# A Semiparametric Approach to Model Effect Modification

arXiv: https://arxiv.org/abs/1804.05373 · HTML: https://mlsanity.com/paper/1804.05373/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2018.

## Built on by (most cited first, 4 of 4)

- [Efficient Learning of Optimal Individualized Treatment Rules for Heteroscedastic or Misspecified Treatment-Free Effect Models](https://mlsanity.com/paper/2109.02570/) (2021)
- [Late Fusion Multi-task Learning for Semiparametric Inference with Nuisance Parameters](https://mlsanity.com/paper/2507.07941/) (2025)
- [Policy Learning for Optimal Individualized Dose Intervals](https://mlsanity.com/paper/2202.12234/) (2022)
- [Co-Supervised Tree Synthesis for Interpretable Subgroup Identification and Honest Treatment Effect Inference in Randomized Trials](https://mlsanity.com/paper/2610.03927/) (2026)

## Abstract (arXiv)

One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for identifying such effect modification. Instead of using the traditional outcome models, we directly posit semiparametric models on contrasts, or expected differences of the outcome under different treatment choices or exposures. Through semiparametric estimation theory, all valid estimating equations, including the efficient scores, are derived. Besides doubly robust loss functions, our approach also enables dimension reduction in presence of many covariates. The asymptotic and non-asymptotic properties of the proposed methods are explored via a unified statistical and algorithmic analysis. Comparison with existing methods in both simulation and real data analysis demonstrates the superiority of our estimators especially for an efficiency improved version.