Adaptive Mantel Test for Penalized Inference, with Applications to Imaging Genetics
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Mantel's test (MT) for association is conducted by testing the linear relationship of similarity of all pairs of subjects between two observational domains. Motivated by applications to neuroimaging and genetics data, and following the succes of shrinkage and kernel methods for prediction with high-dimensional data, we here introduce the adaptive Mantel test as an extension of the MT. By utilizing kernels and penalized similarity measures, the adaptive Mantel test is able to achieve higher statistical power relative to the classical MT in many settings. Furthermore, the adaptive Mantel test is designed to simultaneously test over multiple similarity measures such that the correct type I error rate under the null hypothesis is maintained without the need to directly adjust the significance threshold for multiple testing. The performance of the adaptive Mantel test is evaluated on simulated data, and is used to investigate associations between genetics markers related to Alzheimer's Disease and heatlhy brain physiology with data from a working memory study of 350 college students from Beijing Normal University.
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