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Gene discovery, estimation of heritability captured by SNP arrays, inference on genetic architecture and prediction analyses of complex traits are usually performed using different statistical models and methods, leading to inefficiency and loss of power. Here we use a Bayesian mixture model that simultaneously allows variant discovery, estimation of genetic variance explained by all variants and prediction of unobserved phenotypes in new samples. We apply the method to simulated data of quantitative traits and Welcome Trust Case Control Consortium (WTCCC) data on disease and show that it provides accurate estimates of SNP-based heritability, produces unbiased estimators of risk in new samples, and that it can estimate genetic architecture by partitioning variation across hundreds to thousands of SNPs. We estimated that, depending on the trait, 2,633 to 9,411 SNPs explain all of the SNP-based heritability in the WTCCC diseases. The majority of those SNPs (>96%) had small effects, confirming a substantial polygenic component to common diseases. The proportion of the SNP-based variance explained by large effects (each SNP explaining 1% of the variance) varied markedly between diseases, ranging from almost zero for bipolar disorder to 72% for type 1 diabetes. Prediction analyses demonstrate that for diseases with major loci, such as type 1 diabetes and rheumatoid arthritis, Bayesian methods outperform profile scoring or mixed model approaches., Author Summary Most genome-wide association studies performed to date have focused on testing individual genetic markers for associations with phenotype. Recently, methods that analyse the joint effects of multiple markers on genetic variation have provided further insights into the genetic basis of complex human traits. In addition, there is increasing interest in using genotype data for genetic risk prediction of disease. Often disparate analytical methods are used for each of these tasks. We propose a flexible novel approach that simultaneously performs identification of susceptibility loci, inference on the genetic architecture and provides polygenic risk prediction in the same statistical model. We illustrate the broad applicability of the approach by considering both simulated and real data. In the analysis of seven common diseases we show large differences in the proportion of genetic variation due to loci with different effect sizes and differences in prediction accuracy between complex traits. These findings are important for future studies and the understanding of the complex genetic architecture of common diseases.

We have recently developed analysis methods (GREML) to estimate the genetic variance of a complex trait/disease and the genetic correlation between two complex traits/diseases using genome-wide single nucleotide polymorphism (SNP) data in unrelated individuals. Here we use analytical derivations and simulations to quantify the sampling variance of the estimate of the proportion of phenotypic variance captured by all SNPs for quantitative traits and case-control studies. We also derive the approximate sampling variance of the estimate of a genetic correlation in a bivariate analysis, when two complex traits are either measured on the same or different individuals. We show that the sampling variance is inversely proportional to the number of pairwise contrasts in the analysis and to the variance in SNP-derived genetic relationships. For bivariate analysis, the sampling variance of the genetic correlation additionally depends on the harmonic mean of the proportion of variance explained by the SNPs for the two traits and the genetic correlation between the traits, and depends on the phenotypic correlation when the traits are measured on the same individuals. We provide an online tool for calculating the power of detecting genetic (co)variation using genome-wide SNP data. The new theory and online tool will be helpful to plan experimental designs to estimate the missing heritability that has not yet been fully revealed through genome-wide association studies, and to estimate the genetic overlap between complex traits (diseases) in particular when the traits (diseases) are not measured on the same samples., Author Summary Genome-wide association studies (GWAS) have identified thousands of genetic variants for hundreds of traits and diseases. However, the genetic variants discovered from GWAS only explained a small fraction of the heritability, resulting in the question of “missing heritability”. We have recently developed approaches (called GREML) to estimate the overall contribution of all SNPs to the phenotypic variance of a trait (disease) and the proportion of genetic overlap between traits (diseases). A frequently asked question is that how many samples are required to estimate the proportion of variance attributable to all SNPs and the proportion of genetic overlap with useful precision. In this study, we derive the standard errors of the estimated parameters from theory and find that they are highly consistent with those observed values from published results and those obtained from simulation. The theory together with an online application tool will be helpful to plan experimental design to quantify the missing heritability, and to estimate the genetic overlap between traits (diseases) especially when it is unfeasible to have the traits (diseases) measured on the same individuals.

Genome-wide association studies (GWAS) for quantitative traits and disease in humans and other species have shown that there are many loci that contribute to the observed resemblance between relatives. GWAS to date have mostly focussed on discovery of genes or regulatory regions habouring causative polymorphisms, using single SNP analyses and setting stringent type-I error rates. Genome-wide marker data can also be used to predict genetic values and therefore predict phenotypes. Here, we propose a Bayesian method that utilises all marker data simultaneously to predict phenotypes. We apply the method to three traits: coat colour, %CD8 cells, and mean cell haemoglobin, measured in a heterogeneous stock mouse population. We find that a model that contains both additive and dominance effects, estimated from genome-wide marker data, is successful in predicting unobserved phenotypes and is significantly better than a prediction based upon the phenotypes of close relatives. Correlations between predicted and actual phenotypes were in the range of 0.4 to 0.9 when half of the number of families was used to estimate effects and the other half for prediction. Posterior probabilities of SNPs being associated with coat colour were high for regions that are known to contain loci for this trait. The prediction of phenotypes using large samples, high-density SNP data, and appropriate statistical methodology is feasible and can be applied in human medicine, forensics, or artificial selection programs., Author Summary Results from recent genome-wide association studies indicate that for most complex traits, there are many loci that contribute to variation in observed phenotype and that the effect of a single variant (single nucleotide polymorphism, SNP) on a phenotype is small. Here, we propose a method that combines the effects of multiple SNPs to make a prediction of a phenotype that has not been observed. We apply the method to data on mice, using phenotypic and genomic data from some individuals to predict phenotypes in other, either related or unrelated, individuals. We find that correlations between predicted and actual phenotypes are in the range of 0.4 to 0.9. The method also shows that the SNPs used in the prediction appear in regions that are known to contain genes associated with the traits studied. The prediction of unobserved phenotypes from high-density SNP data and appropriate statistical methodology is feasible and can be applied in human medicine, forensics, or artificial breeding programs.