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

arXiv: https://arxiv.org/abs/2605.26288 · HTML: https://mlsanity.com/paper/2605.26288/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 25 May 2026.

## Builds on (most cited first, 10 of 10)

- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Estimating Heterogeneous Treatment Effects for General Responses](https://mlsanity.com/paper/2103.04277/) (2021)
- [Doing Great at Estimating CATE? On the Neglected Assumptions in Benchmark Comparisons of Treatment Effect Estimators](https://mlsanity.com/paper/2107.13346/) (2021)
- [On Modeling and Estimation for the Relative Risk and Risk Difference](https://mlsanity.com/paper/1510.02430/) (2015)
- [Estimation and Validation of Ratio-based Conditional Average Treatment Effects Using Observational Data](https://mlsanity.com/paper/1912.06977/) (2019)
- [Targeting relative risk heterogeneity with causal forests](https://mlsanity.com/paper/2309.15793/) (2023)

## Abstract (arXiv)

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.