Standard GWAS summary statistics are ordinary least squares (OLS) estimates of the SNP effects and do not have optimal properties for prediction11. Even when LMM association analysis is used, the estimated SNP effects still represent marginal effects and not effects conditional on other SNPs, which is what is desirable for prediction19. Previous studies have shown how OLS summary statistics can be reanalysed in a mixed model framework to produce approximate BLUP predictors (summary statistic BLUP: SBLUP, implemented in the most recent release of GCTA)18,20,21 or approximate mixture model predictors (LDPred). We first extend the SBLUP approach to a multi-trait framework (MT-SBLUP) and find a computational limitation associated with the inversion of a SNP-by-SNP-by-trait matrix. To overcome this, we then derive theory to show how single-trait predictors with BLUP properties can be combined together in a weighted index to generate predictors with equivalent properties to those gained from a MT-BLUP analysis (Fig. 1).Fig. 1Schematic of the methods. a Data and programs used to create predictors. b Terminology to refer to different types of predictors. OLS, ordinary least squares. The most common GWAS methodology to estimate SNP effects is to estimate the effect sizes of one SNP at a time using linear regression. BLUP, best linear unbiased prediction. SNP effects are estimated simultaneously for all SNPs. The estimates depend on the other SNPs included in the analysis, since the contribution from correlated SNPs will be shared between them