We further develop an approximate method (called mtCOJO; URLs) that only requires summary data to conduct a GWAS analysis for a phenotype conditional on multiple covariate phenotypes (Methods). The purpose of developing this method is to estimate the effect of a risk factor on disease adjusting for other risk factors (Methods; Supplementary Note 2; Supplementary Fig. 5), which helps to infer whether the marginal effect of the risk factor on disease depends on other risk factors, and to predict the joint effect of multiple risk factors on disease. It is of note that mtCOJO is free of bias due to shared environmental or genetic effect between the phenotype and covariate as described in Aschard et al.23 (Supplementary Fig. 6).
