When the GWAS summary statistics are reported for logistic regressions of liabilities for categorical outcomes (e.g. case/control status) on the SNP, the logistic regression coefficients can be transformed into covariances as above, by multiplying by the SNP variances. However, it is appropriate to further transform the coefficients and their SEs such that they are scaled relative to unit-variance scaled liability. This can be achieved by dividing by σSNP2×blogitSNP,P2+π23, as a logistic regression model implies a residual variance of π23. If GWAS summary statistics are reported for odds ratios (ORs), they can be transformed to logistic regression coefficients by taking their natural logarithm. Standard errors for the logistic regression coefficient are obtained as SEOR/OR. The derived logistic coefficients and their SEs should further be transformed such that they are scaled relative to unit-variance scaled phenotypes, as per above. Note that when the outcomes are categorical, the liability scale heritabilities and genetic covariances from multivariable LDSC (and not what are referred to as the “observed scale” heritabilities and genetic covariances) should be used to populate the S matrix. This has the desirable
