Genome-wide complex trait analysis

<h2 id="history">History</h2>
Estimation in biology/animal breeding using standard <a href="/facts/Analysis_of_variance/HHR2jkDk">ANOVA</a>/<a href="/facts/Restricted_maximum_likelihood/9tybgT1E">REML</a> methods of variance components such as heritability, shared-environment, maternal effects etc. typically requires individuals of known relatedness such as parent/child; this is often unavailable or the pedigree data unreliable, leading to inability to apply the methods or requiring strict laboratory control of all breeding (which threatens the <a href="/facts/External_validity/M5Q3z42b">external validity</a> of all estimates), and several authors have noted that relatedness could be measured directly from genetic markers (and if individuals were reasonably related, economically few markers would have to be obtained for statistical power), leading Kermit Ritland to propose in 1996 that directly measured pairwise relatedness could be compared to pairwise phenotype measurements (Ritland 1996, <a href="http://www.genetics.forestry.ubc.ca/ritland/reprints/1996_Evolution_HeritInFieldModel.pdf">"A Marker-based Method for Inferences About Quantitative Inheritance in Natural Populations"</a> <a href="https://web.archive.org/web/20090611224719/http://genetics.forestry.ubc.ca/ritland/reprints/1996_Evolution_HeritInFieldModel.pdf">Archived</a> 2009-06-11 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a><a class="footnote-ref" id="fnref:2" href="#fn:2">2</a>).
As genome sequencing costs dropped steeply over the 2000s, acquiring enough markers on enough subjects for reliable estimates using very distantly related individuals became possible. An early application of the method to humans came with Visscher et al. 2006<a class="footnote-ref" id="fnref:3" href="#fn:3">3</a>/2007,<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a> which used SNP markers to estimate the actual relatedness of siblings and estimate heritability from the direct genetics. In humans, unlike the original animal/plant applications, relatedness is usually known with high confidence in the 'wild population', and the benefit of GCTA is connected more to avoiding assumptions of classic behavioral genetics designs and verifying their results, and partitioning heritability by SNP class and chromosomes. The first use of GCTA proper in humans was published in 2010, finding 45% of variance in human height can be explained by the included SNPs.<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a><a class="footnote-ref" id="fnref:6" href="#fn:6">6</a> (Large GWASes on height have since confirmed the estimate.<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a>) The GCTA algorithm was then described and a software implementation published in 2011.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a> It has since been used to study a wide variety of biological, medical, psychiatric, and psychological traits in humans, and inspired many variant approaches.

<h2 id="benefits">Benefits</h2>
<h3>Robust heritability</h3>
Main article: <a href="/facts/Twin_study/J1ykuTtW">Twin study § Criticism</a>
Twin and family studies have long been used to estimate variance explained by particular categories of genetic and environmental causes. Across a wide variety of human traits studied, there is typically minimal shared-environment influence, considerable non-shared environment influence, and a large genetic component (mostly additive), which is on average ~50% and sometimes much higher for some traits such as height or intelligence.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> However, the twin and family studies have been criticized for their reliance on a number of assumptions that are difficult or impossible to verify, such as the equal environments assumption (that the environments of <a href="/facts/Monozygotic/9QSssff4">monozygotic</a> and <a href="/facts/Dizygotic/9QSssff4">dizygotic</a> twins are equally similar), that there is no misclassification of zygosity (mistaking identical for fraternal & vice versa), that twins are unrepresentative of the general population, and that there is no <a href="/facts/Assortative_mating/o1qQDM4R">assortative mating</a>. Violations of these assumptions can result in both upwards and downwards bias of the parameter estimates.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a> (This debate & criticism have particularly focused on the <a href="/facts/Heritability_of_IQ/3PAa75ra">heritability of IQ</a>.)
The use of SNP or whole-genome data from unrelated subject participants (with participants too related, typically >0.025 or ~fourth cousins levels of similarity, being removed, and several <a href="/facts/Principal_component_analysis/pCbVTqdR">principal components</a> included in the regression to avoid & control for <a href="/facts/Population_stratification/ty8jHH7F">population stratification</a>) bypasses many heritability criticisms: twins are often entirely uninvolved, there are no questions of equal treatment, relatedness is estimated precisely, and the samples are drawn from a broad variety of subjects.
In addition to being more robust to violations of the twin study assumptions, SNP data can be easier to collect since it does not require rare twins and thus also heritability for rare traits can be estimated (with due correction for <a href="/facts/Ascertainment_bias/nrr4qR2T">ascertainment bias</a>).

