Pearson's chi-square test and rank correlation inferences for clustered data.

Area of Science:

• Statistics
• Biostatistics
• Data Analysis

Background:

• Traditional association tests (Pearson's chi-square, Spearman, Kendall's tau) assume independent data pairs.
• This assumption is violated in clustered data where sampling units contain multiple paired responses.
• Existing methods lack validity for clustered, possibly tied, paired response data.

Purpose of the Study:

• To develop novel statistical tests and correlation estimators for clustered paired response data.
• To address the violation of independence assumptions in traditional statistical methods.
• To provide reliable methods for analyzing association in complex clustered datasets.

Main Methods:

• Application of within-cluster resampling techniques to U-statistics.
• Development of new rank-based correlation estimators for possibly tied clustered data.
• Theoretical development of large sample properties for proposed tests and estimators.

Main Results:

• Proposed methods provide valid statistical tests and correlation estimators for clustered paired data.
• Large sample properties of the new methods were theoretically derived.
• Simulation studies demonstrated the performance of the proposed techniques.

Conclusions:

• The novel within-cluster resampling approach effectively handles clustered paired response data.
• The developed methods offer improved statistical power and accuracy for association testing in such data.
• The techniques are applicable to real-world data, including PET/CT imaging studies.