emphasized that any factors making SNP genotypes of cases more similar to those of other cases and making the genotypes of controls more similar to those of other controls would produce SNP-based heritability. The fitting as covariates of principal components derived from the SNP data corrects both for population stratification and for genotyping artifacts, but residual population stratification could remain, although this bias should be small38. Partitioning SNP-based heritability by chromosome in analyses where each chromosome was fitted individually compared to analyses where all chromosomes were fitted jointly is an empirical strategy to assess residual stratification35,39, and we found no evidence of this type of stratification here (Supplementary Fig. 1). Stringent quality control (as applied here) helps to remove artifacts, but artifactual differences between cases and controls might remain, particularly for data sets in which cases and controls have been genotyped independently40. As more data sets accumulate, the contributions from artifacts are diluted because the random directional effects of artifacts (including population stratification) are not consistent across data sets. For this reason, significant SNP-based coheritabilities between subsets of the same disorder are unlikely to reflect artifacts and provide a lower bound for SNP-based heritability.