<h3>GWAS power</h3>
GCTA estimates can be used to resolve the <a href="/facts/Missing_heritability_problem/ex1ugFU7">missing heritability problem</a> and <a href="/facts/Design_of_experiments/VMrNftbr">design</a> GWASes which will yield genome-wide statistically-significant hits. This is done by comparing the GCTA estimate with the results of smaller GWASes. If a GWAS of n=10k using SNP data fails to turn up any hits, but the GCTA indicates a high heritability accounted for by SNPs, then that implies that a large number of variants are involved (<a href="/facts/Polygenic/wH8c6Cwm">polygenicity</a>) and thus that much larger GWASes will be required to accurately estimate each SNP's effect and directly account for a fraction of the GCTA heritability.

<h2 id="disadvantages">Disadvantages</h2>
<ol><li>Limited inference: GCTA estimates are inherently limited in that they cannot estimate broadsense heritability like twin/family studies as they only estimate the heritability due to SNPs. Hence, while they serve as a critical check on the unbiasedness of the twin/family studies, GCTAs cannot replace them for estimating total genetic contributions to a trait.</li>
<li>Substantial data requirements: the number of SNPs genotyped per person should be in the thousands and ideally the hundreds of thousands for reasonable estimates of genetic similarity (although this is no longer such an issue for current commercial chips which default to hundreds of thousands or millions of markers); and the number of persons, for somewhat stable estimates of plausible SNP heritability, should be at least n>1000 and ideally n>10000.<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a> In contrast, twin studies can offer precise estimates with a fraction of the sample size.</li>
<li>Computational inefficiency: The original GCTA implementation scales poorly with increasing data size (
 
 
 
 
 
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 (
 
 SNPs
 
 ⋅
 
 n
 
 2
 
 
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 {\displaystyle {\mathcal {O}}({\text{SNPs}}\cdot n^{2})}
 
), so even if enough data is available for precise GCTA estimates, the computational burden may be unfeasible. GCTA can be meta-analyzed as a standard precision-weighted fixed-effect meta-analysis,<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a> so research groups sometimes estimate cohorts or subsets and then pool them meta-analytically (at the cost of additional complexity and some loss of precision). This has motivated the creation of faster implementations and variant algorithms which make different assumptions, such as using <a href="/facts/Method_of_moments_(statistics)/Qfso3fMe">moment matching</a>.<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a></li>
<li>Need for raw data: GCTA requires genetic similarity of all subjects and thus their raw genetic information; due to privacy concerns, individual patient data is rarely shared. GCTA cannot be run on the summary statistics reported publicly by many GWAS projects, and if pooling multiple GCTA estimates, a <a href="/facts/Meta-analysis/IcfChd8z">meta-analysis</a> must be performed. In contrast, there are alternative techniques which operate on summaries reported by GWASes without requiring the raw data<a class="footnote-ref" id="fnref:14" href="#fn:14">14</a> e.g. "<a href="/facts/Linkage_disequilibrium_score_regression/8jxHUX4J">LD score regression</a>"<a class="footnote-ref" id="fnref:15" href="#fn:15">15</a> contrasts <a href="/facts/Linkage_disequilibrium/k84N6kIA">linkage disequilibrium</a> statistics (available from public datasets like <a href="/facts/1000_Genomes/n8n8P60h">1000 Genomes</a>) with the public summary effect-sizes to infer heritability and estimate genetic correlations/overlaps of multiple traits. The <a href="/facts/Broad_Institute/RchJRWLN">Broad Institute</a> runs <a href="http://ldsc.broadinstitute.org/about/">LD Hub</a> <a href="https://web.archive.org/web/20160511100955/http://ldsc.broadinstitute.org/about/">Archived</a> 2016-05-11 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a> which provides a public web interface to >=177 traits with LD score regression.<a class="footnote-ref" id="fnref:16" href="#fn:16">16</a> Another method using summary data is HESS.<a class="footnote-ref" id="fnref:17" href="#fn:17">17</a></li>
<li>Confidence intervals may be incorrect, or outside the 0-1 range of heritability, and highly imprecise due to asymptotics.<a class="footnote-ref" id="fnref:18" href="#fn:18">18</a></li>
<li>Underestimation of SNP heritability: GCTA implicitly assumes all classes of SNPs, rarer or commoner, newer or older, more or less in linkage disequilibrium, have the same effects on average; in humans, rarer and newer variants tend to have larger and more negative effects<a class="footnote-ref" id="fnref:19" href="#fn:19">19</a> as they represent <a href="/facts/Mutation_load/Fj2xzdzq">mutation load</a> being purged by <a href="/facts/Negative_selection_(natural_selection)/DCkRLqb4">negative selection</a>. As with measurement error, this will bias GCTA estimates towards underestimating heritability.</li></ol>
<h2 id="interpretation">Interpretation</h2>
GCTA provides an unbiased estimate of the total variance in phenotype explained by all variants included in the relatedness matrix (and any variation correlated with those SNPs). This estimate can also be interpreted as the maximum prediction accuracy (R^2) that could be achieved from a linear predictor using all SNPs in the relatedness matrix. The latter interpretation is particularly relevant to the development of Polygenic Risk Scores, as it defines their maximum accuracy. GCTA estimates are sometimes misinterpreted as estimates of total (or narrow-sense, i.e. additive) heritability, but this is not a guarantee of the method. GCTA estimates are likewise sometimes misinterpreted as "lower bounds" on the narrow-sense heritability but this is also incorrect: first because GCTA estimates can be biased (including biased upwards) if the model assumptions are violated, and second because, by definition (and when model assumptions are met), GCTA can provide an unbiased estimate of the narrow-sense heritability if all causal variants are included in the relatedness matrix. The interpretation of the GCTA estimate in relation to the narrow-sense heritability thus depends on the variants used to construct the relatedness matrix.
Most frequently, GCTA is run with a single relatedness matrix constructed from common SNPs and will not capture (or not fully capture) the contribution of the following factors:

