Confidence intervals based on some weighting functions for the difference of two binomial proportions

Area of Science:

• Biostatistics
• Statistical Inference

Background:

• Exact confidence intervals for binomial proportions can be overly conservative in small samples.
• Existing methods maximize tail probabilities, leading to wider, less informative intervals.

Purpose of the Study:

• To propose two novel quasi-exact methods for computing confidence intervals for the difference of two independent binomial proportions.
• To reduce conservatism inherent in traditional exact methods for small sample sizes.

Main Methods:

• Developed two new methods weighting p-values with specific functions, instead of using maximum p-value.
• Proposed methods are termed quasi-exact, offering an alternative to exact and approximate intervals.

Main Results:

• Proposed methods are significantly less conservative than the exact method.
• Methods demonstrate coverage probabilities closer to the nominal level and shorter expected confidence widths compared to existing quasi-exact methods.
• The beta weighting method offers an optimal balance between coverage accuracy and interval width.

Conclusions:

• The new quasi-exact methods provide improved confidence intervals for the difference of two independent binomial proportions in small samples.
• These methods offer a less conservative alternative with better performance than existing approaches.