Tests for High Dimensional Generalized Linear Models

TL;DR

This paper examines testing methods for regression coefficients in high-dimensional generalized linear models, identifying limitations of existing tests and proposing a new approach that maintains power across different link functions, with practical application to gene-set analysis.

Contribution

It introduces a new test for high-dimensional GLMs that overcomes the power issues caused by unbounded inverse link functions, improving upon previous methods.

Findings

The new test performs well with bounded inverse link functions like logistic and probit.

It avoids adverse effects of high dimensionality on test power.

Applied successfully to gene-set significance testing in leukemia data.

Abstract

We consider testing regression coefficients in high dimensional generalized linear models. An investigation of the test of Goeman et al. (2011) is conducted, which reveals that if the inverse of the link function is unbounded, the high dimensionality in the covariates can impose adverse impacts on the power of the test. We propose a test formation which can avoid the adverse impact of the high dimensionality. When the inverse of the link function is bounded such as the logistic or probit regression, the proposed test is as good as Goeman et al. (2011)'s test. The proposed tests provide p-values for testing significance for gene-sets as demonstrated in a case study on an acute lymphoblastic leukemia dataset.