TY - JOUR
T1 - Function-on-scalar quantile regression with application to mass spectrometry proteomics data
AU - Liu, Yusha
AU - Li, Meng
AU - Morris, Jeffrey S.
N1 - Funding Information:
Acknowledgements. This research was partially supported by the Grants R01-CA178744 and P50-CA221707 from the National Cancer Institute, 1550088 from the National Science Foundation, 1R24MH117529 of the BRAIN Initiative of the United States National Institutes of Health and an ORAU Ralph E. Powe Junior Faculty Enhancement Award.
Publisher Copyright:
© Institute of Mathematical Statistics, 2020.
PY - 2020
Y1 - 2020
N2 - Mass spectrometry proteomics, characterized by spiky, spatially hetero-geneous functional data, can be used to identify potential cancer biomarkers. Existing mass spectrometry analyses utilize mean regression to detect spec-tral regions that are differentially expressed across groups. However, given the interpatient heterogeneity that is a key hallmark of cancer, many biomark-ers 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 might be more easily detected by quantile-based approaches. Thus, we propose a unified Bayesian framework to perform quantile regression on functional responses. Our approach utilizes an asymmetric Laplace working like-lihood, represents the functional coefficients with basis representations which enable borrowing of strength from nearby locations and places a global-local shrinkage prior on the basis coefficients to achieve adaptive regularization. Different types of basis transform and continuous shrinkage priors can be used in our framework. 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. Our framework performs quantile regression and coefficient regularization in a unified manner, allowing them to inform each other and leading to improvement in performance over com-peting methods, as demonstrated by simulation studies. We also introduce an adjustment procedure to the model to improve its frequentist properties of posterior inference. We apply our 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. Supplementary Material for this article is available online.
AB - Mass spectrometry proteomics, characterized by spiky, spatially hetero-geneous functional data, can be used to identify potential cancer biomarkers. Existing mass spectrometry analyses utilize mean regression to detect spec-tral regions that are differentially expressed across groups. However, given the interpatient heterogeneity that is a key hallmark of cancer, many biomark-ers 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 might be more easily detected by quantile-based approaches. Thus, we propose a unified Bayesian framework to perform quantile regression on functional responses. Our approach utilizes an asymmetric Laplace working like-lihood, represents the functional coefficients with basis representations which enable borrowing of strength from nearby locations and places a global-local shrinkage prior on the basis coefficients to achieve adaptive regularization. Different types of basis transform and continuous shrinkage priors can be used in our framework. 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. Our framework performs quantile regression and coefficient regularization in a unified manner, allowing them to inform each other and leading to improvement in performance over com-peting methods, as demonstrated by simulation studies. We also introduce an adjustment procedure to the model to improve its frequentist properties of posterior inference. We apply our 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. Supplementary Material for this article is available online.
KW - Bayesian hierarchical model
KW - Functional data analysis
KW - Functional response regression
KW - Global-local shrinkage
KW - Proteomic biomarker
KW - Quantile regression
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U2 - 10.1214/19-AOAS1319
DO - 10.1214/19-AOAS1319
M3 - Article
AN - SCOPUS:85087137253
SN - 1932-6157
VL - 14
SP - 521
EP - 541
JO - Annals of Applied Statistics
JF - Annals of Applied Statistics
IS - 2
ER -