# Multiple Imputation for Non-Monotone Missing Not at Random Binary Data using the No Self-Censoring Model

## TL;DR

This paper introduces a multiple imputation method for non-monotone missing not at random binary data using the no self-censoring model, addressing limitations of existing approaches and providing a sensitivity analysis framework.

## Contribution

It proposes a novel multiple imputation approach under the NSC model for binary data, expanding methods for non-monotone MNAR missingness.

## Key findings

- Simulation results show improved imputation accuracy.
- Asymptotic analysis confirms method robustness.
- Application to clinical trial demonstrates practical utility.

## Abstract

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.