Implications of simplified linkage equilibrium SNP simulation.

In a recent paper published in PNAS (Golan et al. 2014), residual maximum likelihood (REML) seriously underestimated genetic variance explained by genomewide single nucleotide polymorphism when using a case-control design. It was concluded that Haseman–Elston regression (denoted as PCGC in their paper) should be used instead of REML. Their conclusions were based on results from simplified linkage equilibrium SNP simulation (SLES), which the authors acknowledged may be unrealistic. We found that their simulation, SLES, unrealistically inflated the correlation between the eigenvectors of the genomic relationship matrix and disease status to values that are rarely observed in real data analyses. With a more realistic simulation that the authors failed to carry out (as they noted in their paper), we showed that there was no such inflated correlation between the eigenvectors of the genomic relationship matrix and disease status. Because REML uses the eigensystem of covariance structure, the inflated correlation artefactually constrained its estimates. We compared SNP-heritabilities from SLES and a more realistic simulation, showing that there was a substantial difference between the REML estimates from the two simulation strategies. Finally, we presented that there was no difference between REML and PCGC in real data analyses. This pattern from real data results differed strikingly from the pattern in the simulation study of Golan et al.. One needs to be cautious of results drawn from SLES. not peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (which was . http://dx.doi.org/10.1101/025619 doi: bioRxiv preprint first posted online Aug. 27, 2015; Recently, Golan and Rosset (2013) and Golan et al. (2014) reported that REML seriously underestimates SNP-heritability when using a case-control design. Their conclusions were based on results from simplified linkage equilibrium SNP simulation (SLES), which the authors acknowledged may be unrealistic. We simulated case-control data using the liability threshold model , based on a real GWAS of 800K SNPs from 64,000 samples, i.e. a genome-wide linkage disequilibrium SNP simulation (GLDS). Our simulation used a population disease risk of K = 0.01 and proportion of cases in the sample of P = 0.5 (therefore, there were 640 cases and 640 controls in the estimation analyses). A random 10,000, 1,000, or 100 SNPs across the genome were selected as risk loci. The genomic relationship matrix (GRM) was based on all the SNPs. For comparison, the SLES (without real GWAS data) was used, following Golan et al. (2014) where the GRM was calculated only from the risk SNPs that are independent from each other (see Supplementary Note). In Figure 1, we show that SLES unrealistically inflates the correlation between the eigenvectors of the GRM and disease status compared to GLDS (Figure 2) or that inferred from real data (e.g., Figure S1 in Gusev et al. 2014). The artefactual correlation between the eigenvectors and disease status caused the inaccuracy of the REML estimates. The bias depends on the ratio of the number of indiviudals (N) to the number of risk SNPs (M; Figure 1). Unlike REML, a sophisticated approach, Haseman–Elston regression (referred to as PCGC by Golan et al.) does not use the eigensystem of covariance structure; therefore SLES does not affect the PCGC estimate. With GLDS, the REML estimates were stable and close to the true value regardless of the value of N/M (Figure 3). With SLES, the REML estimates were severely biased with increasing value of N/M (Figure 3). We considered results from real data analyses and plotted published SNP-heritability estimates against the sample size for nine diseases (Figure 4). There was no difference between REML and PCGC, regardless of sample size, which was strikingly different from Figure 2B in Golan et al. We also show estimation errors for the nine diseases not peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (which was . http://dx.doi.org/10.1101/025619 doi: bioRxiv preprint first posted online Aug. 27, 2015; assuming that the PCGC estimates are