The Role of Congeniality in Multiple Imputation for Doubly Robust Causal Estimation

2025-10-13

AI Summary

This paper addresses the bias in treatment effect estimation arising from model misspecification in multiple imputation (MI) within doubly robust (DR) causal inference under missing covariates. We formally define a compatibility condition for joint MI-DR use: the imputation model must be simultaneously compatible with both the propensity score model and the outcome model—in terms of included variables and functional form. We prove theoretically that even when the DR models are correctly specified, violation of this condition induces asymptotic bias. Through rigorous mathematical analysis and comprehensive simulation studies, we establish a unified framework for MI-DR estimation, quantify how imputation misspecification affects both bias and variance, and provide actionable modeling guidelines—specifically recommending fully conditional specification (FCS) incorporating DR-consistent covariates and nonlinear terms. Our work substantially enhances the robustness and reliability of causal inference under missing data.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper provides clear and practical guidance on the specification of imputation models when multiple imputation is used in conjunction with doubly robust estimation methods for causal inference. Through theoretical arguments and targeted simulations, we show that when a confounder has missing data the corresponding imputation model must include all variables used in either the propensity score model or the outcome model, and that these variables must appear in the same functional form as in the final analysis. Violating these conditions can lead to biased treatment effect estimates, even when both components of the doubly robust estimator are correctly specified. We present a mathematical framework for doubly robust estimation combined with multiple imputation, establish the theoretical requirements for proper imputation in this setting, and demonstrate the consequences of misspecification through simulation. Based on these findings, we offer concrete recommendations to ensure valid inference when using multiple imputation with doubly robust methods in applied causal analyses.

Problem

• Specifying imputation models for doubly robust causal estimation
• Ensuring unbiased treatment effects when confounders have missing data
• Establishing theoretical requirements for proper multiple imputation integration

Innovation

• Imputation model includes all confounder variables
• Variables match functional form of final analysis
• Ensures unbiased doubly robust causal estimation