Semiparametric Inference for Non-Monotone Missing-Not-At-Random Data: The No Self-Censoring Model

• Activity Number: 434 - Robust and Efficient Inferences in Observational Studies and from Nonrandom Samples
• Type: Invited
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Government Statistics Section
• Author(s): Daniel Malinsky* and Ilya Shpitser and Eric Tchetgen Tchetgen
• Companies: Johns Hopkins University and Johns Hopkins University and University of Pennsylvania
• Keywords: missing data; semi-parametric inference; missing not at random; graphical models

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.