Reply To Lee: Downward Bias In Heritability Estimation Is Not Due To Simplified Linkage Equilibrium Snp Simulation

The use of restricted maximum likelihood (REML) to estimate the heritability explained by common SNPs in a genome-wide association study (GWAS) of quantitative traits was proposed by Yang et al. (1) and implemented in the widely used GCTA software. Lee et al. (reference 2 in ref. 2) tries to extend REML to estimate heritability in case–control GWAS of disease. Our paper (3) demonstrates that Lee et al.’s method suffers from consistent downward bias. Most importantly—and contrary to the behavior of any reasonable estimator—the bias increases with study size. To alleviate these problems, we developed an alternative approach—phenotype correlation–genotype correlation (PCGC) regression. The flaws with Lee et al.’s method have been confirmed by others (4⇓–6). They do not affect REML in general, but only the extension to case–control studies. Dr. S. H. Lee (2) claims our paper …