Pairwise Comparisons of k $$ k $$ Binomial Responses

Area of Science:

• Statistics
• Biostatistics
• Clinical Trials

Background:

• Binomially distributed data are common in clinical trials, quality control, and stratified sampling.
• Multinomial data from 2 x k contingency tables can be analyzed as k conditionally independent binomial variables.
• Fisher's conditional test is standard for testing equality of binomial success probabilities but doesn't identify pairwise differences.

Purpose of the Study:

• To develop a statistical method for pairwise comparisons of binomial data.
• To provide strong control of the Family-Wise Error Rate (FWER).
• To achieve excellent statistical power in detecting differences.

Main Methods:

• Combined the closed method of pairwise comparisons with unconditional exact tests for 2x2 tables.
• Utilized Fisher's conditional test for tables larger than 2x2.
• Applied these methods to generate p-values for pairwise comparisons.

Main Results:

• The proposed method achieves strong control of the Family-Wise Error Rate.
• The method demonstrates excellent power properties for detecting pairwise differences.
• The approach is applicable to analyzing binomial and multinomial data.

Conclusions:

• The new method offers an effective way to perform pairwise comparisons for binomial data.
• This approach enhances the analysis of data from 2xk contingency tables.
• The findings are relevant for single-site studies in various research fields.