Doubly robust tests of exposure effects under high‐dimensional confounding

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 lowdimensional regression parameter (eg, the causal effect of an exposure on an outcome) 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.

Principled selection of baseline covariates to account for censoring in randomized trials with a survival endpoint

“…Surprisingly, these standard variable selection procedures do not affect tests of the null hypothesis of no treatment effect in generalized linear models for uncensored outcomes, 20,21 but inflations in Type I error here arise due to the change in censoring assumption with each change in adjustment set. This is the case regardless of whether selection is done through hypothesis testing (eg, stepwise regression) or related approaches such as the Lasso.…”

Ensuring valid inference for hazard ratios after variable selection

“…A test based on the triple selection approach in Section 3.2 enjoys a specific form of double robustness under the null: if either the exposure mean is linear in L or the log hazard of the survival endpoint is linear in L (but not necessarily both), then for similar reasons as in Dukes et al (2020), this test should be valid under the null when there is ultra-sparsity. This is both because the score function has mean zero if either model is correct, and because the proposed method for estimating β * and γ * ensures that the inference is doubly robust.…”

Covariate balancing for causal inference on categorical and continuous treatments

“…In high-dimensional settings (d ≈ n), it has recently been shown that bias due to regularization in estimating correctly specified linear outcome models can be corrected by using relevant weights which are not necessarily based on the true propensity score (Athey et al 2018); see also, e.g., Farrell (2015) and Dukes et al (2020) for double robust estimation with many covariates. An interesting future direction of research is whether one can generalize the results presented herein to high-dimensional situations, balancing many basis functions for the outcome models by using, e.g., regularized GMM techniques (Belloni et al 2018).…”