Polygenic Modeling with Bayesian Sparse Linear Mixed Models

Zhou, Xiang; Carbonetto, Peter; Stephens, Matthew

doi:10.1371/journal.pgen.1003264

Cited by 754 publications

(1,230 citation statements)

References 87 publications

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“…The same correction was derived by others in a Bayesian framework (21). Intuitively, the term K 2 ð1 − KÞ 2 Pð1 − PÞφðtÞ 2 is a generalization of Eq.…”

Section: Resultsmentioning

confidence: 58%

“…Several recent papers (13,21,30,(32)(33)(34)(35) focused on improving the estimation of the genetic correlation matrices, by accounting for sparsity (33,34), LD and LD-dependent genetic architecture (30), prior information regarding effect sizes of different SNPs (35), or the relationship between minor allele frequency and effect size (30). As better methods for estimating the genetic correlation matrix are developed, they may be used in PCGC regression in place of the correction method of Yang et al (9).…”

Section: Discussionmentioning

confidence: 99%

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Measuring missing heritability: Inferring the contribution of common variants

Golan

Lander

2014

Proc. Natl. Acad. Sci. U.S.A.

299

410

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Genome-wide association studies (GWASs), also called common variant association studies (CVASs), have uncovered thousands of genetic variants associated with hundreds of diseases. However, the variants that reach statistical significance typically explain only a small fraction of the heritability. One explanation for the "missing heritability" is that there are many additional disease-associated common variants whose effects are too small to detect with current sample sizes. It therefore is useful to have methods to quantify the heritability due to common variation, without having to identify all causal variants. Recent studies applied restricted maximum likelihood (REML) estimation to case-control studies for diseases. Here, we show that REML considerably underestimates the fraction of heritability due to common variation in this setting. The degree of underestimation increases with the rarity of disease, the heritability of the disease, and the size of the sample. Instead, we develop a general framework for heritability estimation, called phenotype correlation-genotype correlation (PCGC) regression, which generalizes the well-known Haseman-Elston regression method. We show that PCGC regression yields unbiased estimates. Applying PCGC regression to six diseases, we estimate the proportion of the phenotypic variance due to common variants to range from 25% to 56% and the proportion of heritability due to common variants from 41% to 68% (mean 60%). These results suggest that common variants may explain at least half the heritability for many diseases. PCGC regression also is readily applicable to other settings, including analyzing extreme-phenotype studies and adjusting for covariates such as sex, age, and population structure.genome-wide association studies | statistical genetics | heritability estimation C omprehensive genomic studies have begun to uncover the genetic basis of common polygenic inherited diseases and traits, identifying thousands of loci and pointing to key biological pathways. However, the genetic variants implicated so far account for less than half the estimated heritability of most diseases and traits (1). Explaining the remainder of the heritabilityoften termed "missing heritability"-is of considerable biological interest and medical importance. This is our third article on exploring the mystery of missing heritability.In our first paper (2), we noted that some of the apparently missing heritability may arise from a methodological issue. Specifically, we showed that the presence of genetic interactions among loci might substantially inflate estimates of the total (narrow-sense) heritability and thus overstate the extent of missing heritability. However, this likely is only a partial explanation.In our second paper (3), we explored the design of association studies to discover genetic variants associated with the risk of a disease or trait. Specifically, our paper focused on rare variant association studies (RVASs), for which large-scale comprehensive efforts are just becoming feasible with...

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“…The same correction was derived by others in a Bayesian framework (21). Intuitively, the term K 2 ð1 − KÞ 2 Pð1 − PÞφðtÞ 2 is a generalization of Eq.…”

Section: Resultsmentioning

confidence: 58%

Section: Discussionmentioning

confidence: 99%

Measuring missing heritability: Inferring the contribution of common variants

Golan

Lander

2014

Proc. Natl. Acad. Sci. U.S.A.

