= 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 gives
$$
\boxed{\widehat P(Y_2=1)=\frac{58}{102}\frac7{37}+\frac{44}{102}\frac{18}{28}=0.384889\approx38.49\%.}
$$
Equivalently, 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.
Back to article page