Bayesian Network Propensity Score to Evaluate Treatment Effects in Observational Studies

2025-09-03

AI Summary

In observational studies, conventional propensity score methods—such as logistic regression—are prone to model misspecification due to strong parametric assumptions, while popular machine learning approaches—including random forests and balancing weights—often lack consistency and valid asymptotic variance estimation. To address these limitations, we propose Bayesian Network Propensity Scores (BN-PS), which leverages Bayesian networks to flexibly encode complex dependencies among covariates, thereby mitigating modeling constraints under unknown data-generating mechanisms. BN-PS is coupled with the Hájek estimator to yield consistent, asymptotically normal, and efficient estimation of the average treatment effect (ATE). Across 15 simulation scenarios, BN-PS consistently outperforms benchmark methods. Applied to real-world data from 7,162 prostate cancer patients, it robustly identifies the causal effects of pelvic lymph node dissection on hospital length of stay and biochemical recurrence, demonstrating both statistical reliability and practical utility for causal inference.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

This paper focuses on the Bayesian Network Propensity Score (BNPS), a novel approach for estimating treatment effects in observational studies characterized by unknown (and likely unbalanced) designs and complex dependency structures among covariates. Traditional methods, such as logistic regression, often impose rigid parametric assumptions that may lead to misspecification errors, compromising causal inference. Recent classical and machine learning alternatives, such as boosted CART, random forests, and Stable Balancing Weights, seem to be attractive in a predictive perspective, but they typically lack asymptotic properties, such as consistency, efficiency, and valid variance estimation. In contrast, the recently proposed BNPS to estimate propensity scores uses Bayesian Networks to flexibly model conditional dependencies while preserving essential statistical properties such as consistency, asymptotic normality and asymptotic efficiency. Combined with the Hájek estimator, BNPS enables robust estimation of the Average Treatment Effect (ATE) in scenarios with strong covariate interactions and unknown data-generating mechanisms. Through extensive simulations across fifteen realistic scenarios and varying sample sizes, BNPS consistently outperforms benchmark methods in both empirical rejection rates and coverage accuracy. Finally, an application to a real-world dataset of 7,162 prostate cancer patients from San Raffaele Hospital (Milan, Italy) demonstrates BNPS's practical value in assessing the impact of pelvic lymph node dissection on hospitalization duration and biochemical recurrence. The findings support BNPS as a statistically robust, interpretable and transparent alternative for causal inference in complex observational settings, enhancing the reliability of evidence from real-world biomedical data.

Problem

• Evaluating treatment effects in observational studies with unbalanced designs
• Overcoming parametric assumptions in traditional propensity score methods
• Addressing complex covariate dependencies without sacrificing statistical properties

Innovation

• Bayesian Network Propensity Score for flexible dependency modeling
• Combines BNPS with Hájek estimator for robust ATE estimation
• Preserves asymptotic properties like consistency and efficiency