Current work for multivariate analysis of phenotypes in genome-wide association studies often requires that genetic similarity matrices be inverted or decomposed. This can be a computational bottleneck when many phenotypes are presented, each with a different missingness pattern. A usual method in this case is to perform decompositions on subsets of the kinship matrix for each phenotype, with each subset corresponding to the set of observed samples for that phenotype. We provide a new method for decomposing these kinship matrices that can reduce the computational complexity by an order of magnitude by propagating low-rank modifications along a tree spanning the phenotypes. We demonstrate that our method provides speed improvements of around 40% under reasonable conditions.
Keywords: Cholesky decomposition; genome-wide association study; kinship matrix; linear mixed models; multiphenotype analysis.