A general instrumental variable framework for regression analysis with outcome missing not at random.

Area of Science:

• Biostatistics
• Epidemiology
• Econometrics

Background:

• Selection bias due to missing outcomes can lead to biased causal effect estimates.
• Unobserved confounding is a common challenge in observational studies.
• Instrumental variable (IV) methods offer a potential solution for unbiased causal inference.

Purpose of the Study:

• To adapt the instrumental variable (IV) approach for regression analysis with outcomes missing not at random.
• To develop methods for unbiased estimation of causal effects and improved uncertainty quantification.
• To illustrate the application of the proposed methods using data on HIV prevalence.

Main Methods:

• Utilized an instrumental variable (IV) design assuming the IV predicts nonresponse and is independent of the outcome.
• Proposed a complete-case analysis incorporating the IV to adjust for selection bias.
• Developed novel, smooth bounds for marginal mean inference of binary outcomes, addressing uncertainty.

Main Results:

• Demonstrated nonparametric identification of population regression under specific IV assumptions.
• The proposed complete-case analysis effectively accounts for selection bias.
• Novel bounds offer a more honest assessment of uncertainty compared to existing methods.

Conclusions:

• The instrumental variable (IV) approach is effective for addressing selection bias in regression with missing outcomes.
• The developed methods provide robust causal effect estimation and uncertainty quantification.
• The approach is applicable to real-world scenarios, such as estimating HIV prevalence.