Confidence intervals for the common odds ratio based on the inverse sinh transformation

Area of Science:

• Biostatistics
• Statistical Methods
• Epidemiology

Background:

• Accurate estimation of the common odds ratio is crucial in meta-analysis of 2x2 tables.
• Traditional methods for confidence intervals can fail when zero cells are present.
• Existing Woolf and Mantel-Haenszel estimators require robust confidence interval approaches.

Purpose of the Study:

• To propose two new approximate confidence limit methods for the common odds ratio.
• To address interval failure issues caused by zero cells in multiple 2x2 tables.
• To evaluate the performance of novel inverse sinh transformation methods with pseudo-frequencies.

Main Methods:

• Development of modified inverse sinh intervals using pseudo-frequencies (c1 and c2).
• Application of pseudo-frequencies to point estimates (c1) and standard errors (c2).
• Simulation study comparing 22 confidence intervals based on coverage probability and average log length.

Main Results:

• Adjusted inverse sinh intervals with pseudo-frequencies perform well, with coverage probabilities near 95% when c2 > c1.
• Larger c2 values result in narrower intervals but lower coverage probabilities.
• Inverse sinh intervals are consistently shorter than untransformed Woolf and Mantel-Haenszel intervals.

Conclusions:

• The proposed modified inverse sinh intervals offer a reliable approach for common odds ratio estimation.
• Pseudo-frequency adjustments effectively mitigate issues associated with zero cells in 2x2 tables.
• These methods are validated through simulation and illustrated with clinical trial data.