Estimating Optimal Treatment Rules with an Instrumental Variable: A Partial Identification Learning Approach

Abstract

Individualized treatment rules (ITRs) are considered a promising recipe to deliver better policy interventions. One key ingredient in optimal ITR estimation problems is to estimate the average treatment effect conditional on a subject’s covariate information, which is often challenging in observational studies due to the universal concern of unmeasured confounding. Instrumental variables (IVs) are widely used tools to infer the treatment effect when there is unmeasured confounding between the treatment and outcome. In this work, we propose a general framework of approaching the optimal ITR estimation problem when a valid IV is allowed to only partially identify the treatment effect. We introduce a novel notion of optimality called ‘IV‐optimality’. A treatment rule is said to be IV‐optimal if it minimizes the maximum risk with respect to the putative IV and the set of IV identification assumptions. We derive a bound on the risk of an IV‐optimal rule that illuminates when an IV‐optimal rule has favourable generalization performance. We propose a classification‐based statistical learning method that estimates such an IV‐optimal rule, design computationally efficient algorithms, and prove theoretical guarantees. We contrast our proposed method to the popular outcome weighted learning (OWL) approach via extensive simulations, and apply our method to study which mothers would benefit from travelling to deliver their premature babies at hospitals with high‐level neonatal intensive care units. R package ivitr implements the proposed method.

Policy Learning Under Ambiguity

“…However, our estimation procedure crucially differs from theirs for the use of Neyman-orthogonal estimates which, combined with a refined proof-strategy that accounts for the lack of full-differentiability in the welfare criterion, allows us to establish considerably faster rates of convergence. As such, we see our results as improving on those of Pu and Zhang (2021).…”

“…A major contribution of this paper is to account for the role played by the lack of full differentiability as we generalize procedures for learning optimal policies from data to the partially identified setting in Section 3. While we stress the general applicability of our analysis to a wide variety of optimality criteria and identification schemes, we will specialize our results to the minimax regret criterion and the Balke-Pearl bounds of Example 1 to streamline presentation and facilitate comparison with results in Pu and Zhang (2021).…”

“…As a result we see our contribution as complementary to theirs. In contemporaneous work, Pu and Zhang (2021) study policy learning under ambiguity from a classification perspective and derive an optimal policy that coincides with the minimax welfare regret optimal policy studied in this paper. However, our estimation procedure crucially differs from theirs for the use of Neyman-orthogonal estimates which, combined with a refined proof-strategy that accounts for the lack of full-differentiability in the welfare criterion, allows us to establish considerably faster rates of convergence.…”

Individualized Decision Making Under Partial Identification: ThreePerspectives, Two Optimality Results, and One Paradox

“…Therefore, the proposed mixed strategy gives a sharper minimax regret bound than Zhang and Pu (2021) and Pu and Zhang (2021), and therefore is sharper than any deterministic rules.…”

“…In particular, Cui and Tchetgen Tchetgen (2021c) pointed out that one could identify treatment regimes that maximize lower bounds of the value function when one has only partial identification through an IV. Pu and Zhang (2021) further proposed an IVoptimality criterion to learn an optimal treatment regime, which essentially recommends the treatment for patients for whom the estimated conditional average treatment effect bound covers zero based on the length of the bounds, that is, based on the left panel of Figure 1. See more details in Tchetgen Tchetgen (2021a, 2021c) and Zhang and Pu (2021).…”