Although in some settings the approximate methods described above provide results almost identical to those of the exact method1,7, this is not guaranteed in general, and in practice it is hard to know how accurate the approximations will be without running an exact calculation. One possible consequence of inaccuracy in the approximation could be a reduction in power compared with exact methods. For these reasons, the ability to perform exact calculations remains of interest. Here, we present a new, more efficient, method for exact calculations that provides numerically identical results to EMMA (i.e. exact Wald or likelihood ratio test statistics) but is roughly n times faster (computation time per SNP, when using the usual genome-wide relatedness matrix, is quadratic in the number of individuals, with run time similar to EMMAX). This makes exact calculations feasible for large GWAS, obviating the need for approximate methods in most common settings.
