PATTERN GRAPHS: A GRAPHICAL APPROACH TO NONMONOTONE MISSING DATA

We introduce the concept of pattern graphs-directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a missing not at random restriction. We introduce a selection model and a pattern mixture model formulations using the pattern graphs and show that they are equivalent. A pattern graph leads to an inverse probability weighting estimator as well as an imputation-based estimator. We also study the semiparametric efficiency theory and derive a multiply-robust estimator using pattern graphs.