<ol><li>Any rare or low-frequency variants that are not directly genotyped/imputed.</li>
<li>Any non-linear, dominance, or epistatic genetic effects. Note that GCTA can be extended to estimate the contribution of these effects through more complex relatedness matrices.</li>
<li>The effects of Gene-Environment interactions. Note that GCTA can be extended to estimate the contribution of GxE interactions when the E is known, by including additional variance components.</li>
<li>Structural variants, which are typically not genotyped or imputed.</li>
<li>Measurement error: GCTA does not model any uncertainty or error on the measured trait.</li></ol>
GCTA makes several model assumptions and may produce biased estimates under the following conditions:

<ol><li>The distribution of causal variants is systematically different from the distribution of variants included in the relatedness matrix (even if all causal variants are included in the relatedness matrix). For example, if causal variants are systematically at a higher/lower frequency or in higher/lower correlation than all genotyped variants. This can produce either an upwards or downwards bias depending on the relationship between the causal variants and variants used. Various extensions to GCTA have been proposed (for example, GREML-LDMS) to account for these distributional shifts.</li>
<li>Population stratification is not fully accounted for by covariates. GCTA (specifically GREML) accounts for stratification through the inclusion of fixed effect covariates, typically principal components. If these covariates do not fully capture the stratification the GCTA estimate will be biased, generally upwards. Accounting for recent population structure is particularly challenging for studies of rare variants.</li>
<li>Residual genetic or environmental relatedness present in the data. GCTA assumes a homogenous population with an independent and identically distributed environmental term. This assumption is violated if related individuals and/or individuals with substantially shared environments are included in the data. In this case, the GCTA estimate will additionally capture the contribution of any genetic variation correlated with the genetic relationship: either direct genetic effects or correlated environment.</li>
<li>The presence of "indirect" genetic effects. When genetic variants present in the relatedness matrix are correlated with variants present in other individuals that influence the participant's environment, those effects will also be captured in the GCTA estimate. For example, if variants inherited by a participant from their mother influenced their phenotype through their maternal environment, then the effect of those variants will be included in the GCTA estimate even though it is "indirect" (i.e. mediated by parental genetics). This may be interpreted as an upward bias as such "indirect" effects are not strictly causal (altering them in the participant would not lead to a change in phenotype in expectation).</li></ol>
<h2 id="implementations">Implementations</h2>

The original "GCTA" software package is the most widely used; its primary functionality covers the GREML estimation of SNP heritability, but includes other functionality:

