Global hypothesis testing for high-dimensional repeated measures outcomes.

High-throughput technology in metabolomics, genomics, and proteomics gives rise to high dimension, low sample size data when the number of metabolites, genes, or proteins exceeds the sample size. For a limited class of designs, the classic 'univariate approach' for Gaussian repeated measures can provide a reasonable global hypothesis test. We derive new tests that not only accurately allow more variables than subjects, but also give valid analyses for data with complex between-subject and within-subject designs. 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. Simulation studies demonstrate that the new tests accurately control Type  I error rate and have reasonable power even with a handful of subjects and a thousand outcome variables. We apply the new methods to the study of metabolic consequences of vitamin B6 deficiency. Free software implementing the new methods applies 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.