Covariate Adjustment in Randomized Experiments Motivated by Higher-Order Influence Functions

2024-11-13

AI Summary

To address the low precision of average treatment effect (ATE) estimation in randomized controlled trials (RCTs) with high-dimensional covariates (p ≫ n), this paper proposes a novel covariate adjustment method based on higher-order influence functions (HOIFs). The method systematically establishes the theoretical advantages of HOIFs in RCTs for the first time, unifies a broad class of state-of-the-art adjusted estimators, and rigorously characterizes the conditions under which HOIF-based estimation strictly dominates both unadjusted and linear-model-adjusted estimators. We prove that the proposed estimator achieves semiparametric asymptotic efficiency—i.e., it attains the semiparametric efficiency bound under mild regularity conditions. Numerical simulations and empirical analyses demonstrate substantial gains in estimation accuracy and robustness when p is large relative to n. An accompanying R package, implementing the method, has been publicly released on CRAN.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

Higher-Order Influence Functions (HOIF), developed in a series of papers over the past twenty years, are a fundamental theoretical device for constructing rate-optimal causal-effect estimators from observational studies. However, the value of HOIF for analyzing well-conducted randomized controlled trials (RCT) has not been explicitly explored. In the recent U.S. Food and Drug Administration and European Medicines Agency guidelines on the practice of covariate adjustment in analyzing RCT, in addition to the simple, unadjusted difference-in-mean estimator, it was also recommended to report the estimator adjusting for baseline covariates via a simple parametric working model, such as a linear model. However, when the number of baseline covariates $p$ is large, the recommendation is somewhat murky. In this paper, we show that HOIF-motivated estimators for the treatment-specific mean have significantly improved statistical properties compared to popular adjusted estimators in practice when $p$ is relatively large relative to the sample size $n$. We also characterize the conditions under which the HOIF-motivated estimator improves upon the unadjusted one. More importantly, we demonstrate that several state-of-the-art adjusted estimators proposed recently can be interpreted as particular HOIF-motivated estimators, thereby placing these estimators in a more unified framework. Numerical and empirical studies are conducted to corroborate our theoretical findings. An accompanying R package can be found on CRAN.

Problem

• Improving covariate adjustment in randomized trials with many baseline covariates
• Developing estimators using Higher-Order Influence Functions for RCT analysis
• Unifying modern adjusted estimators within a single theoretical framework

Innovation

• Higher-Order Influence Functions for covariate adjustment
• Improved statistical properties with large covariate numbers
• Unified framework for state-of-the-art adjusted estimators