Abstract
Significance testing for high-dimensional generalized linear models (GLMs) has become increasingly important in various applications. However, existing methods are mainly based on a sum of the squares of the elements of the score vector and are only powerful under certain alternative hypotheses. In practice, the density of the true association pattern under an alternative hypothesis dictates whether existing tests are powerful. We propose an adaptive test on a high-dimensional parameter of a GLM (in the presence of a low-dimensional nuisance parameter) that maintains high power across a wide range of scenarios. To evaluate its p-value, its asymptotic null distribution is derived. We conduct simulations to demonstrate the superior performance of the proposed test. In addition, we apply it and other existing tests to an Alzheimer's Disease Neuroimaging Initiative data set to detect possible associations between Alzheimer's disease and gene pathways that have a large number of single nucleotide polymorphisms (SNPs). We implemented the proposed method in the R package GLMaSPU, which is publicly available on GitHub and CRAN.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2163-2186 |
| Number of pages | 24 |
| Journal | Statistica Sinica |
| Volume | 29 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Funding Information:The authors thank the reviewers and editors for their helpful comments. This research was supported by NIH grants R01GM113250, R01HL105397, and R01HL116720, by NSF grants DMS-1712717 and SES-1659328, by NSA grant H98230-17-1-0308, and by the Minnesota Supercomputing Institute. CW was supported by a University of Minnesota Doctoral Dissertation Fellowship. The data collection and sharing for this project were funded by the Alzheimer’s Dis- ease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904).
Funding Information:
Alzheimer’s disease (AD) is the most common form of dementia, affecting millions of people worldwide. The Alzheimer’s Disease Neuroimaging Initiative (ADNI) is a longitudinal multisite observational study of healthy elders, mild cognitive impairment (MCI), and AD (Jack et al. (2008)). It is jointly funded by the National Institutes of Health (NIH) and industry via the Foundation for the NIH. The Principal Investigator of this initiative is Michael W. Weiner, VA Medical Center and University of California. The major goal of the ADNI is to test whether serial MRI, positron emission tomography (PET), and other biological markers can be combined to measure the progression of MCI and early AD. ADNI has recruited more than 1,500 subjects, aged between 55 and 90, to participate in the research. For latest information, see www.adni-info.org.
Funding Information:
The authors thank the reviewers and editors for their helpful comments. This research was supported by NIH grants R01GM113250, R01HL105397, and R01HL116720, by NSF grants DMS-1712717 and SES-1659328, by NSA grant H98230-17-1-0308, and by the Minnesota Supercomputing Institute. CW was supported by a University of Minnesota Doctoral Dissertation Fellowship. The data collection and sharing for this project were funded by the Alzheimer's Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904).
Publisher Copyright:
© 2020 Institute of Statistical Science. All rights reserved.
Keywords
- Adaptive tests
- Generalized linear models
- High-dimensional testing
- Power