= Solution
Let $R_i=1$ indicate an observed outcome. Fitting the conditional outcome model to responders requires
$$
\boxed{Y_i\perp R_i\mid x_i,Z_i,}
$$
with a positive observation probability over the relevant predictor support. This is conditional <missing at random> for the predictors used in the regression: after conditioning on them, observation must not further select participants by their unobserved outcome. It gives $f(Y_i\mid x_i,Z_i,R_i=1)=f(Y_i\mid x_i,Z_i)$, the <complete-case regression under conditional missing at random> condition. Correct specification of the conditional mean model is also required. <Missing completely at random> is sufficient but stronger; simply assuming missingness depends only on a post-randomization variable excluded from this model would not suffice.
Back to article page