Bounding causal effects with an unknown mixture of informative and non-informative missingness

TL;DR

This paper develops bounds on causal effects in data with unknown mixtures of informative and non-informative missing outcomes, providing estimators that are flexible and applicable in real-world scenarios.

Contribution

It introduces a novel framework for bounding causal effects under mixed missingness, with influence-function based estimators and applications to health data.

Findings

Derived bounds as functions of sensitivity parameters

Proposed estimators achieve root-n convergence and asymptotic normality

Applied methodology to study antipsychotic drugs and diabetes risk

Abstract

In experimental and observational data settings, researchers often have limited knowledge of the reasons for missing outcomes. To address this uncertainty, we propose bounds on causal effects for missing outcomes, accommodating the scenario where missingness is an unobserved mixture of informative and non-informative components. Within this mixed missingness framework, we explore several assumptions to derive bounds on causal effects, including bounds expressed as a function of user-specified sensitivity parameters. We develop influence-function based estimators of these bounds to enable flexible, non-parametric, and machine learning based estimation, achieving root-n convergence rates and asymptotic normality under relatively mild conditions. We further consider the identification and estimation of bounds for other causal quantities that remain meaningful when informative missingness reflects a competing outcome, such as death. We conduct simulation studies and illustrate our methodology with a study on the causal effect of antipsychotic drugs on diabetes risk using a health insurance dataset.