Approximate simultaneous confidence intervals for multiple contrasts of binomial proportions

Area of Science:

• Biostatistics
• Statistical Methods
• Clinical Trials

Background:

• Established methods for simultaneous confidence intervals in Gaussian data are not readily available for non-Gaussian distributions like binomial proportions.
• Existing methods for comparing two binomial proportions or single contrasts are insufficient for multiple comparisons.
• Lack of implemented software solutions for non-Gaussian multiple contrast comparisons.

Purpose of the Study:

• To extend existing confidence interval methods for comparing binomial proportions to handle multiple contrasts simultaneously.
• To develop statistically sound methods for non-Gaussian data, specifically binomial proportions, in a one-way layout.
• To evaluate the performance of the proposed methods in small sample scenarios.

Main Methods:

• Extended recently proposed confidence interval methods for the difference of two proportions to multiple contrasts.
• Utilized quantiles of the multivariate normal distribution to account for correlations among binomial proportions.
• Investigated small sample performance through simulation studies and proposed a simple adjustment of adding 2 pseudo-observations.

Main Results:

• The proposed methods demonstrated reasonable coverage probabilities, particularly with the suggested adjustment for small samples.
• The methods effectively handle simultaneous confidence intervals for multiple contrasts of binomial proportions.
• The methodology was successfully illustrated using real-world data from a clinical trial and a toxicological study.

Conclusions:

• The developed methods provide a valuable tool for statistical inference in situations involving multiple binomial proportion comparisons.
• The proposed approach offers a practical solution where traditional Gaussian-based methods are inapplicable.
• The R package MCPAN makes these advanced statistical methods accessible for researchers.