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A note on the control function approach with an instrumental variable and a binary outcome.

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Summary
This summary is machine-generated.

This study introduces a new control function approach for instrumental variable estimation with binary exposure and rare binary outcomes. This method helps address unobserved confounding in causal inference when experimental data is unavailable.

Keywords:
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Area of Science:

  • Epidemiology
  • Biostatistics
  • Econometrics

Background:

  • Unobserved confounding poses a significant challenge to causal inference in non-experimental studies.
  • Instrumental variable (IV) designs offer a potential solution to mitigate bias from unobserved confounders.
  • Existing IV methods for binary outcomes often assume continuous exposure, limiting their application.

Purpose of the Study:

  • To extend the control function approach for instrumental variable estimation to settings with binary exposure and binary outcomes.
  • To provide a robust method for causal inference in the presence of unobserved confounding when dealing with binary variables.

Main Methods:

  • Proposed a modified control function approach for binary exposure and rare binary outcomes.
  • The first stage involves a logistic regression of exposure on the instrumental variable.
  • The second stage uses a logistic regression of the outcome on exposure, including the first stage residual.

Main Results:

  • The study provides a formal justification for the control function approach with binary exposure.
  • Established conditions for valid instrumental variable estimation in this specific setting.
  • Recommended risk ratio regression for non-rare binary outcomes.

Conclusions:

  • The adapted control function approach is suitable for instrumental variable estimation with binary exposure and rare binary outcomes.
  • This methodology enhances causal inference capabilities in epidemiological and other observational studies.
  • The findings broaden the applicability of instrumental variable methods beyond continuous exposures.