An Adaptive Test on High-Dimensional Parameters in Generalized Linear Models

• Activity Number: 584 - Statistical Methods for Genetic Association Analysis
• Type: Contributed
• Date/Time: Wednesday, August 2, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Genomics and Genetics
• Author(s): Chong Wu* and Wei Pan and Gongjun Xu
• Companies: University of Minnesota and University of Minnesota and University of Michigan
• Keywords: Adaptive tests ; Generalized linear models ; High-dimensional testing ; Power

Abstract

Several tests for high-dimensional generalized linear models have been proposed recently, however, they are mainly based on a sum of squares of the score vector and only powerful under certain limited alternative hypotheses. In practice, since the associations in a true alternative hypothesis may be sparse or dense or between, the existing tests may or may not be powerful. In this paper, we propose an adaptive test that maintains high power across a wide range of scenarios. To calculate its p-value, its asymptotic null distribution is derived. We conduct simulations to demonstrate the superior performance of the proposed test. Then we apply it and other existing tests to an Alzheimer's Disease Neuroimaging Initiative data set, detecting possible associations between Alzheimer's disease and sets of a large number of single nucleotide polymorphisms. As an end product, we put R package GLMaSPU implementing the proposed test on GitHub and CRAN.