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I am planning a set of studies that are interlinked. The first study collects information from 400 participants (exposure group), then some psychometrics are performed to assess the questions. In a second study, we plan to collect a control group sample (unaffected/typically developing) to make comparisons with the exposure group using ancova (group difference, plus covariates). A reviewer has suggested that our control group could be reduced to be much smaller.

Is this justified as the sample size required to detect our minimum clinically meaningful effect size is only around 150 in total. The 400 exposure individuals is on the basis to be able to conduct the psychometrics and adequately capture the variability in the exposure sample.

should I specify a smaller control group and use some sort of matching (n-to-1 matching, using all exposures but a smaller proportion of controls), and allow for the unbalanced groups in the sample size calculation? I'm not completely sure on the justification for this.

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I think you've answered your own question.

If your goal is to independently assess the psychometric properties within the control group, collect enough data to do that. If your goal is only to compare the exposure and control groups, and that requires less data, just collect enough for that. If you have two goals, work to whichever requires the most data. Make it clear in your paper what your goal is (or goals are) to justify the sample size you do go with.

Another possibility worth considering here it is evaluating the psychometrics for the control group, but rather than analysing this data in isolation you could use, e.g., multi-group factor analysis to test whether the psychometrics differ between groups. This would require less data than two separate psychometric analyses.

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  • $\begingroup$ Thank you for your answer. So, my point is that the 400 individuals (case) is a fixed and the first study is powered for this, so won't change. For study 2, which of the following options is correct: 1) Take a sample of the case group and match controls to this subsample, giving total sample size of N=150; 2) have a control N=400 to match the existing case group and fit regardless that we don't need this size sample, but don't want to throw away cases; OR 3) have less controls than cases, so retain 400 cases, but have much less controls, say N=100, and adjust the sample size for unbalanced gp? $\endgroup$
    – ReadBeard
    Commented Sep 5, 2022 at 10:54
  • $\begingroup$ There is no problem whatsoever with having more samples in one group than the other, so you never need to throw out data from the larger group, or recruit 400 people for the second group just because that's how many are in the first group. There's no need to "adjust the sample size for unbalanced gp" in any way. $\endgroup$
    – Eoin
    Commented Sep 5, 2022 at 21:28
  • $\begingroup$ Thanks again, and sorry but I'm still not clear. In an experimental study or RCT, I can see that this makes sense, but this is an observational study, so don't we need to allow for confounding? How does this work when we have differing numbers in each group? If we were matching more controls then it's fairly straightforward, but not the other way around when we have more cases? Perhaps just covary the potential confounders instead? (you would do this anyway I think regardless). The No. of controls determined via power calc on two sample t test unequal allocation 4:1 or something? $\endgroup$
    – ReadBeard
    Commented Sep 6, 2022 at 7:21
  • $\begingroup$ Confounding has nothing to do with sample size, but comments are not the place for extended discussion. I suggest asking a new question, and possibly marking the original question as answered if it has been. $\endgroup$
    – Eoin
    Commented Sep 7, 2022 at 14:02

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