Author reply to A Commentary on Pitfalls of predicting complex traits from SNPs

We thank de los Campos and Sorensen (D&S) for their Correspondence, which follows their recent work¹. D&S agree that maximum prediction accuracy depends on h²_M, defined as the variance explained by genotyped markers in the population. They claim that estimates of h²_M in a finite sample (h²_G-BLUP or h²_G) may overestimate h²_M, and that this is exacerbated for unrelated individuals. We respond by showing how and why we disagree with these claims.

h²_G and h²_G-BLUP are estimates of the same parameter from equivalent models^3–6 and so, for the same dataset, they must have the same value. Both measure the proportion of the phenotypic variance that is explained by the markers. This proportion depends on linkage disequilibrium (LD) between the SNPs and causal variants or quantitative trait loci (QTL). If the LD is imperfect, then h²_M will be less than the conventional heritability, h², which is the proportion of variance explained by all causal variants. The extent of LD depends on the relatedness of the sample of individuals used. If closely related individuals are included in the sample, there is long range LD generated even between SNPs and QTL on different chromosomes. Thus, inclusion of close relatives increases h²_M and its estimates. Usually, the parameter we wish to estimate is the h²_M among individuals who are no more closely related than randomly sampled individuals from the population (e.g.⁷).

D&S state that the accuracy of prediction R²_TST does not approach h²_M even in an infinite sample. This is incorrect. R²_TST depends on two factors – h²_M and the accuracy with which the marker effects are estimated ^{3; 8}. If the marker effects are estimated with no error then R²_TST = h²_M. In practice the accuracy of estimating SNP effects is usually low in humans and this also explains the low R²_TST often reported. Ref. ¹ claims that “the estimated h²_G did not provide a good indication of prediction R²”. In their simulations of unrelated individuals (GEN cohort; h²=0.8), they state “when [non-causal] markers were used we observed only a small extent of missing heritability [h²_G=0.737, vs. h²_G=0.773 for causal markers] but the reduction in R² due to use of markers that were in imperfect LD with causal loci was dramatic [R²=0.071, vs. R²=0.517 for causal markers]”. Even though the number of causal loci was the same, the number of markers differed: 300,000, corresponding to M=60,000 independent markers² vs M=5,000 in the causal set. Equation (1) of ref. ² demonstrates that R² decreases with higher M (which increases the variance of the estimated genetic relationships).

D&S say that R²_TST is zero if the training and testing datasets are independent. This is a distracting statement because individuals within a species are always related to some degree. D&S also question our focus on the prediction accuracy that can be obtained in an independent validation sample². We disagree with the opinion of D&S that the prediction accuracy that can be obtained in a non-independent validation sample is a quantity of equal interest.