the PRS Odds Ratio (OR) became infinity, Firth’s penalised likelihood method was used to compute regression statistics, as implemented in the R package “logistf”16. ORs from these calculations were then meta-analysed using a fixed-effects model in the R package “metafor”17. To ensure stability of the estimates, meta-analysis was conservatively restricted to case-control samples which contained more than 10 individuals in the top 1% PRS, with at least one of them being a control. Analogous analyses were conducted to assess the ORs between individuals at the top and bottom quantiles. To assess the performance of PRS as a predictor of schizophrenia case status, we calculated liability R2, Nagelkerke’s R2 following Lee et. al. 201218 and a combined area under the receiver operating characteristic curve (AUROC). Both liability R2 and Nagelkerke’s R2 included any principal components marginally associated with the outcome within each cohort, in the baseline model. AUROC was estimated using the non-parametric meta-analysis implemented in the R package “nsROC”19. Polygenic score analysis of the African-American and Latino cohorts were conducted by the authors of the study reporting those datasets20.
