Missing at random (MAR)

Data are missing at random when the probability of missingness, conditional on observed data, does not depend further on the missing values.

For each fixed observation pattern, the probability of that pattern may depend on observed response components and fully observed covariates, but not on the response components missing under that pattern. Conditional missing completely at random is the special case with no dependence on observed response components either.

When a response $Y$ is missing at random conditional on a fully observed category $X$, 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.