Doubly robust tests of exposure effects under high-dimensional confounding

TL;DR

This paper introduces doubly robust hypothesis tests for exposure effects in high-dimensional settings, maintaining validity under model misspecification without sample-splitting, and demonstrates their effectiveness through simulations and real data analysis.

Contribution

It develops uniformly valid, doubly robust tests for low-dimensional parameters in high-dimensional models that are valid even when one model is misspecified, without needing sample-splitting.

Findings

Tests remain valid under weaker sparsity conditions.

The methods perform well in simulations.

Application to ICU data illustrates practical utility.

Abstract

After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is exacerbated in high-dimensional settings, where variable selection becomes unavoidable. This has prompted a flurry of activity in developing uniformly valid hypothesis tests for a low-dimensional regression parameter (e.g. the causal effect of an exposure A on an outcome Y) in high-dimensional models. So far there has been limited focus on model misspecification, although this is inevitable in high-dimensional settings. We propose tests of the null that are uniformly valid under sparsity conditions weaker than those typically invoked in the literature, assuming working models for the exposure and outcome are both correctly specified. When one of the models is misspecified, by amending the procedure for estimating the nuisance parameters, our tests continue to be valid; hence they are doubly robust. Our proposals are straightforward to implement using existing software for penalized maximum likelihood estimation and do not require sample-splitting. We illustrate them in simulations and an analysis of data obtained from the Ghent University Intensive Care Unit.