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

arXiv: https://arxiv.org/abs/2010.03390 · HTML: https://mlsanity.com/paper/2010.03390/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2020.

## Built on by (most cited first, 2 of 2)

- [Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox](https://mlsanity.com/paper/2110.10961/) (2021)
- [Optimal Treatment Regimes for Proximal Causal Learning](https://mlsanity.com/paper/2212.09494/) (2022)

## Abstract (arXiv)

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.