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Title: Function-on-scalar quantile regression with application to mass spectrometry proteomics data Authors:  Jeffrey Morris - University of Pennsylvania (United States) [presenting]
Yusha Liu - Rice University (United States)
Meng Li - Rice University (United States)
Abstract: Mass spectrometry proteomics, characterized by spiky, spatially heterogeneous functional data, can be used to identify potential cancer biomarkers. Existing mass spectrometry analyses utilize mean regression to detect spectral regions that are differentially expressed across groups. However, given the inter-patient heterogeneity that is a key hallmark of cancer, many biomarkers are only present at aberrant levels for a subset of, not all, cancer samples. Differences in these biomarkers can easily be missed by mean regression, but may be detected by quantile-based approaches, so we propose a quantile regression framework for functional responses. Our approach utilizes an asymmetric Laplace working likelihood, and uses basis representations and global-local shrinkage priors to enable borrowing of strength from nearby locations. A scalable Gibbs sampler is developed to generate posterior samples that can be used to perform Bayesian estimation and inference while accounting for multiple testing. We apply this model to identify proteomic biomarkers of pancreatic cancer that are differentially expressed for a subset of cancer patients compared to the normal controls, which were missed by previous mean-regression based approaches, and also discuss follow-up work providing faster approaches for these results along with theoretical properties.