MAR standardization over a fully observed covariate ($\hat{\theta }={\sum }_x{\hat{p}}_x{\hat{m}}_x$)

When a response $Y$ is missing at random conditional on a fully observed category $X$, with positive response probability in every occupied category, estimate its conditional probabilities using respondents within each category and average them with the category frequencies from all patients. For a binary response, $\hat{P}(Y=1)={\sum }_x\hat{P}(X=x)\hat{P}(Y=1\mid X=x,R=1)$. The weighting uses the full cohort rather than only complete cases.