Unifying regression-based and design-based causal inference in time-series experiments

2025-10-26

AI Summary

This paper addresses the sensitivity of causal effect estimation in time-series experiments—such as switchback designs in healthcare and industrial settings—to regression model misspecification. We propose a unified “design-driven + regression-assisted” causal inference framework that does not rely on correct regression specification; instead, it leverages the randomization inherent in experimental design. By applying covariate transformations followed by ordinary least squares, the framework delivers consistent estimates of treatment effects. It supports simultaneous estimation of multiple treatment effects and remains robust under high-dimensional covariates. We establish asymptotic normality of the estimator and construct a conservative heteroskedasticity- and autocorrelation-robust variance estimator whose asymptotic upper bound dominates the true design-based variance. The proposed method substantially enhances the robustness, broad applicability, and statistical reliability of causal inference in time-series experimental settings.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Time-series experiments, also called switchback experiments or N-of-1 trials, play increasingly important roles in modern applications in medical and industrial areas. Under the potential outcomes framework, recent research has studied time-series experiments from the design-based perspective, relying solely on the randomness in the design to drive the statistical inference. Focusing on simpler statistical methods, we examine the design-based properties of regression-based methods for estimating treatment effects in time-series experiments. We demonstrate that the treatment effects of interest can be consistently estimated using ordinary least squares with an appropriately specified working model and transformed regressors. Our analysis allows for estimating a diverging number of treatment effects simultaneously, and establishes the consistency and asymptotic normality of the regression-based estimators. Additionally, we show that asymptotically, the heteroskedasticity and autocorrelation consistent variance estimators provide conservative estimates of the true, design-based variances. Importantly, although our approach relies on regression, our design-based framework allows for misspecification of the regression model.

Problem

• Unifying regression-based and design-based causal inference methods
• Establishing consistency and asymptotic normality of regression estimators
• Allowing model misspecification while maintaining design-based validity

Innovation

• Uses ordinary least squares with transformed regressors
• Allows simultaneous estimation of diverging treatment effects
• Provides conservative variance estimates under model misspecification