A Universal Framework for Factorial Matched Observational Studies with General Treatment Types: Design, Analysis, and Applications

2025-12-21

AI Summary

Existing matching-based causal inference methods are limited to single treatment types (e.g., binary, ordinal, or continuous) or binary multi-factor treatments, rendering them inadequate for real-world policy evaluation involving multi-factor treatments with continuous or ordinal components. To address this gap, we propose the first general matching framework supporting non-binary, multi-factor treatments. Our approach employs a two-stage non-bipartite matching procedure to construct comparable unit sets, enabling unbiased estimation of both main and interaction effects. We introduce the generalized factorial Neyman estimator—unifying factorial structure modeling with arbitrary treatment types—and develop a Fisher- and Neyman-type randomization inference framework, augmented by a covariate-driven variance tuning method. Evaluated on nationwide U.S. county-level COVID-19 data, the framework successfully identifies causal effects of work/non-work mobility reduction on disease transmission and drug-related outcomes, demonstrating its validity and robustness.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Matching is one of the most widely used causal inference frameworks in observational studies. However, all the existing matching-based causal inference methods are designed for either a single treatment with general treatment types (e.g., binary, ordinal, or continuous) or factorial (multiple) treatments with binary treatments only. To our knowledge, no existing matching-based causal methods can handle factorial treatments with general treatment types. This critical gap substantially hinders the applicability of matching in many real-world problems, in which there are often multiple, potentially non-binary (e.g., continuous) treatment components. To address this critical gap, this work develops a universal framework for the design and analysis of factorial matched observational studies with general treatment types (e.g., binary, ordinal, or continuous). We first propose a two-stage non-bipartite matching algorithm that constructs matched sets of units with similar covariates but distinct combinations of treatment doses, thereby enabling valid estimation of both main and interaction effects. We then introduce a new class of generalized factorial Neyman-type estimands that provide model-free, finite-population-valid definitions of marginal and interaction causal effects under factorial treatments with general treatment types. Randomization-based Fisher-type and Neyman-type inference procedures are developed, including unbiased estimators, asymptotically valid variance estimators, and variance adjustments incorporating covariate information for improved efficiency. Finally, we illustrate the proposed framework through a county-level application that evaluates the causal impacts of work- and non-work-trip reductions (social distancing practices) on COVID-19-related and drug-related outcomes during the COVID-19 pandemic in the United States.

Problem

• Develops a universal framework for factorial matched observational studies with general treatment types.
• Proposes a two-stage non-bipartite matching algorithm to estimate main and interaction effects.
• Introduces generalized factorial Neyman-type estimands for model-free causal effect definitions.

Innovation

• Two-stage non-bipartite matching algorithm for general factorial treatments
• Generalized factorial Neyman-type estimands for model-free causal effects
• Randomization-based Fisher and Neyman inference with variance adjustments