Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 207 / 3 / 2

Let $A_i$ be treatment, $Y_i=(Y_{i0},\dots ,Y_{i,12})$, and $R_i\in \{0,\dots ,12\}$ the last observed visit. The missing at random assumption isfor every feasible $r$. Equivalently, each conditional dropout hazard may depend on treatment and observed QoL history but not on current or future unobserved QoL after conditioning on that history.

In this trial, MAR means that among patients assigned the same treatment who have the same recorded QoL trajectory up to a visit, the probability of dropping out next is unrelated to what their later QoL values would have been. Dropout may depend strongly on previous poor QoL, treatment assignment, and other observed history; MAR only rules out residual dependence on the unobserved outcomes.

MAR is plausible if clinic withdrawal is driven by recorded QoL, observed side effects, treatment, and other measured history. It is doubtful if patients leave because of an unrecorded deterioration, an imminent recovery, treatment toxicity not included in the analysis, or dissatisfaction that predicts their unseen 12-month QoL. The large dropout fraction makes such missing not at random mechanisms a serious concern, so MAR should be supported by rich predictors and sensitivity analysis rather than assumed without examination.