Improved exact confidence intervals for the odds ratio in two independent binomial samples

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Exact confidence intervals for the odds ratio are commonly used in statistical analysis.
• Conditional confidence intervals can be overly conservative, especially with small sample sizes.
• Unconditional intervals have been shown to be preferable for small sample sizes.

Purpose of the Study:

• To develop a modified unconditional confidence interval for the odds ratio.
• To improve the accuracy and efficiency of confidence intervals for odds ratios.
• To provide a more reliable statistical tool for analyzing binomial data.

Main Methods:

• Utilizing the unconditional approach for constructing confidence intervals.
• Modifying the standard unconditional interval to enhance its properties.
• Evaluating the performance of the proposed interval through coverage probability and length.

Main Results:

• The modified unconditional interval demonstrates shorter length compared to traditional intervals.
• The coverage probability of the modified interval is closer to the nominal confidence level.
• The modified interval ensures coverage probability is at least the nominal confidence coefficient, outperforming conservative conditional intervals.

Conclusions:

• The proposed modified unconditional confidence interval is a superior alternative to the conditional exact interval for two independent binomial samples.
• This method offers improved precision and reliability in estimating the odds ratio, particularly in scenarios with limited data.
• The findings support the use of unconditional intervals for more accurate statistical inference in biostatistics and epidemiology.