<ul><li>Estimate the genetic relationship from genome-wide SNPs;</li>
<li>Estimate the <a href="/facts/Inbreeding_coefficient/DLo60l4x">inbreeding coefficient</a> from genome-wide SNPs;</li>
<li>Estimate the variance explained by all the <a href="/facts/Autosomal/uN3B2AhI">autosomal</a> SNPs;</li>
<li>Partition the genetic variance onto individual chromosomes;</li>
<li>Estimate the genetic variance associated with the X-chromosome;</li>
<li>Test the effect of dosage compensation on genetic variance on the <a href="/facts/X-chromosome/hpJxhSUr">X-chromosome</a>;</li>
<li>Predict the genome-wide additive genetic effects for individual subjects and for individual SNPs;</li>
<li>Estimate the LD structure encompassing a list of target SNPs;</li>
<li>Simulate GWAS data based upon the observed genotype data;</li>
<li>Convert <a href="/facts/Illumina_(company)/0nofTkVp">Illumina</a> raw genotype data into <a href="/facts/PLINK/SDYmhD8N">PLINK</a> format;</li>
<li>Conditional & joint analysis of GWAS summary statistics without individual level genotype data</li>
<li>Estimating the <a href="/facts/Genetic_correlation/qzKazGr6">genetic correlation</a> between two traits (diseases) using SNP data</li>
<li><a href="/facts/Mixed_linear_model/PovxPrAy">Mixed linear model</a> association analysis — GCTA, <a href="http://cnsgenomics.com/software/gcta/">cnsgenomics.com/software/gcta/</a></li></ul>
Other implementations and variant algorithms include:

<ul><li>FAST-LMM<a class="footnote-ref" id="fnref:20" href="#fn:20">20</a></li>
<li>FAST-LMM-Select:<a class="footnote-ref" id="fnref:21" href="#fn:21">21</a> like GCTA in using <a href="/facts/Ridge_regression/Le6KJgJ1">ridge regression</a><a class="footnote-ref" id="fnref:22" href="#fn:22">22</a> but including <a href="/facts/Feature_selection/gxbuF4VG">feature selection</a> to try to exclude irrelevant SNPs which only add noise to the relatedness estimates</li>
<li>LMM-<a href="/facts/Lasso_regression/R9yE8HDQ">Lasso</a><a class="footnote-ref" id="fnref:23" href="#fn:23">23</a></li>
<li>GEMMA<a class="footnote-ref" id="fnref:24" href="#fn:24">24</a></li>
<li>EMMAX<a class="footnote-ref" id="fnref:25" href="#fn:25">25</a></li>
<li><a href="http://www.epcc.ed.ac.uk/projects-portfolio/reacta">REACTA (formerly ACTA)</a> <a href="https://web.archive.org/web/20160523120255/http://www.epcc.ed.ac.uk/projects-portfolio/reacta">Archived</a> 2016-05-23 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a> claims order of magnitude runtime reductions<a class="footnote-ref" id="fnref:26" href="#fn:26">26</a><a class="footnote-ref" id="fnref:27" href="#fn:27">27</a></li>
<li><a href="http://www.hsph.harvard.edu/alkes-price/software/">BOLT-REML</a>/BOLT-LMM<a class="footnote-ref" id="fnref:28" href="#fn:28">28</a> (<a href="https://data.broadinstitute.org/alkesgroup/BOLT-LMM/">manual</a> <a href="https://web.archive.org/web/20160611003139/https://data.broadinstitute.org/alkesgroup/BOLT-LMM/">Archived</a> 2016-06-11 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a>), faster & better scaling;<a class="footnote-ref" id="fnref:29" href="#fn:29">29</a> with potentially better efficiency in the meta-analysis scenario<a class="footnote-ref" id="fnref:30" href="#fn:30">30</a></li>
<li><a href="http://scholar.harvard.edu/tge/software/megha">MEGHA</a><a class="footnote-ref" id="fnref:31" href="#fn:31">31</a></li>
<li>PLINK >1.9 (December 2013) supports <a href="https://www.cog-genomics.org/plink2/">"the use of genetic relationship matrices in mixed model association analysis and other calculations"</a></li>
<li>LDAK:<a class="footnote-ref" id="fnref:32" href="#fn:32">32</a> loosens the GCTA assumption that all SNPs, regardless of genotyping quality or frequency, have same averaged expected effect, allowing for potentially finding much more SNP heritability</li>
<li>GREML-IBD:<a class="footnote-ref" id="fnref:33" href="#fn:33">33</a> GCTA for <a href="/facts/Identity_by_descent/XhTTX2Qt">identity by descent</a>, attempting to estimate heritability based on shared genome segments in distant otherwise-unrelated relatives, in order to capture the effect of rarer variants which are not measured by SNP panels or otherwise imputed</li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Animal_breeding/a9VgVI2I">Animal breeding</a></li>
<li><a href="/facts/Best_linear_unbiased_prediction/nIEUoYh7">Best linear unbiased prediction</a></li>
<li><a href="/facts/Mendelian_randomization/u3Lu2ggP">Mendelian randomization</a></li>
<li><a href="/facts/Pleiotropy/c14XQQ7g">Pleiotropy</a></li>
<li>"<a href="/facts/The_Correlation_between_Relatives_on_the_Supposition_of_Mendelian_Inheritance/mSUdGjc8">The Correlation between Relatives on the Supposition of Mendelian Inheritance</a>", <a href="/facts/Ronald_Fisher/I2FVIpy9">Fisher</a> 1918</li></ul>

