Transportable inference using target population summary statistics under covariate shift

2026-03-02

AI Summary

This study addresses the challenge of transporting causal conclusions from a source population to a target population when only summary statistics of covariates—not individual-level data—are available for the target, leading to potential covariate shift. The authors propose a novel and flexible approach that integrates entropy balancing into transportability inference, enabling simultaneous covariate shift adjustment and uncertainty quantification through moment matching of covariate distributions. Under relatively weak assumptions, they establish the asymptotic normality and consistent variance estimation of the resulting estimator. Extensive simulations and an empirical analysis of SEER breast cancer data demonstrate that the proposed method outperforms existing approaches in both estimation accuracy and inferential robustness.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Transporting findings from a study population to a target population is central to evidence-based decision-making in real-world settings. Most existing methods require individual-level data from both populations to account for covariate shift. However, privacy regulations and data-sharing constraints often preclude access to such data from the target population, leaving only covariate summaries available for analysis. In this paper, we develop transportability methods that enable valid inference using source individual-level data and target covariate summaries. Firstly, we apply entropy balancing to transportability, enabling source individual-level data to be adjusted to match the target covariate moments. We establish asymptotic normality for the entropy balancing estimator and propose a variance estimator to account for uncertainty in covariate summaries. Secondly, we develop a new transportability method that allows flexible modeling of covariate shift, thereby accounting for covariate shift and uncertainty in covariate summaries simultaneously. Asymptotic normality for the proposed estimator is established and its asymptotic variance is consistently estimated. The proposed method offers greater flexibility in accounting for covariate shift and thus permits consistent estimation and valid inference under weaker conditions than those required by entropy balancing. The proposed methods are evaluated by simulations and illustrated with an analysis of Surveillance, Epidemiology, and End Results breast cancer data.

Problem

• transportability
• covariate shift
• summary statistics
• target population
• evidence-based decision-making

Innovation

• transportability
• covariate shift
• entropy balancing
• summary statistics
• asymptotic normality