On high-dimensional misspecified mixed model analysis in genome-wide association study

Jiang, Jiming; Liu, Cong; Paul, Debashis; Yang, Can; Zhao, Hongyu

doi:10.1214/15-aos1421

Cited by 61 publications

(84 citation statements)

References 36 publications

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“…Probably the potential advantage of contrasting out the fixed effects is small when the number of random effects is large. REML may have a larger advantage in very sparse settings [29] or when the number of fixed effects is large with respect to n. Estimates from the conjugate Bayes model are very similar to those by MML. We show that estimating τ 2 along with σ 2 highly improves the σ 2 estimates presented by [24], where a fixed value of τ 2 is used.…”

Section: Discussionmentioning

confidence: 85%

Estimation of variance components, heritability and the ridge penalty in high-dimensional generalized linear models

Veerman

Leday

Wiel

2019

Communications in Statistics - Simulation and Computation

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For high-dimensional linear regression models, we review and compare several estimators of variances τ 2 and σ 2 of the random slopes and errors, respectively. These variances relate directly to ridge regression penalty λ and heritability index h 2 , often used in genetics. Direct and indirect estimators of these, either based on cross-validation (CV) or maximum marginal likelihood (MML), are also discussed. The comparisons include several cases of covariate matrix X n×p , with p n, such as multi-collinear covariates and data-derived ones. In addition, we study robustness against departures from the model such as sparse instead of dense effects and non-Gaussian errors.An example on weight gain data with genomic covariates confirms the good performance of MML compared to CV. Several extensions are presented. First, to the high-dimensional linear mixed effects model, with REML as an alternative to MML. Second, to the conjugate Bayesian setting, which proves to be a good alternative. Third, and most prominently, to generalized linear models for which we derive a computationally efficient MML estimator by re-writing the marginal likelihood as an n-dimensional integral. For Poisson and Binomial ridge regression, we demonstrate the superior accuracy of the resulting MML estimator of λ as compared to CV. Software is provided to enable reproduction of all results presented here.

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Section: Discussionmentioning

confidence: 85%

Estimation of variance components, heritability and the ridge penalty in high-dimensional generalized linear models

Veerman

Leday

Wiel

2019

Communications in Statistics - Simulation and Computation

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“…To estimate PVE GREX , we introduce the following probabilistic structure for the effects in model (1) and (2): which is motivated by a recent theoretical justification [58] for heritability estimation on a mis-specified linear mixed model (LMM). This prior specification in (4) provides a great computational advantage as well as a stable performance for IGREX under model mis-specification, as demonstrated in the simulation studies.…”

Section: Methodsmentioning

confidence: 99%

Quantifying the impact of genetically regulated expression on complex traits and diseases

Cai

Chen

Liu

et al. 2019

Preprint

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By leveraging existing GWAS and eQTL resources, transcriptome-wide association studies 1 (TWAS) have achieved many successes in identifying trait-associations of genetically-regulated 2 expression (GREX) levels. TWAS analysis relies on the shared GREX variation across GWAS 3 and the reference eQTL data, which depends on the cellular conditions of the eQTL data. 4 Considering the increasing availability of eQTL data from different conditions and the often 5 unknown trait-relevant cell/tissue-types, we propose a method and tool, IGREX, for precisely 6 quantifying the proportion of phenotypic variation attributed to the GREX component. IGREX 7 takes as input a reference eQTL panel and individual-level or summary-level GWAS data. Using 8 eQTL data of 48 tissue types from the GTEx project as a reference panel, we evaluated the 9 tissue-specific IGREX impact on a wide spectrum of phenotypes. We observed strong GREX 10 effects on immune-related protein biomarkers. By incorporating trans-eQTLs and analyzing 11 genetically-regulated alternative splicing events, we evaluated new potential directions for 12 TWAS analysis. 13 * Correspondence should be addressed to Jin Liu (jin.liu@duke-nus.edu.sg) and Can Yang (macyang@ust.hk) Genome-wide association studies (GWAS) have successfully identified tens of thousands of 15 unique associations between single-nucleotide polymorphisms (SNPs) and a wide range of 16 complex traits/diseases (http://www.ebi.ac.uk/gwas/). More than 90% of identified risk 17 variants are located in non-coding regions [1], making it challenging to understand their 18 functional mechanisms. Increasing evidence [2, 3, 4, 5, 6, 7, 8, 9] has suggested that many of 19 those risk variants may affect traits/diseases via the modulation of their cis gene expression 20 levels. For example, a study of 18 complex traits revealed an enrichment for expression 21 quantitative trait loci (eQTLs) in 11% of 729 tissue-trait pairs [10]. There is great interest in 22 precisely characterizing the specific role of genetically regulated gene expression (GREX) in 23 human traits and diseases. 24It is well known that the effects of genetic variation on gene expressions depend on cellular 25 contexts [11]. The rapidly increasing availability of eQTL data from different tissue types, 26 cell types, populations and other conditions provides an unprecedented opportunity to study 27 and evaluate GREX effects in a variety of conditions. For example, the V7 release of the 28 Genotype-Tissue Expression (GTEx) project (https://gtexportal.org/home/) has collected 29 gene expression samples from 53 non-diseased tissues across 714 individuals [11]. Multiple 30 blood eQTL resources comprising thousands of individuals are made publicly available [12, 13]; 31 and other ongoing projects such as Genetics of DNA Methylation Consortium (GoDMC) and 32 eQTLGen consortium are collecting expression data with sample sizes larger than 10, 000 33 [14, 15]. Those data serve as rich eQTL resources for a comprehensive evaluation of GREX 34 effects. 35T...

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“…Such models may include fixed effects as well, useful for accommodating covariates like age or known biomarkers in a clinical prediction model. Jiang, Li, Debashis, Yang, and Zhao () discuss the well‐known restricted maximum likelihood (REML) estimator of ( τ 2 , σ 2 ). They prove the consistency of the REML estimator in the high‐dimensional setting, even when the prior is misspecified, in the sense that only a fraction of regression parameters are nonzero in reality.…”

Section: Empirical Bayes Methodologiesmentioning

confidence: 99%

Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Wiel

Beest

Münch

2018

Scandinavian J Statistics

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Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p , the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.

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On high-dimensional misspecified mixed model analysis in genome-wide association study

Cited by 61 publications

References 36 publications

Estimation of variance components, heritability and the ridge penalty in high-dimensional generalized linear models

Estimation of variance components, heritability and the ridge penalty in high-dimensional generalized linear models

Quantifying the impact of genetically regulated expression on complex traits and diseases

Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

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