<h2 id="further-reading">Further reading</h2>
<ul><li><a href="http://espace.library.uq.edu.au/view/UQ:342517/UQ342517_OA.pdf">"Research review: Polygenic methods and their application to psychiatric traits"</a>, Wray et al. 2014</li>
<li><a href="http://medicine.tums.ac.ir:803/Users/Javad_TavakoliBazzaz/Medical%20Genetics-2/Heritability%20in%20the%20genomics%20era.pdf">"Heritability in the genomics era — concepts and misconceptions"</a> <a href="https://web.archive.org/web/20160522201032/http://medicine.tums.ac.ir:803/Users/Javad_TavakoliBazzaz/Medical%20Genetics-2/Heritability%20in%20the%20genomics%20era.pdf">Archived</a> 2016-05-22 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a>, Visscher et al. 2008</li>
<li><a href="http://www.sciencedirect.com/science/article/pii/S2001037015000458">"Uncovering the Genetic Architectures of Quantitative Traits"</a>, Lee et al. 2016</li>
<li><a href="http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12129/pdf">"Estimating heritability using genomic data"</a>, Stanton-Geddes et al. 2013</li>
<li><a href="http://genome.cshlp.org/content/24/9/1550.full">"MultiBLUP: improved SNP-based prediction for complex traits"</a>, Speed & Balding 2012</li>
<li><a href="http://www.montefiore.ulg.ac.be/~kvansteen/GeneticEpi-Engineering/ac1415/PART4/Yang2014.pdf">"Advantages and pitfalls in the application of mixed-model association methods"</a>, Yang et al. 2013</li>
<li><a href="http://www.genetics.org/content/157/4/1819.full">"Prediction of Total Genetic Value Using Genome-Wide Dense Marker Maps"</a>, Meuwissen et al. 2001</li>
<li><a href="http://rstb.royalsocietypublishing.org/content/365/1537/73.full">"Understanding and using quantitative genetic variation"</a>, Hill 2009</li>
<li><a href="https://www.dropbox.com/s/jr1sa6o6ba89wy1/2015-gianola.pdf">"One Hundred Years of Statistical Developments in Animal Breeding"</a>, Gianola & Rosa 2015</li>
<li><a href="http://biorxiv.org/content/early/2014/03/04/003160">"Conditions for the validity of SNP-based heritability estimation"</a>, Lee & Chow 2014</li>
<li><a href="http://www.pnas.org/content/111/49/E5272">"Measuring missing heritability: Inferring the contribution of common variants"</a>, Golan et al. 2014</li>
<li><a href="https://www.dropbox.com/s/2a585h6l77qm59p/2017-yang.pdf">"Concepts, estimation and interpretation of SNP-based heritability"</a>, Yang et al. 2017</li>
<li>Maier et al. 2017, <a href="https://www.cambridge.org/core/journals/psychological-medicine/article/embracing-polygenicity-a-review-of-methods-and-tools-for-psychiatric-genetics-research/4EBE208EA66EB49588D7C52FAB5AF4A1/core-reader">"Embracing polygenicity: a review of methods and tools for psychiatric genetics research"</a></li>
<li>Ronald & Pain 2018, <a href="https://www.dropbox.com/s/ccmzu8l2j7w46jf/2018-ronald.pdf?dl=0">"A systematic review of genome-wide research on psychotic experiences and negative symptom traits: new revelations and implications for psychiatry"</a></li></ul>
<h2 id="external-links">External links</h2>
<ul><li><a href="https://cnsgenomics.shinyapps.io/gctaPower/">GCTA-GREML Power Calculator</a> (<a href="http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1004269">"Statistical Power to Detect Genetic (Co)Variance of Complex Traits Using SNP Data in Unrelated Samples"</a>, Visscher et al. 2014)</li>
<li><a href="https://www.youtube.com/watch?v=b32OwqBPHkI">"Genomics, Big Data, Medicine, and Complex Traits"</a> (Peter Visscher talk)</li>
<li><a href="https://www.dropbox.com/s/1otmbu840xejjv1/MCTFR_talk.pdf">"The Genetic Architectures of Psychological Traits"</a>, Lee 2014 slides</li>
<li><a href="https://www.youtube.com/watch?v=VI-5HlYQpNE">"Heritability-based models for prediction of complex traits"</a>, <a href="https://sites.google.com/site/baldingstatisticalgenetics/home">David Balding</a> <a href="https://web.archive.org/web/20161008184835/https://sites.google.com/site/baldingstatisticalgenetics/home">Archived</a> 2016-10-08 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a> 2015</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Figure 3 of Yang et al 2010, or Figure 3 of Ritland & Ritland 1996 <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3232052/figure/F3/" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3232052/figure/F3/</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">see