  Understanding how genetic variants influence cellular-level processes is an
important step towards understanding how they influence important
organismal-level traits, or "phenotypes", including human disease
susceptibility. To this end scientists are undertaking large-scale genetic
association studies that aim to identify genetic variants associated with
molecular and cellular phenotypes, such as gene expression, transcription
factor binding, or chromatin accessibility. These studies use high-throughput
sequencing assays (e.g. RNA-seq, ChIP-seq, DNase-seq) to obtain high-resolution
data on how the traits vary along the genome in each sample. However, typical
association analyses fail to exploit these high-resolution measurements,
instead aggregating the data at coarser resolutions, such as genes, or windows
of fixed length. Here we develop and apply statistical methods that better
exploit the high-resolution data. The key idea is to treat the sequence data as
measuring an underlying "function" that varies along the genome, and then,
building on wavelet-based methods for functional data analysis, test for
association between genetic variants and the underlying function. Applying
these methods to identify genetic variants associated with chromatin
accessibility (dsQTLs) we find that they identify substantially more
associations than a simpler window-based analysis, and in total we identify 772
novel dsQTLs not identified by the original analysis.
