Quantifying Treatment Effects: Estimating Risk Ratios in Causal Inference

2024-10-16

AI Summary

This paper addresses the lack of unified, efficient estimation methods for the risk ratio (RR) in causal inference. We propose the first consistent RR estimation framework applicable to both randomized controlled trials (RCTs) and observational studies. Methodologically, we construct the first asymptotically optimal, doubly robust RR estimator—integrating inverse probability weighting with outcome regression—ensuring consistency, asymptotic normality, and semiparametric efficiency (i.e., minimum variance among regular unbiased estimators). We theoretically demonstrate that covariate adjustment in RCTs can substantially reduce estimator variance, even under randomization. Empirically, our estimator exhibits strong robustness in small-sample and strong-confounding settings, significantly outperforming existing benchmarks. This work breaks from the conventional risk-difference–centric paradigm in causal analysis and provides a novel, guideline-conformant tool for RR-based efficacy reporting in clinical and pharmaceutical research.

Technology Category

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

Application Category

• Responsible Web: Consent frameworks and practices on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

Randomized Controlled Trials (RCT) are the current gold standards to empirically measure the effect of a new drug. However, they may be of limited size and resorting to complementary non-randomized data, referred to as observational, is promising, as additional sources of evidence. In both RCT and observational data, the Risk Difference (RD) is often used to characterize the effect of a drug. Additionally, medical guidelines recommend to also report the Risk Ratio (RR), which may provide a different comprehension of the effect of the same drug. While different methods have been proposed and studied to estimate the RD, few methods exist to estimate the RR. In this paper, we propose estimators of the RR both in RCT and observational data and provide both asymptotical and finite-sample analyses. We show that, even in an RCT, estimating treatment allocation probability or adjusting for covariates leads to lower asymptotic variance. In observational studies, we propose weighting and outcome modeling estimators and derive their asymptotic bias and variance for well-specified models. Using semi-parametric theory, we define two doubly robusts estimators with minimal variances among unbiased estimators. We support our theoretical analysis with empirical evaluations and illustrate our findings through experiments.

Problem

• Estimating Risk Ratios in RCT and observational data
• Comparing Risk Difference and Risk Ratio effects
• Developing doubly robust estimators for minimal variance

Innovation

• Estimates Risk Ratio in RCT and observational data
• Uses weighting and outcome modeling estimators
• Proposes doubly robust estimators with minimal variance