Statistical Power to Detect Genetic (Co)Variance of Complex Traits Using SNP Data in Unrelated Samples

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.

[1]  S Purcell,et al.  Equivalence between Haseman-Elston and variance-components linkage analyses for sib pairs. , 2001, American journal of human genetics.

[2]  M. Goddard,et al.  Prediction of total genetic value using genome-wide dense marker maps. , 2001, Genetics.

[3]  K. Roeder,et al.  Genomic Control for Association Studies , 1999, Biometrics.

[4]  Peter Kraft,et al.  Bayesian inference analyses of the polygenic architecture of rheumatoid arthritis , 2012, Nature Genetics.

[5]  Naomi R. Wray,et al.  Author reply to A commentary on Pitfalls of predicting complex traits from SNPs , 2013, Nature Reviews Genetics.

[6]  J Blangero,et al.  Power of variance component linkage analysis to detect quantitative trait loci. , 1999, Annals of human genetics.

[7]  Judy H. Cho,et al.  Finding the missing heritability of complex diseases , 2009, Nature.

[8]  E. Reeve.  The Variance of the Genetic Correlation Coefficient , 1955 .

[9]  F. Dudbridge.  Power and Predictive Accuracy of Polygenic Risk Scores , 2013, PLoS genetics.

[10]  Jianxin Shi,et al.  Genetic relationship between five psychiatric disorders estimated from genome-wide SNPs , 2013, Nature Genetics.

[11]  F. Collins,et al.  Potential etiologic and functional implications of genome-wide association loci for human diseases and traits , 2009, Proceedings of the National Academy of Sciences.

[12]  W. G. Hill,et al.  Genome partitioning of genetic variation for complex traits using common SNPs , 2011, Nature Genetics.

[13]  Doug Speed,et al.  Improved heritability estimation from genome-wide SNPs. , 2012, American journal of human genetics.

[14]  P. Visscher,et al.  A Commentary on ‘Common SNPs Explain a Large Proportion of the Heritability for Human Height’ by Yang et al. (2010) , 2010, Twin Research and Human Genetics.

[15]  P. Visscher,et al.  Estimating missing heritability for disease from genome-wide association studies. , 2011, American journal of human genetics.

[16]  Sang Hong Lee,et al.  Estimation of pleiotropy between complex diseases using single-nucleotide polymorphism-derived genomic relationships and restricted maximum likelihood , 2012, Bioinform..

[17]  G. Abecasis,et al.  Estimating the power of variance component linkage analysis in large pedigrees , 2006, Genetic epidemiology.

[18]  Naomi R. Wray,et al.  Estimation and partitioning of polygenic variation captured by common SNPs for Alzheimer's disease, multiple sclerosis and endometriosis , 2012, Human molecular genetics.

[19]  P. Visscher,et al.  Common SNPs explain a large proportion of heritability for human height , 2011 .

[20]  Hon-Cheong So,et al.  Uncovering the total heritability explained by all true susceptibility variants in a genome‐wide association study , 2011, Genetic epidemiology.

[21]  P. Visscher,et al.  Power of regression and maximum likelihood methods to map QTL from sib‐pair and DZ twin data , 2001 .

[22]  Pak C Sham,et al.  Analytic power calculation for QTL linkage analysis of small pedigrees , 2001, European Journal of Human Genetics.

[23]  H. D. Patterson,et al.  Recovery of inter-block information when block sizes are unequal , 1971 .

[24]  P. Visscher,et al.  Estimation and partition of heritability in human populations using whole-genome analysis methods. , 2013, Annual review of genetics.

[25]  J. Gibson,et al.  Realized sampling variances of estimates of genetic parameters and the difference between genetic and phenotypic correlations. , 1996, Genetics.

[26]  M. Goddard.  Genomic selection: prediction of accuracy and maximisation of long term response , 2009, Genetica.

[27]  M. Lynch,et al.  Genetics and Analysis of Quantitative Traits , 1996 .

[28]  P. Visscher,et al.  GCTA: a tool for genome-wide complex trait analysis. , 2011, American journal of human genetics.

[29]  P. Sham,et al.  Power of linkage versus association analysis of quantitative traits, by use of variance-components models, for sibship data. , 2000, American journal of human genetics.

[30]  A. Robertson.  THE SAMPLING VARIANCE OF THE GENETIC CORRELATION COEFFICIENT , 1959 .

[31]  D. Falconer,et al.  Introduction to Quantitative Genetics. , 1961 .

[32]  S. Leal.  Genetics and Analysis of Quantitative Traits , 2001 .

[33]  P. Visscher.  On the sampling variance of intraclass correlations and genetic correlations. , 1998, Genetics.

[34]  Ian J. Deary,et al.  Genetic contributions to stability and change in intelligence from childhood to old age , 2012, Nature.

[35]  Daniel J. Benjamin,et al.  The genetic architecture of economic and political preferences , 2012, Proceedings of the National Academy of Sciences.