A single common factor gSEM (Fig. 1a) fit the GENOA, MVP-SAGE-YP, PGC-SUD, and PH summary statistics for OA well, with high Akaike information criterion and comparative fit index, and low standardized root mean squared root (SRMR) values (Fig. 1a). Testing the association of 2.4 million variants available across all cohorts (Supplementary Tables 6 and 7 for LDSC and gSEM SNP QC and derivation of available variants, respectively) with the latent genetic factor (effective sample size N = 88,114) identified two GWS loci (Fig. 1b; Q–Q plot Supplementary Fig. 8): one on chromosome 6 with 32 GWS variants (top variant rs9478500-C, beta = 0.136, p = 2.56 × 10–9; Supplementary Table 8; forest plot Supplementary Fig. 9a) and the other represented by a single variant on chromosome 16 (rs13333582-C, beta = − 0.219, p = 3.58 × 10–8; forest plot Supplementary Fig. 10, LocusZoom plot Supplementary Fig. 12). The LDSC intercept of approximately 1 for this model (Fig. 1b), indicates that these results are not due to uncontrolled inflation, as would be expected if the overlap in the cohorts contributing to some of the summary statistics used here was not adequately accounted for30.