Semiparametric Inference for Non-monotone Missing-Not-at-Random Data: the No Self-Censoring Model

TL;DR

This paper introduces a semiparametric approach to identify and estimate functionals of multivariate data with non-monotone, not-at-random missingness, using the no self-censoring assumption, and proposes a robust estimator with practical applications.

Contribution

It develops a novel identification strategy and an efficient estimator for complex missing data mechanisms under the no self-censoring assumption.

Findings

The estimator achieves double-robustness in high-dimensional settings.

Simulation studies demonstrate the estimator's favorable performance.

Application to HIV data illustrates practical utility.

Abstract

We study the identification and estimation of statistical functionals of multivariate data missing non-monotonically and not-at-random, taking a semiparametric approach. Specifically, we assume that the missingness mechanism satisfies what has been previously called "no self-censoring" or "itemwise conditionally independent nonresponse," which roughly corresponds to the assumption that no partially-observed variable directly determines its own missingness status. We show that this assumption, combined with an odds ratio parameterization of the joint density, enables identification of functionals of interest, and we establish the semiparametric efficiency bound for the nonparametric model satisfying this assumption. We propose a practical augmented inverse probability weighted estimator, and in the setting with a (possibly high-dimensional) always-observed subset of covariates, our proposed estimator enjoys a certain double-robustness property. We explore the performance of our estimator with simulation experiments and on a previously-studied data set of HIV-positive mothers in Botswana.