Statistical Analysis of Randomized Experiments with Nonignorable Missing Binary Outcomes

Missing data are frequently encountered in the statistical analysis of randomized experiments. In this paper, I propose statistical methods that can be used to analyze randomized experiments with a nonignorable missing binary outcome where the missing-data mechanism may depend on the unobserved values of the outcome variable itself. I first introduce an identification strategy for the average treatment effect and compare it with the existing alternative approaches in the literature. I then derive the maximum likelihood estimator and its asymptotic properties, and discuss possible estimation methods. Furthermore, since the proposed identification assumption is not directly verifiable from the data, I show how to conduct a sensitivity analysis based on the parameterization that links the key identification assumption with the causal quantities of interest. Then, the proposed methodology is extended to the analysis of randomized experiments with noncompliance. Although the method introduced in this paper may not directly apply to randomized experiments with non-binary outcomes, I briefly discuss possible identification strategies in more general situations. Finally, I apply the proposed methodology to analyze data from the German election experiment and the influenza vaccination study, which originally motivated the methodological problems addressed in this paper.