A robust likelihood approach to inference about the difference between two multinomial distributions in paired...

Area of Science:

• Statistics
• Biostatistics
• Statistical Modeling

Background:

• Pairing reduces heterogeneity but increases model complexity and inference intricacy.
• Existing methods for paired data can be overly complicated due to increased parameters.

Purpose of the Study:

• To develop a robust score statistic for testing the equality of two multinomial distributions in paired designs.
• To simplify inference in paired data analysis by utilizing a parallel design structure.
• To incorporate within-pair correlation in a data-driven manner without full model specification.

Main Methods:

• Development of a robust score statistic based on the parallel design structure.
• Incorporation of within-pair correlation in a non-parametric way.
• Application to paired binary data, where the statistic simplifies to McNemar's test.

Main Results:

• The proposed robust score statistic effectively tests for the equality of multinomial distributions in paired designs.
• The test accounts for within-pair correlation without requiring a fully specified probability model.
• In the binary case, the robust statistic is equivalent to McNemar's test, a known powerful test.

Conclusions:

• The robust score statistic provides a simpler and more tractable approach for analyzing paired multinomial data.
• This method offers advantages in statistical inference for paired designs, especially in scenarios with binary outcomes.
• The procedure is validated through simulations and real-world data analysis, demonstrating its practical utility.