# Selective inference for effect modification via the lasso

arXiv: https://arxiv.org/abs/1705.08020 · HTML: https://mlsanity.com/paper/1705.08020/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2017.

## Built on by (most cited first, 12 of 12)

- [Image-based Treatment Effect Heterogeneity](https://mlsanity.com/paper/2206.06417/) (2022)
- [Valid Inference After Causal Discovery](https://mlsanity.com/paper/2208.05949/) (2022)
- [Shrinkage Bayesian Causal Forests for Heterogeneous Treatment Effects Estimation](https://mlsanity.com/paper/2102.06573/) (2021)
- [Feature Selection for Discovering Distributional Treatment Effect Modifiers](https://mlsanity.com/paper/2206.00516/) (2022)
- [Optimizing Pessimism in Dynamic Treatment Regimes: A Bayesian Learning Approach](https://mlsanity.com/paper/2210.14420/) (2022)
- [Adaptive debiased machine learning using data-driven model selection techniques](https://mlsanity.com/paper/2307.12544/) (2023)
- [Estimating Heterogeneous Treatment Effects on Survival Outcomes Using Counterfactual Censoring Unbiased Transformations](https://mlsanity.com/paper/2401.11263/) (2024)
- [The Connection Between R-Learning and Inverse-Variance Weighting for Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/2307.09700/) (2023)
- [Differentiable Pareto-Smoothed Weighting for High-Dimensional Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2404.17483/) (2024)
- [Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap](https://mlsanity.com/paper/2301.05703/) (2023)
- [Nonparametric estimation of a covariate-adjusted counterfactual treatment regimen response curve](https://mlsanity.com/paper/2309.16099/) (2023)
- [Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Data](https://mlsanity.com/paper/2602.23602/) (2026)

## Abstract (arXiv)

Effect modification occurs when the effect of the treatment on an outcome varies according to the level of other covariates and often has important implications in decision making. When there are tens or hundreds of covariates, it becomes necessary to use the observed data to select a simpler model for effect modification and then make valid statistical inference. We propose a two stage procedure to solve this problem. First, we use Robinson's transformation to decouple the nuisance parameters from the treatment effect of interest and use machine learning algorithms to estimate the nuisance parameters. Next, after plugging in the estimates of the nuisance parameters, we use the Lasso to choose a low-complexity model for effect modification. Compared to a full model consisting of all the covariates, the selected model is much more interpretable. Compared to the univariate subgroup analyses, the selected model greatly reduces the number of false discoveries. We show that the conditional selective inference for the selected model is asymptotically valid given the rate assumptions in classical semiparametric regression. Extensive simulation studies are conducted to verify the asymptotic results and an epidemiological application is used to demonstrate the method.