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Ultra-High Dimensional Quantile Regression for Longitudinal Data: An Application to Blood Pressure Analysis

Version 3 2022-11-11, 09:20
Version 2 2022-10-06, 18:40
Version 1 2022-09-29, 21:00
posted on 2022-11-11, 09:20 authored by Tianhai Zu, Heng Lian, Brittany Green, Yan Yu

Despite major advances in research and treatment, identifying important genotype risk factors for high blood pressure remains challenging. Traditional genome-wide association studies (GWAS) focus on one single nucleotide polymorphism (SNP) at a time. We aim to select among over half a million SNPs along with time-varying phenotype variables via simultaneous modeling and variable selection, focusing on the most dangerous blood pressure levels at high quantiles. Taking advantage of rich data from a large-scale public health study, we develop and apply a novel quantile penalized generalized estimating equations (GEE) approach, incorporating several key aspects including ultra-high dimensional genetic SNPs, the longitudinal nature of blood pressure measurements, time-varying covariates, and conditional high quantiles of blood pressure. Importantly, we identify interesting new SNPs for high blood pressure. Besides, we find blood pressure levels are likely heterogeneous, where the important risk factors identified differ among quantiles. This comprehensive picture of conditional quantiles of blood pressure can allow more insights and targeted treatments. We provide an efficient computational algorithm and prove consistency, asymptotic normality, and the oracle property for the quantile penalized GEE estimators with ultra-high dimensional predictors. Moreover, we establish model-selection consistency for high-dimensional BIC. Simulation studies show the promise of the proposed approach. Supplementary materials for this article are available online.


The Framingham Heart Study is conducted and supported by the National Heart, Lung, and Blood Institute (NHLBI) in collaboration with Boston University (Contract No. N01-HC-25195, HHSN268201500001I and 75N92019D00031). This manuscript was not prepared in collaboration with investigators of the Framingham Heart Study and does not necessarily reflect the opinions or views of the Framingham Heart Study, Boston University, or NHLBI. Funding for SHARe Affymetrix genotyping was provided by NHLBI Contract N02-HL64278. SHARe Illumina genotyping was provided under an agreement between Illumina and Boston University. Funding for Affymetrix genotyping of the FHS Omni cohorts was provided by Intramural NHLBI funds from Andrew D. Johnson and Christopher J. O’Donnell. The research of Heng Lian is partially supported by RGC GRF 11300519, 11300721, and 11311822.