Selective inference for effect modification via the lasso

TL;DR

This paper introduces a two-stage method combining Robinson's transformation, machine learning, and Lasso for valid selective inference on effect modification in high-dimensional covariate settings, improving interpretability and reducing false discoveries.

Contribution

It proposes a novel two-stage procedure integrating machine learning and Lasso for effect modification analysis with valid selective inference in high-dimensional data.

Findings

Method achieves asymptotic validity under classical semiparametric assumptions.

Simulation studies confirm the theoretical properties.

Application demonstrates practical utility in epidemiology.

Abstract

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.