The validity of approximation methods for interval estimation of the odds ratio

Area of Science:

• Biostatistics
• Statistical Inference
• Epidemiology

Background:

• Confidence intervals are crucial for estimating parameter uncertainty.
• Interval validity depends on coverage probability matching the confidence coefficient.
• Accurate confidence intervals for odds ratios are essential in 2x2 table analysis.

Purpose of the Study:

• To assess the validity of three approximate confidence interval construction methods for the odds ratio parameter.
• To compare Cornfield's, Miettinen's, and Woolf's methods under conditional hypergeometric sampling.
• To identify reliable methods for odds ratio interval estimation in 2x2 contingency tables.

Main Methods:

• Examined the validity of confidence intervals for the odds ratio.
• Utilized the conditional hypergeometric sampling situation for 2x2 tables.
• Evaluated three specific construction methods: Cornfield's, Miettinen's, and Woolf's.

Main Results:

• Cornfield's method demonstrated validity over a broad range of true odds ratios.
• Miettinen's and Woolf's methods were frequently found to be invalid.
• Qualitative results from additional examples corroborated these findings.

Conclusions:

• Cornfield's method is a more reliable approach for constructing valid confidence intervals for odds ratios in 2x2 tables.
• Miettinen's and Woolf's methods may produce invalid intervals, potentially leading to inaccurate statistical inference.
• The choice of confidence interval construction method significantly impacts the validity of odds ratio estimation.