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

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.

尽管在高血压的研究与治疗领域已取得诸多重大进展，但识别高血压的关键基因型风险因子仍颇具挑战。传统全基因组关联研究（Genome-Wide Association Studies, GWAS）每次仅聚焦单个单核苷酸多态性（Single Nucleotide Polymorphism, SNP）。本研究旨在通过同时建模与变量选择，从逾50万个SNP及时变表型变量中筛选有效变量，并重点关注高血压的高危分位数水平。依托一项大规模公共卫生研究的丰富数据，我们提出并应用了一种新颖的分位数惩罚广义估计方程（Quantile Penalized Generalized Estimating Equations, GEE）方法，该方法兼顾了超高维遗传SNP、血压测量的纵向特性、时变协变量以及血压的条件高分位数等多项关键维度。值得注意的是，我们识别出了与高血压相关的新型SNP。此外，我们发现血压水平存在显著异质性，不同分位数下识别出的重要风险因子存在明显差异。这一针对血压条件分位数的全面分析框架，能够为临床提供更具针对性的研究见解与治疗方案。我们还开发了高效的计算算法，并证明了在超高维预测变量下，分位数惩罚GEE估计量具有相合性、渐近正态性及先知性质。同时，我们确立了高维贝叶斯信息准则（Bayesian Information Criterion, BIC）的模型选择相合性。模拟研究证实了所提方法的良好应用前景。本文的补充材料可在线获取。