  Advances of modern sensing and sequencing technologies generate a deluge of
high dimensional space-temporal physiological and next-generation sequencing
(NGS) data. Physiological traits are observed either as continuous random
functions, or on a dense grid and referred to as function-valued traits. Both
physiological and NGS data are highly correlated data with their inherent
order, spacing, and functional nature which are ignored by traditional
summary-based univariate and multivariate regression methods designed for
quantitative genetic analysis of scalar trait and common variants. To capture
morphological and dynamic features of the data and utilize their dependent
structure, we propose a functional linear model (FLM) in which a trait curve is
modeled as a response function, the genetic variation in a genomic region or
gene is modeled as a functional predictor, and the genetic effects are modeled
as a function of both time and genomic position (FLMF) for genetic analysis of
function-valued trait with both GWAS and NGS data. By extensive simulations, we
demonstrate that the FLMF has the correct type 1 error rates and much higher
power to detect association than the existing methods. The FLMF is applied to
sleep data from Starr County health studies where oxygen saturation were
measured in 22,670 seconds on average for 833 individuals. We found 65 genes
that were significantly associated with oxygen saturation functional trait with
P-values ranging from 2.40E-06 to 2.53E-21. The results clearly demonstrate
that the FLMF substantially outperforms the traditional genetic models with
scalar trait.
