-- KathrynStoltzfus - 05 Feb 2018

Significance testing for high-dimensional generalized linear models (GLMs) has been increasingly needed in various applications. Motivated by the analysis of an Alzheimer’s disease dataset, I will first present an adaptive test on a high-dimensional parameter of a GLM in the presence of a low-dimensional nuisance parameter, which can maintain correct Type 1 error rate and high power across a wide range of scenarios.

In the second part, I will consider the case with a high-dimensional nuisance parameter. I will present a new method that combines non-convex penalized regression and adaptive testing, aiming to control Type 1 error rate and maintain high power. To calculate its p-value analytically, the asymptotic distribution of the test statistic is derived.

I will illustrate the applications of the newly proposed methods to the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset, detecting possible associations between Alzheimer’s disease and genetic variants in some gene pathways, and identifying possible gene pathway-gender interactions for Alzheimer’s disease.
Topic revision: r1 - 05 Feb 2018, KathrynStoltzfus

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