Test-based exact confidence intervals for the difference of two binomial proportions

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• Confidence intervals are essential for estimating treatment differences in clinical trials.
• Large sample approximations for confidence intervals can be unreliable with small sample sizes common in early-phase trials.

Purpose of the Study:

• To propose and evaluate test-based methods for constructing exact confidence intervals for the difference between two binomial proportions.
• To ensure reliable coverage levels for confidence intervals in small sample settings.

Main Methods:

• Development of exact confidence intervals derived from the unconditional distribution of two binomial responses.
• Comparison of proposed methods against confidence intervals based solely on the observed difference.
• Utilizing a standardized Z test with a constrained maximum likelihood estimate of the variance.

Main Results:

• The proposed test-based exact confidence intervals guarantee the specified level of coverage.
• Significant performance improvement was demonstrated compared to methods relying only on the observed difference.
• The standardized Z test with constrained variance estimation proved particularly effective.

Conclusions:

• Test-based exact confidence intervals offer a reliable alternative to approximate methods for small sample sizes in clinical trials.
• The proposed methodology enhances the accuracy of treatment difference estimation in early-phase research.
• Adoption of these exact methods can lead to more precise and dependable statistical inferences.