Instrumental Variable Estimators for Binary Outcomes

Abstract

Instrumental variables (IVs) can be used to construct estimators of exposure effects on the outcomes of studies affected by nonignorable selection of the exposure. Estimators that fail to adjust for the effects of nonignorable selection will be biased and inconsistent. Such situations commonly arise in observational studies, but are also a problem for randomized experiments affected by nonignorable noncompliance. In this article, we review IV estimators for studies in which the outcome is binary, and consider the links between different approaches developed in the statistics and econometrics literatures. The implicit assumptions made by each method are highlighted and compared within our framework. We illustrate our findings through the reanalysis of a randomized placebo-controlled trial, and highlight important directions for future work in this area.

Keywords:

• Bounds
• Causal inference
• Generalized method of moments
• Local average treatment effects
• Marginal structural models
• Noncompliance
• Parameter identification
• Potential outcomes
• Structural mean models
• Structural models

Acknowledgments

This work was funded by UK Economic & Social Research Council grant RES-060-23-0011 and U.K. Medical Research Council grant G0601625. The authors thank the editors, Dalene Stangl and Alyson Wilson, and the anonymous reviewers for comments that substantially improved the scope, accuracy, and presentation of this work; furthermore, we thank Vanessa Didelez, Roger Harbord, Koen Jochmans, Tom Palmer, and Nuala Sheehan for their helpful comments on earlier drafts.