Bayesian inference for causal effects with noncompliance and nonignorable missing data

The paper proposes a range of models for randomized experiments with noncompliance and nonignorable missing data, in the setting of binary assignment, binary treatment received, and binary outcomes. The conditions for model identification stem from the analysis of the contingency table for the observable data. Identified models are proposed for three scenarios: missingness in all the three variables, with and without a binary pretreatment variable, and missingness in the outcome and in the treatment received without pretreatment variables. A Bayesian approach is developed for inference. The method is illustrated by a simulated comparative example.