ABSTRACT
For most parts of the book we assume that the missingness is ignorable (or MAR). In this chapter we discuss the issue of nonignorable missing data (or MNAR) and how we should carry out multiple imputation analysis when we suspect MNAR happens. The first strategy is to use the inclusive imputation strategy so that the missingness assumption is closer to MAR. If there is still suspicion of MNAR, we present two major modeling frameworks: the selection models and pattern-mixture models. However we point out that in general MNAR models would incur model identifiability issues. One approach is to directly impute missing data under MNAR models. We present one example based on a Heckman selection model. The example dataset is from a hospital clinical database. However, a more reasonable strategy is to carry out a sensitivity analysis by varying the parameter govern the ignorability of missingness (i.e., the sensitivity parameter). By doing so we can assess how sensitive the analysis results would be with respect to the extent of nonignorability. We provide examples of sensitivity analysis under both the pattern-mixture model and selection model using real data and simulation studies. In general, we recommend using sensitivity analysis for multiple imputation if missing data are susceptible to MNAR.
