A Nonparametric Three-Sample Test
Ashlynn Crisp, Portland State University
Identifying the onset of Alzheimer's disease poses a challenge, as individuals gradually deviate from a healthy reference group, as evidenced by biomarkers. However, this early stage offers the greatest potential for treatment. Therefore, there is a need for a statistical approach that can determine if a treated group is closer to a healthy reference group than to an untreated control group.
In this study, we propose a versatile nonparametric procedure to assess whether a population of interest is more similar to a reference population than a control population is. Our method builds upon the kernel two-sample maximum mean discrepancy (MMD) test, which measures the largest discrepancy in expectations across functions within a unit ball of a reproducing kernel Hilbert space. This allows us to compare distances among three populations: the population of interest, the control, and the reference.
We present asymptotic results and a procedure for calculating the required sample size. To showcase the effectiveness of our approach, we apply it to a simplified example using image groups from the CIFAR-10 dataset. Our analysis reveals that images of birds exhibit greater similarity to images of planes than to images of cars. Furthermore, we apply our method to data from the Wisconsin Registry for Alzheimer's Prevention (WRAP) to investigate the longitudinal progression of biomarkers for Alzheimer's detection.
Abstract Author(s): Ashlynn Crisp, Michael Wells, Adam Macbale, Daniel Taylor Rodriguez, Bruno Jedynak