# Model-Assisted Inference for Covariate-Specific Treatment Effects with High-dimensional Data

arXiv: https://arxiv.org/abs/2105.11362 · HTML: https://mlsanity.com/paper/2105.11362/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2021.

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

- [TDR-CL: Targeted Doubly Robust Collaborative Learning for Debiased Recommendations](https://mlsanity.com/paper/2203.10258/) (2022)
- [Policy Learning for Balancing Short-Term and Long-Term Rewards](https://mlsanity.com/paper/2405.03329/) (2024)
- [Learning Counterfactual Outcomes Under Rank Preservation](https://mlsanity.com/paper/2502.06398/) (2025)
- [Incorporating External Controls for Estimating the Average Treatment Effect on the Treated with High-Dimensional Data: Retaining Double Robustness and Ensuring Double Safety](https://mlsanity.com/paper/2509.20586/) (2025)

## Abstract (arXiv)

Covariate-specific treatment effects (CSTEs) represent heterogeneous treatment effects across subpopulations defined by certain selected covariates. In this article, we consider marginal structural models where CSTEs are linearly represented using a set of basis functions of the selected covariates. We develop a new approach in high-dimensional settings to obtain not only doubly robust point estimators of CSTEs, but also model-assisted confidence intervals, which are valid when a propensity score model is correctly specified but an outcome regression model may be misspecified. With a linear outcome model and subpopulations defined by discrete covariates, both point estimators and confidence intervals are doubly robust for CSTEs. In contrast, confidence intervals from existing high-dimensional methods are valid only when both the propensity score and outcome models are correctly specified. We establish asymptotic properties of the proposed point estimators and the associated confidence intervals. We present simulation studies and empirical applications which demonstrate the advantages of the proposed method compared with competing ones.