Analyzing the tail quantiles of a response distribution is sometimes more important than analyzing the mean in biomarker studies. Inferences in a quantile regression are complicated when there exist a large number of candidate markers, together with some prespecified controlled covariates. In this study, we develop a new and simple testing procedure to detect the effects of biomarkers in a high-dimensional quantile regression in the presence of protected covariates. The test is based on the maximum-score-type statistic obtained from a conditional marginal regression. We establish the asymptotic properties of the proposed test statistic under both null and alternative hypotheses and propose an alternative multiplier bootstrap method, with theoretical justifications. We use numerical studies to show that the proposed method provides adequate controls of the family-wise error rate with competitive power, and that it can also be used as a stopping rule in a forward regression. The proposed method is applied to a motivating genome-wide association study to detect single nucleotide polymorphisms associated with low glomerular filtration rates in type 1 diabetes patients.
|Original language||English (US)|
|Number of pages||24|
|State||Published - Apr 2022|
Bibliographical noteKAUST Repository Item: Exported on 2022-09-14
Acknowledged KAUST grant number(s): OSR-2015-CRG4-2582
Acknowledgements: The authors thank two the anonymous reviewers, associate editor, and editor for their constructive comments and helpful suggestions. This work was partially supported by King Abdullah University of Science and Technology, Office of Sponsored Research under Award No. OSR-2015-CRG4-2582, National Science Foundation (NSF) grant DMS-1712760, National Natural Science Foundation of China grants 11801355 and 11871376, Shanghai Pujiang Program 18PJ1409800, and the IR/D program from the NSF.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.