Avoid Estimating the Unknown Function in a Semiparametric Nonignorable Propensity Model

TL;DR

This paper introduces a novel semiparametric approach to estimate parameters and functionals in nonignorable missing data models without modeling the outcome regression, enhancing robustness and simplifying the estimation process.

Contribution

It proposes a new class of estimators that avoid modeling the outcome function in nonignorable missing data scenarios, supported by theoretical and empirical validation.

Findings

Estimators perform well without modeling the outcome regression.

The approach is robust to misspecification of the missingness dependence.

The method is validated through simulations and real data analysis.

Abstract

We study the problem of estimating a functional or a parameter in the context where outcome is subject to nonignorable missingness. We completely avoid modeling the regression relation, while allowing the propensity to be modeled by a semiparametric logistic relation where the dependence on covariates is unspecified. We discover a surprising phenomenon in that the estimation of the parameter in the propensity model as well as the functional estimation can be carried out without assessing the missingness dependence on covariates. This allows us to propose a general class of estimators for both model parameter estimation and functional estimation, including estimating the outcome mean. The robustness of the estimators are nonstandard and are established rigorously through theoretical derivations, and are supported by simulations and a data application.