also Ritland 1996b, "Estimators for pairwise relatedness and individual inbreeding coefficients" Archived 2017-01-16 at the Wayback Machine; Ritland & Ritland 1996, "Inferences about quantitative inheritance based on natural population structure in the yellow monkeyflower, Mimulus guttatus" Archived 2016-09-24 at the Wayback Machine; Lynch & Ritland 1999, "Estimation of Pairwise Relatedness With Molecular Markers"; Ritland 2000, "Marker-inferred relatedness as a tool for detecting heritability in nature" Archived 2016-09-25 at the Wayback Machine; Thomas 2005, "The estimation of genetic relationships using molecular markers and their efficiency in estimating heritability in natural populations" <a href="http://genetics.forestry.ubc.ca/ritland/reprints/1996_GenetResearch_r.pdf" target="_blank">http://genetics.forestry.ubc.ca/ritland/reprints/1996_GenetResearch_r.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Visscher et al 2006, "Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings" <a href="http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.0020041" target="_blank">http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.0020041</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Visscher et al 2007, "Genome partitioning of genetic variation for height from 11,214 sibling pairs" <a href="http://www.sciencedirect.com/science/article/pii/S0002929707638841" target="_blank">http://www.sciencedirect.com/science/article/pii/S0002929707638841</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">"Common SNPs explain a large proportion of heritability for human height", Yang et al 2010 <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3232052/" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3232052/</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">"A Commentary on ‘Common SNPs Explain a Large Proportion of the Heritability for Human Height’ by Yang et al. (2010)", Visscher et al 2010 <a href="https://www.ncbi.nlm.nih.gov/pubmed/21142928" target="_blank">https://www.ncbi.nlm.nih.gov/pubmed/21142928</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">"Defining the role of common variation in the genomic and biological architecture of adult human height", Wood et al 2014 <a href="http://neurogenetics.qimrberghofer.edu.au/papers/Wood2014NatGenet.pdf" target="_blank">http://neurogenetics.qimrberghofer.edu.au/papers/Wood2014NatGenet.pdf</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">"GCTA: A Tool for Genome-wide Complex Trait Analysis", Yang et al 2011 <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3014363/" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3014363/</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">"Meta-analysis of the heritability of human traits based on fifty years of twin studies", Polderman et al 2015 <a href="http://www.gwern.net/docs/genetics/2015-polderman.pdf" target="_blank">http://www.gwern.net/docs/genetics/2015-polderman.pdf</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Barnes, J. C.; Wright, John Paul; Boutwell, Brian B.; Schwartz, Joseph A.; Connolly, Eric J.; Nedelec, Joseph L.; Beaver, Kevin M. (2014-11-01). "Demonstrating the Validity of Twin Research in Criminology". Criminology. 52 (4): 588–626. doi:10.1111/1745-9125.12049. ISSN 1745-9125. <a href="https://www.researchgate.net/publication/267158254" target="_blank">https://www.researchgate.net/publication/267158254</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">"GCTA will eventually provide direct DNA tests of quantitative genetic results based on twin and adoption studies. One problem is that many thousands of individuals are required to provide reliable estimates. Another problem is that more SNPs are needed than even the million SNPs genotyped on current SNP microarrays because there is much DNA variation not captured by these SNPs. As a result, GCTA cannot estimate all heritability, perhaps only about half of the heritability. The first reports of GCTA analyses estimate heritability to be about half the heritability estimates from twin and adoption studies for height (Lee, Wray, Goddard, & Visscher, 2011; Yang et al., 2010; Yang, Manolio, et al" 2011), and intelligence (Davies