Beyond Differences: Doubly Robust Meta-Learners for Ratio-Based Treatment Effects

2026-05-25

AI Summary

This study addresses the challenge of robustly estimating the conditional average treatment effect expressed as a ratio (ratio-CATE), which arises in domains such as medicine, pricing, and marketing. Existing methods often rely on restrictive log-linear assumptions, limiting their applicability. To overcome this, the authors propose Q-Learner, a novel nonparametric framework that decomposes ratio-CATE into a product of two odds ratios and reformulates estimation as two propensity score-based classification tasks. Building on this formulation, they develop S/T- and Q-type doubly robust meta-learners with distinct robustness properties. Empirical evaluation demonstrates that Q-Learner achieves state-of-the-art performance across seven randomized controlled trials with low conversion rates, while the proposed doubly robust variants significantly outperform existing baselines on four observational datasets with confounding.

Abstract

When treatment effects are naturally expressed as ratios -- as in medicine, pricing, and marketing -- the ratio-based CATE $τ(x) = E[Y|W=1,X=x] / E[Y|W=0,X=x]$ is the appropriate estimand. Yet existing estimators either impose a log-linear parametric structure or apply generic regression without robustness guarantees for this functional. We introduce the Q-Learner, which decomposes $τ(x)$ into a product of two odds ratios, reducing ratio-CATE estimation for binary outcomes to two propensity classification tasks. We further derive doubly robust augmentations for both S/T- and Q-style ratio learners and characterize their distinct robustness properties. In benchmarks on seven RCT datasets, the Q-Learner is the most consistently competitive method in low-conversion regimes, where its propensity-only construction sidesteps the imbalanced regression that hurts outcome-based estimators. On four observational datasets, where propensity must be estimated and confounding cannot be ruled out, the DR learners introduced here decisively come out on top, making them practitioners' natural default for confounded observational data.

Problem

• ratio-based treatment effects
• conditional average treatment effect
• causal inference
• observational data
• robust estimation

Innovation

• ratio-based CATE
• Q-Learner
• doubly robust
• propensity classification
• treatment effect estimation