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.

未测量的混杂是对因果推断和个性化决策的威胁。类似于 Cui 和 Tchetgen Tchetgen (2020)；邱等人。(2020); Han (2020a)，我们考虑了用有效的工具变量识别最佳个体化治疗方案的问题。Han (2020a) 使用 Cui 和 Tchetgen Tchetgen (2020) 的条件 Wald 估计提供了最佳治疗方案的替代识别条件；邱等人。(2020) 当治疗分配受内生性影响并且有效的二元工具变量可用时。在本说明中，我们提供了使用条件 Wald 估计确定最佳治疗方案的必要和充分条件。我们的新条件必然被 Cui 和 Tchetgen Tchetgen (2020) 的条件所暗示；邱等人。(2020);