Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 32 / 3 / b / ii / Solution

Apply MAR standardization over a fully observed covariate. All first-year statuses are known, so the estimated probabilities of no use and use in year one are $58/102$ and $44/102$. Within those categories, missing at random lets the observed second-year probabilities represent the corresponding dropout outcomes as well. They are estimated by $7/37$ and $18/28$.

The law of total probability then givesEquivalently, impute expected drug-use counts $21(7/37)$ and $16(18/28)$ for the two dropout groups, add these to the 25 observed second-year users, and divide by 102. This uses both the complete records and the fully observed first-year information.