On Varieties of Doubly Robust Estimators Under Missingness Not at Random With a Shadow Variable

TL;DR

This paper develops and compares new doubly robust estimators for the mean of an outcome variable that is missing not at random, utilizing a shadow variable to improve identification and estimation.

Contribution

It introduces two novel doubly robust estimators for outcomes missing not at random, extending methods under missingness at random with different properties and validation techniques.

Findings

Proposed estimators are valid under certain conditions.

Goodness-of-fit tests can assess model correctness.

Extensions improve robustness in missing data scenarios.

Abstract

Suppose we are interested in the mean of an outcome variable missing not at random. Suppose however that one has available a fully observed shadow variable, which is associated with the outcome but independent of the missingness process conditional on covariates and the possibly unobserved outcome. Such a variable may be a proxy or a mismeasured version of the outcome available for all individuals. We have previously established necessary and sufficient conditions for identification of the full data law in such a setting, and have described semiparametric estimators including a doubly robust estimator of the outcome mean. Here, we propose two alternative doubly robust estimators for the outcome mean, which may be viewed as extensions of analogous methods under missingness at random, but enjoy different properties. We assess correctness of the required working models via straightforward goodness-of-fit tests.