Ultra-high-dimensional threshold selection for quantile feature screening with false discovery rate error rate control: a case study on high blood pressure analysis

Identifying important genetic risk factors for high blood pressure is paramount for targeted interventions and comprehensive management strategies for this prevalent health condition. With ultra-high-dimensional genetic factors, feature screening plays a vital role in retaining the important risk factors and screening out the unimportant ones. However, its efficacy depends on selecting the appropriate threshold in different data contexts. We propose a novel quantile mirror (QM) approach for data-adaptive threshold selection with false discovery rate (FDR) control in quantile feature screening, where abnormally high blood pressure levels are of the most interest. The symmetric QM statistics enable the estimation of the FDR. Multiple data splitting is employed for result stability, and different thresholds are allowed for different quantiles. Additionally, we introduce the Quantile REflection via Data Splitting (QREDS) and the Hard Threshold with QREDS feature screening procedures. We apply our proposed methods to the Framingham Heart Study data. While many of the retained high-blood-pressure-related genetic features are validated from medical literature, some new risk factors are discovered. We show that our proposed procedures asymptotically control the FDR under suitable conditions. We further demonstrate the performance of the proposed methods through extensive numerical analysis and simulation studies.