Nonparametric inverse probability weighted estimators based on the highly adaptive lasso

TL;DR

This paper introduces a new class of nonparametric inverse probability weighted estimators that use the highly adaptive lasso for improved efficiency and robustness in causal effect estimation, avoiding model misspecification.

Contribution

It proposes a novel nonparametric estimator based on undersmoothing the highly adaptive lasso, achieving asymptotic efficiency without needing the influence function or outcome model.

Findings

Estimators are asymptotically linear with variance reaching the efficiency bound.

Perform well in simulations and real epidemiologic data.

Require no model specification for the outcome or influence function.

Abstract

Inverse probability weighted estimators are the oldest and potentially most commonly used class of procedures for the estimation of causal effects. By adjusting for selection biases via a weighting mechanism, these procedures estimate an effect of interest by constructing a pseudo-population in which selection biases are eliminated. Despite their ease of use, these estimators require the correct specification of a model for the weighting mechanism, are known to be inefficient, and suffer from the curse of dimensionality. We propose a class of nonparametric inverse probability weighted estimators in which the weighting mechanism is estimated via undersmoothing of the highly adaptive lasso, a nonparametric regression function proven to converge at $n^{-1/3}$-rate to the true weighting mechanism. We demonstrate that our estimators are asymptotically linear with variance converging to the nonparametric efficiency bound. Unlike doubly robust estimators, our procedures require neither derivation of the efficient influence function nor specification of the conditional outcome model. Our theoretical developments have broad implications for the construction of efficient inverse probability weighted estimators in large statistical models and a variety of problem settings. We assess the practical performance of our estimators in simulation studies and demonstrate use of our proposed methodology with data from a large-scale epidemiologic study.