Investigations of sharp bounds for causal effects under selection bias

Area of Science:

• Epidemiology
• Biostatistics
• Causal Inference

Background:

• Selection bias poses a threat to both internal and external validity in research.
• Quantifying the maximum potential selection bias is crucial for accurate causal inference.
• Existing methods for bounding selection bias rely on sensitivity parameters.

Purpose of the Study:

• To analyze the properties of previously proposed bounds for selection bias.
• To derive improved bounds for selection bias that incorporate selection probabilities.
• To assess the performance of these bounds in various scenarios.

Main Methods:

• Demonstrated the variation independence of sensitivity parameters.
• Established conditions under which the proposed bounds are sharp.
• Derived new, improved bounds for selection bias.
• Utilized an empirical example and numerical experiments for illustration and performance evaluation.

Main Results:

• Sensitivity parameters for selection bias bounds were found to be variation independent.
• The previously proposed bounds were shown to be sharp under specific conditions.
• Improved bounds were derived, requiring additional information on selection probabilities.
• Empirical and numerical analyses demonstrated the utility and performance of the bounds.

Conclusions:

• The derived bounds offer a more refined approach to quantifying selection bias.
• Understanding selection probabilities enhances the accuracy of causal effect estimation.
• These methods provide valuable tools for assessing the impact of selection bias in observational studies.