= Post-randomization adjustment changes a treatment estimand
A treatment consequence is not interchangeable with a <baseline covariate> in an <intention-to-treat analysis>. Let randomized $Z$ be independent of $U,\varepsilon$, and let actual intervention use be $D=Z+U$, with $Y=D+\varepsilon$ and independent centered errors. The assignment changes the mean outcome by one. But the <conditional expectation> $\mathbb E[Y\mid Z,D]=D$ has coefficient zero on $Z$. Thus adjustment for the post-randomization variable $D$ changes the <estimand> even in a simple identified <linear regression>.
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