Sample-constrained partial identification with application to selection bias.

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Partial identification problems often involve estimating both a function and a set from empirical data.
• Statistical inference for these problems, especially non-convex ones, is underdeveloped.
• Selection bias in population-based cohort studies presents a significant challenge in causal inference.

Purpose of the Study:

• To develop a general statistical inference framework for the optimal value in partially identified models.
• To apply this framework to address selection bias in population-based cohort studies.
• To enhance existing sensitivity analyses by incorporating auxiliary population information.

Main Methods:

• Derivation of an asymptotically valid confidence interval for the optimal value via set relaxation.
• Formulation of sensitivity analyses within the new framework.
• Utilizing population-level auxiliary information to improve estimation and inference.

Main Results:

• The proposed method provides a general approach for statistical inference in partially identified models.
• Sensitivity analyses are made more informative and easier to implement.
• The method yields informative bounds for causal effects, demonstrated in the education-income relationship using UK Biobank data.

Conclusions:

• The developed statistical inference procedure offers a powerful tool for handling selection bias in cohort studies.
• Auxiliary population constraints can significantly improve the informativeness of causal effect estimates.
• The methodology is implemented in an R package for practical application.