of 0.00001% be worth the cost or possible side effects of the treatment? If not, at what point does a difference matter?). .../ $\endgroup$
    – J-J-J
    Aug 29, 2023 at 15:58

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Let me emphasize what many commenters said. You need to distinguish two entirely different (but related) questions:

  • Decide what is the smallest difference in mean cholesterol (or LDL...) concentration that matters scientifically or clinically. Then compute the needed sample size (you'll need to choose values for alpha and power).
  • Decide on your sample size per group, and compute how large a mean difference in cholesterol (or LDL...) you can detect (with chosen values for alpha and power). Then you can decide if the study is worth doing or not.

You wrote your question in a way that mangles those two issues.

The free program G*Power lets you do both kinds of calculations.

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