Our algorithms rely on fully observed phenotypes. To make the method more widely applicable, we developed a phenotype imputation scheme to impute missing phenotypes where necessary (Supplementary Note). To show the power gain of our imputation scheme versus simply dropping individuals with partially missing phenotypes, we performed a simulation study. Specifically, we used the same set of simulated phenotypes described above, but randomly made 2.5%, 5% or 10% of the individuals to have one phenotype missing. We calculated p values for each SNP-phenotype pair from the two approaches using GEMMA, and calculated statistical power at the conventional 0.05 level after Bonferroni correction.
