The performance of three approximate confidence limit methods for the odds ratio

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Inference

Background:

• Accurate confidence intervals for the odds ratio (R) are crucial in statistical analysis.
• Evaluating approximate methods is essential for reliable inference, especially in unconditional sample spaces.

Purpose of the Study:

• To compare the performance of three approximate confidence limit methods for the odds ratio (R) at the 95% confidence level.
• To determine the most accurate method for constructing confidence intervals for the odds ratio in unconditional settings.

Main Methods:

• The study evaluated Cornfield's method, the logit method with 1/2 corrections, and Miettinen's test-based method.
• Performance was assessed based on achieving the nominal 95% confidence coefficient in the unconditional sample space.

Main Results:

• Cornfield's method demonstrated the closest adherence to the nominal confidence coefficient.
• The logit method resulted in actual coefficients larger than nominal with unequal tail areas, partly due to logit transformation skewness.
• The test-based method showed coefficients uniformly less than nominal for R not equal to 1, with underestimation worsening in finite samples.

Conclusions:

• Cornfield's method without continuity correction is recommended as the preferred approximate method for odds ratio confidence limits in unconditional sample spaces.
• This finding extends previous recommendations for conditional sample spaces.