et al., 2011)." pg110, Behavioral Genetics, Plomin et al 2012 <a href="https://www.dropbox.com/s/1iz7o1hqb8isas2/2012-plomin-behavioralgenetics.pdf" target="_blank">https://www.dropbox.com/s/1iz7o1hqb8isas2/2012-plomin-behavioralgenetics.pdf</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">"Meta-analysis of GREML results from multiple cohorts", Yang 2015 <a href="http://gcta.freeforums.net/thread/213/analysis-greml-results-multiple-cohorts" target="_blank">http://gcta.freeforums.net/thread/213/analysis-greml-results-multiple-cohorts</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">Ge, Tian; Chen, Chia-Yen; Neale, Benjamin M.; Sabuncu, Mert R.; Smoller, Jordan W. (2016). "Phenome-wide Heritability Analysis of the UK Biobank". bioRxiv 10.1101/070177. <a href="/wiki/BioRxiv_(identifier)" target="_blank">/wiki/BioRxiv_(identifier)</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">Pasaniuc & Price 2016, "Dissecting the genetics of complex traits using summary association statistics" <a href="https://www.dropbox.com/s/4mgmun29xbund7z/2016-pasaniuc.pdf" target="_blank">https://www.dropbox.com/s/4mgmun29xbund7z/2016-pasaniuc.pdf</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">Bulik-Sullivan, B. K.; Loh, P. R.; Finucane, H.; Ripke, S.; Yang, J.; Schizophrenia Working Group of the Psychiatric Genomics Consortium; Patterson, N.; Daly, M. J.; Price, A. L.; Neale, B. M. (2015). "LD Score Regression Distinguishes Confounding from Polygenicity in Genome-Wide Association Studies". Nature Genetics. 47 (3): 291–295. doi:10.1038/ng.3211. PMC 4495769. PMID 25642630. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4495769" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4495769</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
<li id="fn:16">"LD Hub: a centralized database and web interface to LD score regression that maximizes the potential of summary level GWAS data for SNP heritability and genetic correlation analysis", Zheng et al 2016 <a href="http://biorxiv.org/content/biorxiv/early/2016/05/03/051094.full.pdf" target="_blank">http://biorxiv.org/content/biorxiv/early/2016/05/03/051094.full.pdf</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></li>
<li id="fn:17">"Contrasting the genetic architecture of 30 complex traits from summary association data", Shi et al 2016 <a href="http://biorxiv.org/content/early/2016/01/14/035907" target="_blank">http://biorxiv.org/content/early/2016/01/14/035907</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></li>
<li id="fn:18">Schweiger, Regev; Kaufman, Shachar; Laaksonen, Reijo; Kleber, Marcus E.; März, Winfried; Eskin, Eleazar; Rosset, Saharon; Halperin, Eran (2 June 2016). "Fast and Accurate Construction of Confidence Intervals for Heritability". The American Journal of Human Genetics. 98 (6): 1181–1192. doi:10.1016/j.ajhg.2016.04.016. PMC 4908190. PMID 27259052. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4908190" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4908190</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></li>
<li id="fn:19">"Linkage disequilibrium–dependent architecture of human complex traits shows action of negative selection", Gazal et al 2017 <a href="https://www.dropbox.com/s/idh2vm1dkar3qho/2017-gazal.pdf" target="_blank">https://www.dropbox.com/s/idh2vm1dkar3qho/2017-gazal.pdf</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></li>
<li id="fn:20">"Fast linear mixed models for genome-wide association studies", Lippert 2011 <a href="https://www.researchgate.net/profile/David_Heckerman/publication/51618535_FaST_linear_mixed_models_for_genome-wide_association_studies/links/5485d3a70cf268d28f00456a.pdf" target="_blank">https://www.researchgate.net/profile/David_Heckerman/publication/51618535_FaST_linear_mixed_models_for_genome-wide_association_studies/links/5485d3a70cf268d28f00456a.pdf</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></li>
<li id="fn:21">"Improved linear mixed models for genome-wide association studies", Listgarten et al 2012 <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3597090/" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3597090/</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></li>
