Open AccessAn optimal kernel-based multivariate U-statistic to test for associations with multiple phenotypes
Author(s) -
Yalu Wen,
Qing Lu
Publication year - 2020
Publication title -
biostatistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.493
H-Index - 82
eISSN - 1468-4357
pISSN - 1465-4644
DOI - 10.1093/biostatistics/kxaa049
Subject(s) - multivariate statistics , kernel (algebra) , type i and type ii errors , test statistic , statistic , score , computer science , set (abstract data type) , statistics , multivariate analysis , data mining , statistical hypothesis testing , mathematics , combinatorics , programming language
Set-based analysis that jointly considers multiple predictors in a group has been broadly conducted for association tests. However, their power can be sensitive to the distribution of phenotypes, and the underlying relationships between predictors and outcomes. Moreover, most of the set-based methods are designed for single-trait analysis, making it hard to explore the pleiotropic effect and borrow information when multiple phenotypes are available. Here, we propose a kernel-based multivariate U-statistics (KMU) that is robust and powerful in testing the association between a set of predictors and multiple outcomes. We employed a rank-based kernel function for the outcomes, which makes our method robust to various outcome distributions. Rather than selecting a single kernel, our test statistics is built based on multiple kernels selected in a data-driven manner, and thus is capable of capturing various complex relationships between predictors and outcomes. The asymptotic properties of our test statistics have been developed. Through simulations, we have demonstrated that KMU has controlled type I error and higher power than its counterparts. We further showed its practical utility by analyzing a whole genome sequencing data from Alzheimer's Disease Neuroimaging Initiative study, where novel genes have been detected to be associated with imaging phenotypes.