Thus, it is possible to approximate the likelihood function for λ by N(λˆ|λ,V[λˆ]) using a SNP correlation estimate from a reference panel and single-SNP z-scores from a standard GWAS software, as previously done in GCTA (Yang et al., 2011), PAINTOR and CAVIARBF. Note that with z-scores for quantitative traits we can assume that σ2=1 without any loss of generality. For binary traits, a similar approximation applies with z-scores originating from logistic regression and σ2≈1/{φ(1−φ)}, where φ is the proportion of cases among the n individuals (Pirinen et al., 2013).
