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I'm facing a dilemma in a pre/post cohort matching analysis for a healthcare intervention:

  • Matching on the pre-treatment outcome $Y_0$ (a continuous variable) will likely lead to regression to the mean bias in the treatment effect estimate on $Y_1$.
  • However, $Y_0$ is a strong confounder that's causally associated with the treatment $A$ and $Y_1$, therefore we want to control for $Y_0$ in some capacity.

Given ANCOVA is the standard remedy for removing regression to the mean effects, is it valid to not match (exact or propensity score) on $Y_0$ but include $Y_0$ in the post-matching outcome model? This protects us from both regression to the mean bias and confounder bias.

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I assume that the baseline (pre-treatment) was recorded before, then intervention was applied on a subset of the population.The expected difference in means at baseline is zero. The correct linear model should be: post = pre + treatment

If treatment is applied before the baseline was recorded, the change score should be used (post-pre) as response variable. Here you don't expect zero difference at baseline

The best practice is related to the design. Jeffrey Walker provide a clear and extensive explanation of the problem and reports each case with examples in R (https://www.middleprofessor.com/files/applied-biostatistics_bookdown/_book/issues.html#issues-pre-post)

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    $\begingroup$ Correct, $Y_0$ precedes treatment. We do not observe zero difference between mean $Y_0$ in trmt and ctrl groups - I'm thinking post = pre + trmt + trmt*pre would be an appropriate model. Thank you for the link. Have you read Tennant et al. "Analyses of ‘change scores’ do not estimate causal effects in observational data" (2021)? The authors argue that change scores may be useful in longitudinal RCTs but produce biased estimates in observational studies, where ANCOVA is preferred. $\endgroup$
    – RobertF
    Feb 3, 2023 at 13:32
  • $\begingroup$ I agree, I think your idea to include the interaction is better than just using the difference (post-pre), in this way you allow the slope to change. Moreover, I was thinking about this, using the difference (although is handy) means that you are making assumtpions on the relation between post and pre. Thank you for the reference. $\endgroup$
    – andrew_lor
    Feb 6, 2023 at 14:33

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