The method and its computational complexity is described and derived in detail in the Online Methods section. Briefly, the method requires complete or imputed genotype data12,13 for all SNPs, and involves only one eigen-decomposition of the relatedness matrix at the beginning (computational complexity O(n3)). For each SNP tested, it effectively replaces the expensive additional eigen-decomposition step in EMMA with one matrix and vector multiplication (computational complexity O(n2)). After this, like EMMA, each iteration of the following optimization step requires cheap operations (complexity O(n)) to evaluate both first and second derivatives of the target functions. We refer to our method as Genome-wide Efficient Mixed Model Association (GEMMA) because it builds on EMMA and facilitates its genome-wide application.
