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Abstract:
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We model the Alzheimer's Disease (AD) related phenotype response variables observed on irregular time points in longitudinal Genome-Wide Association Studies (GWAS) as sparse functional data and propose nonparametric test procedures to detect functional genotype effects, while controlling the confounding effects of environmental covariates. Existing nonparametric tests do not take into account within-subject correlations, suffer from low statistical power, and fail to reach the genome-wide significance level. We propose a new class of functional analysis of covariance (fANCOVA) tests based on a seemingly unrelated (SU) kernel smoother, which can incorporate the correlations. We show that the proposed SU-fANCOVA test combined with a uniformly consistent nonparametric covariance function estimator enjoys the Wilks phenomenon and is minimax most powerful. In an application to the Alzheimer's Disease Neuroimaging Initiative data, the proposed test leads to discovery of new genes that may be related to AD.
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