Robust inference on the average treatment effect using the outcome highly adaptive lasso

Abstract

Many estimators of the average effect of a treatment on an outcome require estimation of the propensity score, the outcome regression, or both. It is often beneficial to utilize flexible techniques, such as semiparametric regression or machine learning, to estimate these quantities. However, optimal estimation of these regressions does not necessarily lead to optimal estimation of the average treatment effect, particularly in settings with strong instrumental variables. A recent proposal addressed these issues via the outcome‐adaptive lasso, a penalized regression technique for estimating the propensity score that seeks to minimize the impact of instrumental variables on treatment effect estimators. However, a notable limitation of this approach is that its application is restricted to parametric models. We propose a more flexible alternative that we call the outcome highly adaptive lasso. We discuss the large sample theory for this estimator and propose closed‐form confidence intervals based on the proposed estimator. We show via simulation that our method offers benefits over several popular approaches.

Why Machine Learning Cannot Ignore Maximum Likelihood Estimation

“…And k can now be selected with crossvalidation based on the loss function L(Q) for Q 0 , or a AIC/BIC type selector to avoid the double cross-validation. This approach can now be used, for example, to select the L 1 -norm in a HAL-MLE, the truncation level, but also to select the maximal degree of the tensor products, or maximal sparsity of the basis functions, and so on [3,8,25,33,26]. Simulations have demonstrated that this collaborative (C-TMLE) procedure can dramatically outperform a TMLE that uses pure likelihood based estimation of G 0 when there are positivity issues [8].…”

“…This approach can now be used, for example, to select the L 1 -norm in a HAL-MLE, the truncation level, but also to select the maximal degree of the tensor products, or maximal sparsity of the basis functions, and so on [3,8,25,33,26]. Simulations have demonstrated that this collaborative (C-TMLE) procedure can dramatically outperform a TMLE that uses pure likelihood based estimation of G 0 when there are positivity issues [8]. One can also let a HAL-MLE fit of Q 0 impact the basis functions included in the HAL-MLE of G 0 , and use this C-TMLE procedure to select the L 1 -norm in the HAL-MLE of Q 0 and the resulting HAL-MLE of G 0 (as well as the truncation level).…”

“…We will argue that the HAL-MLE is a particularly powerful sieve MLE, generally theoretically superior to other types of sieve MLEs. Moreover, for obtaining statistical inference for estimands that aim to equal or approximate a causal quantity defined in an underlying causal model, we discuss the combination of HAL-MLE with targeted maximum likelihood estimators (TMLEs) [30,31,32] in HAL-TMLEs as well as using undersmoothed HAL-MLE by itself as a powerful statistical approach [8,24,25,31]. HALs can be used for the initial estimator in TMLEs as well as for nuisance functions representing the treatment and missingness/censoring mechanism.…”

hal9001: Scalable highly adaptive lasso regression in R

“…While a variety of procedures have been proposed to overcome the issues posed by instrumental variables, a particularly successful idea was given by Shortreed & Ertefaie (2017), who proposed standard lasso regression to select covariates for the exposure model based on an estimated outcome model. The work of Ju et al (2020) replaces the standard lasso with HAL regression, effectively screening for infinitesimal instrumental basis functions rather than instrumental variables, providing much enhanced flexibility. Here, the authors demonstrate how HAL regression provides exceptionally fine-grained control over screening problematic covariates while simultaneously facilitating the construction of causal effect estimators with desirable asymptotic properties.…”

Inference in high-dimensional time series models

“…Many more refinements of such procedures have acquired a great deal of space and interest in the statistics and econometrics literatures. Econometrics applications of these procedures see among others: instrumental variables estimation (see among others: Belloni, Chernozhukov, and Hansen, 2011b;Belloni, Chen, et al, 2012;Belloni, Chernozhukov, and Wang, 2014;Windmeijer et al, 2019), treatment effect models (see among others: Belloni, Chernozhukov, Fernández-Val, et al, 2015;Li and Bell, 2017;Ju et al, 2020), time series models (see among others: Kock and Callot, 2015;Medeiros and Mendes, 2016b).…”