Ranking procedures for repeated measures designs with missing data: Estimation, testing and asymptotic theory

Area of Science:

• Statistics
• Biostatistics
• Nonparametric Methods

Background:

• Repeated measures designs are common in various scientific fields.
• Missing data pose significant challenges in statistical analysis.
• Existing methods may lack flexibility for complex data structures.

Purpose of the Study:

• To develop purely nonparametric methods for analyzing repeated measures designs with missing values.
• To formulate hypotheses in terms of nonparametric treatment effects, accommodating diverse data distributions.
• To provide a unified approach for metric, discrete, ordinal, and binary data.

Main Methods:

• Development of nonparametric procedures for hypothesis testing in repeated measures.
• Solution to the nonparametric Behrens-Fisher problem for repeated measures.
• Construction of global testing, multiple contrast tests, and simultaneous confidence intervals.

Main Results:

• The proposed methods are applicable to various data types (metric, discrete, ordinal, binary).
• Simulations demonstrate satisfactory control of type-I error rates.
• Effective even with small sample sizes and up to 30% missing data.

Conclusions:

• The developed nonparametric methods offer a robust and flexible approach for analyzing repeated measures data with missing values.
• The unified methodology simplifies analysis across different data types.
• The approach is validated through simulations and real-data application.