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.