Causal Inference with MNAR Self-Masking Confounders: A Stratified Delta-Imputed Propensity Estimation Method

TL;DR

This paper introduces SDIPE, a robust stratified delta-imputed method for causal inference with self-masking MNAR confounders, outperforming existing approaches in bias and coverage.

Contribution

The paper proposes SDIPE, a novel stratified delta-imputed estimator that effectively handles self-masking MNAR confounders without strong assumptions, improving causal effect estimation.

Findings

SDIPE achieves low bias and high coverage in simulations.

SDIPE is robust to delta parameter choices.

Applied to NHANES data, SDIPE estimates effects with confidence intervals.

Abstract

In observational studies, causal inference becomes difficult when confounders are missing-not-at-random (MNAR), particularly where the missingness depends on the confounder's own unreported value (self-masking). Existing methods for handling MNAR confounders often rely on strong, unverifiable assumptions, leading to biased estimates. We propose a simple approach with Stratified Delta-Imputed Propensity Estimator (SDIPE) in the presence of self-masking confounders. SDIPE first stratifies data into observed and missing groups, imputes missing confounders via delta-adjusted multiple imputation. Then, within each group, average-treatment-effects (ATEs) are estimated by stabilized-inverse-probability-weights. The final ATE is obtained by combining the subgroup-specific estimates, weighted by respective proportions in the sample. Simulation study shows that SDIPE achieves low bias and near-nominal coverage (94-96%) across varying missingness, sample sizes, and treatment prevalence. In contrast, conventional sensitivity-based multiple imputation exhibits substantial bias and poor coverage (18-89%). Additionally, SDIPE is robust to the choice of the delta parameter. Applied to NHANES-2017-2018, SDIPE estimates that married individuals have a 1.19-point lower depression score than unmarried individuals (95% CI: -1.76, -0.64), adjusting for MNAR income data. SDIPE provides a practical and robust approach for causal inference with self-masking MNAR confounders, offering improved performance over existing methods without requiring restrictive assumptions about the missingness mechanism.