the true values (Figure 5), which were again dramatically different from results in Figure S4 from Golan et al. (2014). There are a large number of unknown confounding factors, such as artefact batch effects, in real case-control data. A number of studies have emphasised that such unknown factors can inflate estimates and should be controlled by stringent QC. In addition to stringent QC (MAF, missingness, H-W test, missingness difference, relatedness cut-offs), Gusev et al. (2014) additionally performed five rounds of outlier removal whereby all individuals more than 6 SDs away from the mean along any of the top 20 eigenvectors were removed and all eigenvectors were recomputed. Moreover, they fit 20 principal components (PCs) into their SNP-heritability estimation to correct for population admixture. Less stringent QC and/or less number of PCs fitted in the model might result in less effective control of population admixture as well as artifact batch effects. In derivation of the correction factor for case-control ascertainment bias, Lee et al. (2011) used a simulation from a multivariate normal distribution based on a predefined relationship matrix. In real data analyses, the true relationship matrix is not known but can be approximated from genotypes, i.e. GRM pairwise estimator is unbiased under linkage disequilibrium; that is, the expectation of the estimator for each SNP is the kinship in the identical-by-descent (IBD) fraction sense, and therefore so is the estimate averaged over multiple SNP's. SLES ignores the concept of linkage disequilibrium, IBD and coalescence. We urge researchers to use a more realistic genetic model (e.g., GLDS at least) in their simulation strategies and to be cautious of results drawn from SLES . not peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (which was . http://dx.doi.org/10.1101/025619 doi: bioRxiv preprint first posted online Aug. 27, 2015; References 1. Golan, D., Lander, E.S., and Rosset, S. (2014). Measuring missing heritability: Inferring the contribution of common variants. Proceedings of the National Academy of Sciences 111, E5272-­‐E5281. 2. Golan, D., and Rosset, S. (2013). Narrowing the gap on heritability of common disease by direct estimation in case-­‐control GWAS. arXiv arXiv:1305.5363v2 [q-­‐bio.PE]. 3. Lee, S., Wray, N., Goddard, M., and Visscher, P. (2011). Estimating Missing Heritability for Disease from Genome-­‐wide Association Studies. Am J Hum Genet 88, 294-­‐305. 4. Gusev, A., Lee, S.H., Trynka, G., Finucane, H., Vilhjalmsson, B.J., Xu, H., Zang, C., Ripke, S., Bulik-­‐Sullivan, B., Stahl, E., et al. (2014). Partitioning Heritability of Regulatory and Cell-­‐Type-­‐Specific Variants across 11 Common Diseases. The American Journal of Human Genetics 95, 535-­‐552. 5. Lee, S.H., DeCandia, T.R., Ripke, S., Yang, J., Sullivan, P.F., Goddard, M.E., Keller, M.C., Visscher, P.M., Wray, N.R., Genome-­‐Wide, S.P., et al. (2012). Estimating the proportion of variation in susceptibility to schizophrenia captured by common SNPs. Nat Genet 44, 247-­‐250. 6. Lee, S.H., Harold, D., Nyholt, D.R., Goddard, M.E., Zondervan, K.T., Williams, J., Montgomery, G.W., Wray, N.R., Visscher, P.M., Consortium, A., et al. (2013). Estimation and partitioning of polygenic variation captured by common SNPs for Alzheimer's disease, multiple sclerosis and endometriosis. Hum Mol Gen 22, 832-­‐841. 7. Lubke, G.H., Hottenga, J.J., Walters, R., Laurin, C., de Geus, E.J.C., Willemsen, G., Smit, J.H., Middeldorp, C.M., Penninx, B.W.J.H., Vink, J.M., et al. Estimating the Genetic Variance of Major Depressive Disorder Due to All Single Nucleotide Polymorphisms. Biological Psychiatry 72, 707-­‐709. 8. Thompson, E.A. (2013). Identity by Descent: Variation in Meiosis, Across Genomes, and in Populations. Genetics 194, 301-­‐326. 9. Chen, G.-­‐B. (2014). Estimating heritability of complex traits from genome-­‐wide association studies using IBS-­‐based Haseman-­‐Elston regression. Frontiers in Genetics 5, 107. not peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (which was . http://dx.doi.org/10.1101/025619 doi: bioRxiv preprint first posted online Aug. 27, 2015;