Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding

Abstract

Data-driven individualized decision making has recently received increasing research interest. However, most existing methods rely on the assumption of no unmeasured confounding, which cannot be ensured in practice especially in observational studies. Motivated by the recently proposed proximal causal inference, we develop several proximal learning methods to estimate optimal individualized treatment regimes (ITRs) in the presence of unmeasured confounding. Explicitly, in terms of two types of proxy variables, we are able to establish several identification results for different classes of ITRs respectively, exhibiting the tradeoff between the risk of making untestable assumptions and the potential improvement of the value function in decision making. Based on these identification results, we propose several classification-based approaches to finding a variety of restricted in-class optimal ITRs and establish their theoretical properties. The appealing numerical performance of our proposed methods is demonstrated via extensive simulation experiments and a real data application. Supplementary materials for this article are available online.

KEYWORDS:

• Double robustness
• Endogeneity
• Proximal causal inference
• Treatment regime identification

Supplementary Materials

All technical proofs, implementation details and additional numerical results are given in supplementary materials.

Acknowledgments

The authors thank the editor, an associate editor, and three referees for their constructive comments and suggestions.

Additional information

Funding

Xiaoke Zhang’s research is partially supported by the George Washington University University Facilitating Fund.