Optimal confidence intervals for the relative risk and odds ratio

Area of Science:

• Biostatistics
• Biomedical Research Methodology
• Statistical Inference

Background:

• Relative risk and odds ratio are crucial for comparing treatments in biomedical research.
• Existing confidence intervals for these parameters can be approximate, liberal, or conservative.
• There is a need for improved confidence intervals that maintain accuracy and reduce conservatism.

Purpose of the Study:

• To develop an improved method for constructing confidence intervals for relative risk and odds ratio.
• To transform approximate intervals into exact ones and shorten conservative exact intervals.
• To provide more precise statistical inference for comparing two treatments.

Main Methods:

• Application of the $$-function method to intervals derived from two independent binomials.
• Iterative application of the method to further refine intervals until no further shortening is possible.
• Validation using three real-world biomedical datasets.

Main Results:

• The $$-function method successfully converts approximate confidence intervals into exact ones.
• Conservative exact confidence intervals are demonstrably shortened using this novel approach.
• The method's effectiveness is illustrated with practical examples from real datasets.

Conclusions:

• The $$-function method offers a significant improvement over existing interval estimation techniques.
• Two specific exact intervals are recommended for practical application in different estimation scenarios.
• This work enhances the reliability and precision of statistical comparisons in biomedical studies.