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How should I best analyze data that have "2x pairing"? E.g., N set of twins, each twin randomly assigned to active drug or placebo, then measure indicator X at timepoints A (before administration) and B (after administration).

My understanding here is that there are 2 pairings: between time A and B, and between drug and placebo.

Does it make sense to manually calculate the difference in X between the timepoints and just perform a simple paired t-test / Wilcoxon on the differences?

If that's OK, then is there a difference if I do it the other way around, i.e. manually calculate the difference in X between drug and placebo, and perform a simple paired test across the timepoints? (It feels less logical, but I can't place why exactly)

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If your question of interest is "What effect on risk does drug have over placebo?", then it sounds like you are taking advantage of such matches simply to reduce unobserved sources of between group variability, rather than to make inferences about differences between twins.

So your suggestion to measure change in $X$ across the trial period (i.e. $X_{\text{B}}-X_{\text{A}}$) and base your inference on a paired t test or sign-rank test, would seem to be about right.

If you based your inference on $X_{\text{sib drug}}-X_{\text{sib control}}$, and then performed your test (paired t or signed rank), you would then be inferring that there was a change (or not) in drug-placebo differences in prevalence/levels before and after treatment. Possibly also useful. But aren't clinical trials more often used to characterize effects on risk/change?

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  • $\begingroup$ Sorry, I didn't know [enter] submitted the comment. Yup, the main purpose is to compare difference between drug and placebo. I guess what I meant was, is there a difference if I calculate X_B - X_A then perform a paired test across X_drug and X_ctrl, vs. calculating X_drug - X_ctrl then performing a paired test across X_B and X_A? Both methods seem to account for the differences between time period and drug/control... does it matter which particular pair is operated on by the statistical test? $\endgroup$
    – TLK
    May 5, 2014 at 7:44
  • $\begingroup$ Does my edit help clarify? The first tests for differences in risk/change, the second tests for differences in prevalence/levels among matched pairs. $\endgroup$
    – Alexis
    May 5, 2014 at 12:45

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