  Although approaches for handling missing data from longitudinal studies are
well-developed when the patterns of missingness are monotone, fewer methods are
available for non-monotone missingness. Moreover, the conventional missing at
random (MAR) assumption -- a natural benchmark for monotone missingness -- does
not model realistic beliefs about non-monotone missingness processes (Robins
and Gill, 1997). This has provided the impetus for alternative non-monotone
missing not at random (MNAR) mechanisms. The "no self-censoring" (NSC) model is
such a mechanism and assumes the probability an outcome variable is missing is
independent of its value when conditioning on all other possibly missing
outcome variables and their missingness indicators. As an alternative to
"weighting" methods that become computationally demanding with increasing
number of outcome variables, we propose a multiple imputation approach under
NSC. We focus on the case of binary outcomes and present results of simulation
and asymptotic studies to investigate the performance of the proposed
imputation approach. We describe a related approach to sensitivity analysis to
departure from NSC. Finally, we discuss the relationship between MAR and NSC
and prove that one is not a special case of the other. The proposed methods are
illustrated with application to a substance use disorder clinical trial.
