= Solution
Use a baseline-adjusted <linear regression> for an <intention-to-treat analysis>:
$$
Y_i=\alpha+\beta Z_i+\gamma^{\mathsf T}x_i+\varepsilon_i,
\qquad \varepsilon_i\overset{\mathrm{ind}}\sim N(0,\sigma^2).
$$
Condition on the observed <baseline covariates> and assignment. The parameter of primary interest is \b[$\beta$, 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.
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