299

410

View full text Add to dashboard Cite

show abstract

“…18,20,24 Let Z k denote the sub-matrix (columns of matrix Z) that corresponds to the SNPs in group k. The general form of a K-component LMM can be written as:…”

Section: Lmm and Blup For Complex Traitsmentioning

confidence: 99%

Leveraging Multi-ethnic Evidence for Risk Assessment of Quantitative Traits in Minority Populations

Coram

Fang

Candille

et al. 2017

The American Journal of Human Genetics

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An essential component of precision medicine is the ability to predict an individual's risk of disease based on genetic and non-genetic factors. For complex traits and diseases, assessing the risk due to genetic factors is challenging because it requires knowledge of both the identity of variants that influence the trait and their corresponding allelic effects. Although the set of risk variants and their allelic effects may vary between populations, a large proportion of these variants were identified based on studies in populations of European descent. Heterogeneity in genetic architecture underlying complex traits and diseases, while broadly acknowledged, remains poorly characterized. Ignoring such heterogeneity likely reduces predictive accuracy for minority individuals. In this study, we propose an approach, called XP-BLUP, which ameliorates this ethnic disparity by combining trans-ethnic and ethnic-specific information. We build a polygenic model for complex traits that distinguishes candidate trait-relevant variants from the rest of the genome. The set of candidate variants are selected based on studies in any human population, yet the allelic effects are evaluated in a population-specific fashion. Simulation studies and real data analyses demonstrate that XP-BLUP adaptively utilizes trans-ethnic information and can substantially improve predictive accuracy in minority populations. At the same time, our study highlights the importance of the continued expansion of minority cohorts.

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“…In keeping with other methods that use marker-based estimates of relatedness to correct for confounding due to population stratification or familial relationships (Yu et al 2006;Kang et al 2008;Lippert et al 2011;Listgarten et al 2012;Zhou et al 2013), we included only the additive portion of the polygenic effect. The rationale is that dominance effects typically make a much smaller contribution to the variance of a complex trait.…”

Section: Pedigree-and Marker-based Estimates Of Genetic Sharingmentioning

confidence: 99%

High-Resolution Genetic Mapping of Complex Traits from a Combined Analysis of F2 and Advanced Intercross Mice

et al. 2014

Self Cite

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Genetic influences on anxiety disorders are well documented; however, the specific genes underlying these disorders remain largely unknown. To identify quantitative trait loci (QTL) for conditioned fear and open field behavior, we used an F 2 intercross (n = 490) and a 34th-generation advanced intercross line (AIL) (n = 687) from the LG/J and SM/J inbred mouse strains. The F 2 provided strong support for several QTL, but within wide chromosomal regions. The AIL yielded much narrower QTL, but the results were less statistically significant, despite the larger number of mice. Simultaneous analysis of the F 2 and AIL provided strong support for QTL and within much narrower regions. We used a linear mixed-model approach, implemented in the program QTLRel, to correct for possible confounding due to familial relatedness. Because we recorded the full pedigree, we were able to empirically compare two ways of accounting for relatedness: using the pedigree to estimate kinship coefficients and using genetic marker estimates of "realized relatedness." QTL mapping using the marker-based estimates yielded more support for QTL, but only when we excluded the chromosome being scanned from the marker-based relatedness estimates. We used a forward model selection procedure to assess evidence for multiple QTL on the same chromosome. Overall, we identified 12 significant loci for behaviors in the open field and 12 significant loci for conditioned fear behaviors. Our approach implements multiple advances to integrated analysis of F 2 and AILs that provide both power and precision, while maintaining the advantages of using only two inbred strains to map QTL.

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Polygenic Modeling with Bayesian Sparse Linear Mixed Models

Cited by 754 publications

References 87 publications

Measuring missing heritability: Inferring the contribution of common variants

Measuring missing heritability: Inferring the contribution of common variants

Leveraging Multi-ethnic Evidence for Risk Assessment of Quantitative Traits in Minority Populations

High-Resolution Genetic Mapping of Complex Traits from a Combined Analysis of F2 and Advanced Intercross Mice

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