On a necessary and sufficient identification condition of optimal treatment regimes with an instrumental variable

TL;DR

This paper establishes a necessary and sufficient condition for identifying optimal treatment regimes using instrumental variables, advancing causal inference methods under unmeasured confounding.

Contribution

It provides a complete characterization of the conditions needed for identification, extending prior work with a more comprehensive criterion.

Findings

The new condition is necessary and sufficient for identification.

It generalizes previous results to broader settings.

The condition applies even when prior assumptions are not met.

Abstract

Unmeasured confounding is a threat to causal inference and individualized decision making. Similar to Cui and Tchetgen Tchetgen (2020); Qiu et al. (2020); Han (2020a), we consider the problem of identification of optimal individualized treatment regimes with a valid instrumental variable. Han (2020a) provided an alternative identifying condition of optimal treatment regimes using the conditional Wald estimand of Cui and Tchetgen Tchetgen (2020); Qiu et al. (2020) when treatment assignment is subject to endogeneity and a valid binary instrumental variable is available. In this note, we provide a necessary and sufficient condition for identification of optimal treatment regimes using the conditional Wald estimand. Our novel condition is necessarily implied by those of Cui and Tchetgen Tchetgen (2020); Qiu et al. (2020); Han (2020a) and may continue to hold in a variety of potential settings not covered by prior results.