RT Journal Article SR Electronic T1 Sequence kernel association tests for large sets of markers: tail probabilities for large quadratic forms JF bioRxiv FD Cold Spring Harbor Laboratory SP 085639 DO 10.1101/085639 A1 Thomas Lumley A1 Jennifer A Brody A1 Gina Peloso A1 Kenneth M Rice YR 2016 UL http://biorxiv.org/content/early/2016/11/04/085639.abstract AB The Sequence Kernel Association Test (SKAT) is widely used to test for associations between a phenotype and a set of (usually rare) genetic variants. Evaluating tail probabilities or quantiles of the null distribution for SKAT requires computing the eigenvalues of a matrix related to the genotype covariance between markers. Extracting the full set of eigenvalues of this matrix (an n × n matrix, for n subjects) has computational complexity proportional to n3. As SKAT is used when n > 104 is common, this step becomes a major bottleneck in its use. We propose fastSKAT, a new computationally-inexpensive but accurate approximations to the tail probabilities, in which the k largest eigenvalues of a weighted genotype covariance matrix or the largest singular values of a weighted genotype matrix are extracted, and a single term based on the Satterthwaite approximation is used for the remaining eigenvalues. While the method is not particularly sensitive to the choice of k, we also describe how to choose its value, and show how fastSKAT can automatically alert users to the rare cases where the choice may affect results. As well as providing faster implementation of SKAT, the new method also enables entirely new applications of SKAT, that were not possible before; we give examples grouping variants by topologically assisted domains, and comparing chromosome-wide association by class of histone marker.