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.
This work is partially supported by NSF Grants DMS-1810960, DMS-1952781 and DMS-2112907, and NIH Grant U01 AG016976.
We thank Adrian Dobra, Mathias Drton, Mauricio Sadinle, Daniel Suen, Thomas Richardson for very helpful comments on the paper.
"Pattern graphs: A graphical approach to nonmonotone missing data." Ann. Statist. 50 (1) 129 - 146, February 2022. https://doi.org/10.1214/21-AOS2094