Sensitivity analysis of causal inference in a clinical trial subject to crossover

In many clinical trials it is possible for some subjects to cross over between treatment arms. One can evaluate the effect of crossover by modeling it as a missing-data problem, where for subjects who cross over, one treats the unobserved value of the outcome in the original randomization arm as the missing data. The as-treated analysis is invalid if the crossover is nonignorable, in the sense that the crossovers represent a nonrandom sample of the randomized subjects. A recent area of general interest is the development of methods for measuring the sensitivity of inferences to nonignorability in the missing-data mechanism; one such approach is that of Troxel et al. In this paper we apply their method to the problem of measuring sensitivity to nonignorable crossover in randomized trials, extending it to the case where the crossover mechanism may differ between arms. Our method allows us to identify circumstances under which the as-treated analysis may be more or less sensitive to nonignorable crossover. We illustrate it with the example of a randomized clinical trial (RCT) in multiple sclerosis and a study of the effect of military service on income.