Hypothesis Testing for Pathway or Gene Set-Based Analysis

Abstract

The complexity of system biology means that any metabolic, genetic, or proteomic pathway typically includes so many components (e.g., molecules) that statistical methods specialized for overall testing of high dimensional and commensurate outcomes are required. We derive new tests that provide accurate control of the Type I error rate when the number of biomarkers is large, or even greater than the sample size. Our derivations capitalize on the dual of the error covariance matrix, which is nonsingular when the number of variables exceeds the sample size, to ensure correct statistical inference and enhance computational efficiency. The new tests apply to a wide range of designs, including one group pre-intervention and post-intervention comparisons, multiple parallel group comparisons with one-way or factorial designs, and the adjustment and evaluation of covariate effects. Simulation studies demonstrate that the tests accurately control the Type I error rate and have reasonable power even with a handful of subjects and a thousand outcome variables. The new methods are applied to the study of metabolic consequences of vitamin B6 deficiency.