LD Score regression works optimally when variance explained per SNP is uncorrelated with LD Score (this means that rare variants have larger effect sizes than common variants, which may be appropriate for a disease phenotype under moderate negative selection). A potential limitation of LD Score regression is that variance explained per SNP may be correlated with LD Score for some phenotypes. For an example where this might occur, consider a phenotype that is selectively neutral, so that per-allele effect size is uncorrelated with MAF (which means that variance explained is positively correlated with MAF, as additive genetic variance is defined as 2pqa2 where p and q are the major and minor allele frequency and a is the additive genetic effect). Since LD Score is also positively correlated with MAF, in this case we would expect variance explained to be positively correlated with LD Score, which will introduce downward bias in the LD Score regression intercept and upward bias in the LD Score regression slope, leading to an underestimate of potential bias.
