Propensity Score Propagation: A General Framework for Design-Based Inference with Unknown Propensity Scores

2026-01-19

AI Summary

In observational studies, real-world surveys, and settings with missing data, the propensity score is typically unknown, and conventional design-based inference methods often suffer from severe undercoverage due to either ignoring the uncertainty in its estimation or relying on strong modeling assumptions. This work proposes a Propensity Score Propagation framework that automatically propagates estimation uncertainty into downstream inference through a resample-and-merge procedure. The framework accommodates both parametric and nonparametric models and seamlessly integrates classical tools such as inverse probability weighting. It establishes, for the first time, a unified and general approach for design-based inference under unknown propensity scores, overcoming existing limitations regarding model form and covariate types. Simulation studies demonstrate that the method successfully recovers nominal coverage in scenarios where traditional approaches fail, substantially enhancing inferential reliability.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Calibration & Uncertainty Quantification
• 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

Design-based inference, also known as randomization-based or finite-population inference, provides a principled framework for causal and descriptive analyses that attribute randomness solely to the design mechanism (e.g., treatment assignment, sampling, or missingness) without imposing distributional or modeling assumptions on the outcome data of study units. Despite its conceptual appeal and long history, this framework becomes challenging to apply when the underlying design probabilities (i.e., propensity scores) are unknown, as is common in observational studies, real-world surveys, and missing-data settings. Existing plug-in or matching-based approaches either ignore the uncertainty stemming from estimated propensity scores or rely on the post-matching uniform-propensity condition (an assumption typically violated when there are multiple or continuous covariates), leading to systematic under-coverage. Finite-population M-estimation partially mitigates these issues but remains limited to parametric propensity score models. In this work, we introduce propensity score propagation, a general framework for valid design-based inference with unknown propensity scores. The framework introduces a regeneration-and-union procedure that automatically propagates uncertainty in propensity score estimation into downstream design-based inference. It accommodates both parametric and nonparametric propensity score models, integrates seamlessly with standard tools in design-based inference with known propensity scores, and is universally applicable to various important design-based inference problems, such as observational studies, real-world surveys, and missing-data analyses, among many others. Simulation studies demonstrate that the proposed framework restores nominal coverage levels in settings where conventional methods suffer from severe under-coverage.

Problem

• design-based inference
• propensity score
• observational studies
• missing data
• survey sampling

Innovation

• propensity score propagation
• design-based inference
• regeneration-and-union
• finite-population inference
• uncertainty propagation