<li id="fn:22">"Advantages and pitfalls in the application of mixed-model association methods", Yang et al 2014 <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3989144/" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3989144/</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></li>
<li id="fn:23">"A lasso multi-marker mixed model for association mapping with population structure correction", Rakitsch et al 2012 <a href="https://web.archive.org/web/20151204193223/http://bioinformatics.oxfordjournals.org/content/29/2/206.full#aff-1" target="_blank">https://web.archive.org/web/20151204193223/http://bioinformatics.oxfordjournals.org/content/29/2/206.full#aff-1</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></li>
<li id="fn:24">"Genome-wide efficient mixed-model analysis for association studies", Zhou & Stephens 2012 <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3386377/" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3386377/</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></li>
<li id="fn:25">"Variance component model to account for sample structure in genome-wide association studies", Kang et al 2012 <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3092069/" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3092069/</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></li>
<li id="fn:26">"Advanced Complex Trait Analysis", Gray et al 2012 <a href="https://web.archive.org/web/20160522235202/http://bioinformatics.oxfordjournals.org/content/early/2012/09/27/bioinformatics.bts571.full.pdf" target="_blank">https://web.archive.org/web/20160522235202/http://bioinformatics.oxfordjournals.org/content/early/2012/09/27/bioinformatics.bts571.full.pdf</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></li>
<li id="fn:27">"Regional Heritability Advanced Complex Trait Analysis for GPU and Traditional Parallel Architecture", Cebamanos et al 2012 <a href="https://www.semanticscholar.org/paper/Regional-heritability-advanced-complex-trait-Cebamanos-Gray/c340835e1baf4b9fcafbfb001841bbd4793f598f/pdf" target="_blank">https://www.semanticscholar.org/paper/Regional-heritability-advanced-complex-trait-Cebamanos-Gray/c340835e1baf4b9fcafbfb001841bbd4793f598f/pdf</a> <a href="#fnref:27" class="footnote-back-ref">↩</a></li>
<li id="fn:28">"Efficient Bayesian mixed model analysis increases association power in large cohorts", Loh et al 2012 <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4342297/" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4342297/</a> <a href="#fnref:28" class="footnote-back-ref">↩</a></li>
<li id="fn:29">"Contrasting genetic architectures of schizophrenia and other complex diseases using fast variance-components analysis", Loh et al 2015; see also "Contrasting regional architectures of schizophrenia and other complex diseases using fast variance components analysis", Loh et al 2015 <a href="http://biorxiv.org/content/biorxiv/early/2015/06/05/016527.full.pdf" target="_blank">http://biorxiv.org/content/biorxiv/early/2015/06/05/016527.full.pdf</a> <a href="#fnref:29" class="footnote-back-ref">↩</a></li>
<li id="fn:30">"Mixed Models for Meta-Analysis and Sequencing", Bulik-Sullivan 2015 <a href="http://biorxiv.org/content/early/2015/05/29/020115" target="_blank">http://biorxiv.org/content/early/2015/05/29/020115</a> <a href="#fnref:30" class="footnote-back-ref">↩</a></li>
<li id="fn:31">"Massively expedited genome-wide heritability analysis (MEGHA)", Ge et al 2015 <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4345618/" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4345618/</a> <a href="#fnref:31" class="footnote-back-ref">↩</a></li>
<li id="fn:32">Speed et al 2016, "Re-evaluation of SNP heritability in complex human traits" <a href="http://biorxiv.org/content/early/2017/01/15/074310" target="_blank">http://biorxiv.org/content/early/2017/01/15/074310</a> <a href="#fnref:32" class="footnote-back-ref">↩</a></li>
<li id="fn:33">Evans et al 2017, "Narrow-sense heritability estimation of complex traits using identity-by-descent information." <a href="http://www.biorxiv.org/content/early/2017/07/17/164848" target="_blank">http://www.biorxiv.org/content/early/2017/07/17/164848</a> <a href="#fnref:33" class="footnote-back-ref">↩</a></li>
</ol>

Genome-wide complex trait analysis open-in-new

Genome-wide complex trait analysis