A FUNCTIONAL PERSPECTIVE ON THE CONDITIONAL COVARIANCE COMPARISON PROBLEM IN DEMENTIA ANALYSIS.

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Comparing covariance structures is crucial in multivariate analysis but existing methods often fail to account for covariates.
• Adjusting for covariates by removing their effects may lead to loss of valuable information.

Purpose of the Study:

• To propose a novel functional nonparametric covariance matrix estimator that accounts for covariates.
• To enable comparison of functional covariance structures in multivariate data.
• To apply the method to real-world data, such as in Alzheimer's disease research.

Main Methods:

• A functional nonparametric covariance matrix estimator is proposed.
• A test statistic based on the first eigenvalue of combined covariance matrices is used for comparison.
• Parametric (Tracy-Widom), semi-parametric (Forkman's test), and nonparametric (Permutation) methods are employed for p-value computation.
• Extensive simulation studies were conducted to evaluate type I error and power.

Main Results:

• The proposed method effectively accounts for covariates in comparing covariance structures.
• Simulation studies demonstrated the reliability and power of the hypothesis testing approaches.
• The application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset provided insights into biomarker covariance differences.

Conclusions:

• The novel method offers a robust approach for comparing functional covariance structures in the presence of covariates.
• The findings have implications for clinical applications and understanding complex biological data.
• The study highlights significant differences in the covariance structures of cerebrospinal fluid biomarkers between dementia and non-dementia cohorts, considering age, sex, and education.