We illustrate our method and compare the analysis results with the exact method EMMA and the approximation methods EMMAX and GRAMMAR, using two examples, a mouse GWAS for high-density lipoprotein cholesterol (HDL-C) levels from the Hybrid Mouse Diversity Panel (HMDP)14 and a human GWAS for Crohn's disease from the Wellcome Trust Case Control Consortium (WTCCC)15. The size of this second study makes it computationally impractical to analyze with EMMA3. Table 1 summarizes the computational complexity for the four methods along with CPU time for the two data sets on a single desktop CPU. Table 1 also includes results for the recently-published FaST-LMM8, which can produce identical p values to EMMA and GEMMA in the same time complexity as GEMMA; see below for further discussion. As expected GEMMA is comparable in speed with EMMAX, completing the larger (WTCCC) example in under 4 hours.
