Robust Q-learning

Abstract

Q-learning is a regression-based approach that is widely used to formalize the development of an optimal dynamic treatment strategy. Finite dimensional working models are typically used to estimate certain nuisance parameters, and misspecification of these working models can result in residual confounding and/or efficiency loss. We propose a robust Q-learning approach which allows estimating such nuisance parameters using data-adaptive techniques. We study the asymptotic behavior of our estimators and provide simulation studies that highlight the need for and usefulness of the proposed method in practice. We use the data from the "Extending Treatment Effectiveness of Naltrexone" multi-stage randomized trial to illustrate our proposed methods.

Keywords: Cross-fitting; Data-adaptive techniques; Dynamic treatment strategies; Residual confounding.

Figure 1:

ExTENd study design. The ® notation represents instances of randomization; the N values in this figure represent the subsequent number of patients assigned to each treatment option.

Figure 2:

ExTENd study. Covariate imbalance across different treatment groups. A₁: stage 1 treatment option; A_2NR: stage 2 treatment options among non-responders; A_2R: stage 2 treatment options among responders. The dashed vertical lines show cut points at ± 0.2.