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I am trying to work out the most appropriate way to adjust for multiple comparisons.

I have 20 biomarkers which have been measured at 4 timepoints (baseline & three unevenly spaced follow-ups). I will analyse each biomarker separately using either anova measuring changes from baseline at each time point (3 tests), or used mixed-models to assess changes over time (1 test).

If I use the Bonferroni correction, my cut-off for significance is very low & I lose a lot of power. Would I be correct in saying for the first case (comparison at each time point), the adjusted p-value threshold would be 0.05/(20*3) = 0.0008 & for the second example (over time), the threshold would be 0.05/20 = 0.0025?

Is there a more suitable correction method that would help me retain power someone could recommend?

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I would first do the omnibus test per biomarker to assess changes over time, i.e., 20 F-tests. And then correct these 20 p-values for multiple testing using the Holms or Bonferroni correction.

Then from the ones that remain significant I would look to see which time points differ with each other using post-Hoc testing and adjusting for the tests per biomarker.

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Might the harmonic mean p-value approach be useful to you? https://en.wikipedia.org/wiki/Harmonic_mean_p-value

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