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Measure baseline covariates before the intervention can change them. These measurements describe the recruited population, permit assessment of covariate balance, and provide prognostic predictors that can improve statistical efficiency. In particular, including prognostic baseline covariates in a linear regression reduces unexplained outcome variation without conditioning on a treatment consequence.

Use a baseline-adjusted linear regression for an intention-to-treat analysis:Condition on the observed baseline covariates and assignment. The parameter of primary interest is $\beta$, the mean effect of assignment to the experimental intervention, under this constant-effect conditional mean model. Independent normal distributions with common variance give the usual Gaussian likelihood and regression inference. Prognostic baseline covariates improve precision by explaining outcome variability.

Do not include the actual intervention-use variable $D_i$ as an ordinary adjustment variable for this estimand: it is measured after assignment and can mediate the effect being estimated. Post-randomization adjustment changes a treatment estimand; the resulting coefficient on $Z_i$ would generally represent a different comparison. Participants remain in their assigned groups even when adherence differs.

A treatment consequence is not interchangeable with a baseline covariate in an intention-to-treat analysis. Let randomized $Z$ be independent of $U,\epsilon$, and let actual intervention use be $D=Z+U$, with $Y=D+\epsilon$ 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.