Minimax Powerful Functional Analysis of Covariance Tests: with Application to Longitudinal Genome-Wide Association Studies.

We model the Alzheimer's Disease-related phenotype response variables observed on irregular time points in longitudinal Genome-Wide Association Studies as sparse functional data and propose nonparametric test procedures to detect functional genotype effects while controlling the confounding effects of environmental covariates. Our new functional analysis of covariance tests are based on a seemingly unrelated kernel smoother, which takes into account the within-subject temporal correlations, and thus enjoy improved power over existing functional tests. We show that the proposed test combined with a uniformly consistent nonparametric covariance function estimator enjoys the Wilks phenomenon and is minimax most powerful. Data used in the preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database, where an application of the proposed test lead to the discovery of new genes that may be related to Alzheimer's Disease.