Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Here we conducted a large-scale genetic association analysis of educational attainment in a sample of approximately 1.1 million individuals and identify 1,271 independent genome-wide-significant SNPs. For the SNPs taken together, we found evidence of heterogeneous effects across environments. The SNPs implicate genes involved in brain-development processes and neuron-to-neuron communication. In a separate analysis of the X chromosome, we identify 10 independent genome-wide-significant SNPs and estimate a SNP heritability of around 0.3% in both men and women, consistent with partial dosage compensation. A joint (multi-phenotype) analysis of educational attainment and three related cognitive phenotypes generates polygenic scores that explain 11-13% of the variance in educational attainment and 7-10% of the variance in cognitive performance. This prediction accuracy substantially increases the utility of polygenic scores as tools in research.

/pdf/gene-discovery-and-polygenic-prediction-from-a-genome-wide-28jxdgwqo5.pdf

Gene discovery and polygenic prediction from a genome-wide association study of educational attainment in 1.1 million individuals

Common variant genome-wide association studies (GWASs) have, to date, identified >24 risk loci for Parkinson's disease (PD). To discover additional loci, we carried out a GWAS comparing 6,476 PD cases with 302,042 controls, followed by a meta-analysis with a recent study of over 13,000 PD cases and 95,000 controls at 9,830 overlapping variants. We then tested 35 loci (P < 1 × 10-6) in a replication cohort of 5,851 cases and 5,866 controls. We identified 17 novel risk loci (P < 5 × 10-8) in a joint analysis of 26,035 cases and 403,190 controls. We used a neurocentric strategy to assign candidate risk genes to the loci. We identified protein-altering or cis-expression quantitative trait locus (cis-eQTL) variants in linkage disequilibrium with the index variant in 29 of the 41 PD loci. These results indicate a key role for autophagy and lysosomal biology in PD risk, and suggest potential new drug targets for PD.

A meta-analysis of genome-wide association studies identifies 17 new Parkinson's disease risk loci.

Advancing from statistical associations of complex traits with genetic markers to understanding the functional genetic variants that influence traits is often a complex process. Fine-mapping can select and prioritize genetic variants for further study, yet the multitude of analytical strategies and study designs makes it challenging to choose an optimal approach. We review the strengths and weaknesses of different fine-mapping approaches, emphasizing the main factors that affect performance. Topics include interpreting results from genome-wide association studies (GWAS), the role of linkage disequilibrium, statistical fine-mapping approaches, trans-ethnic studies, genomic annotation and data integration, and other analysis and design issues.

From genome-wide associations to candidate causal variants by statistical fine-mapping.

The vast majority of genome-wide association study (GWAS) risk loci fall in non-coding regions of the genome. One possible hypothesis is that these GWAS risk loci alter the individual's disease risk through their effect on gene expression in different tissues. In order to understand the mechanisms driving a GWAS risk locus, it is helpful to determine which gene is affected in specific tissue types. For example, the relevant gene and tissue could play a role in the disease mechanism if the same variant responsible for a GWAS locus also affects gene expression. Identifying whether or not the same variant is causal in both GWASs and expression quantitative trail locus (eQTL) studies is challenging because of the uncertainty induced by linkage disequilibrium and the fact that some loci harbor multiple causal variants. However, current methods that address this problem assume that each locus contains a single causal variant. In this paper, we present eCAVIAR, a probabilistic method that has several key advantages over existing methods. First, our method can account for more than one causal variant in any given locus. Second, it can leverage summary statistics without accessing the individual genotype data. We use both simulated and real datasets to demonstrate the utility of our method. Using publicly available eQTL data on 45 different tissues, we demonstrate that eCAVIAR can prioritize likely relevant tissues and target genes for a set of glucose- and insulin-related trait loci.

Colocalization of GWAS and eQTL Signals Detects Target Genes

Two recently developed fine-mapping methods, CAVIAR and PAINTOR, demonstrate better performance over other fine-mapping methods. They also have the advantage of using only the marginal test statistics and the correlation among SNPs. Both methods leverage the fact that the marginal test statistics asymptotically follow a multivariate normal distribution and are likelihood based. However, their relationship with Bayesian fine mapping, such as BIMBAM, is not clear. In this study, we first show that CAVIAR and BIMBAM are actually approximately equivalent to each other. This leads to a fine-mapping method using marginal test statistics in the Bayesian framework, which we call CAVIAR Bayes factor (CAVIARBF). Another advantage of the Bayesian framework is that it can answer both association and fine-mapping questions. We also used simulations to compare CAVIARBF with other methods under different numbers of causal variants. The results showed that both CAVIARBF and BIMBAM have better performance than PAINTOR and other methods. Compared to BIMBAM, CAVIARBF has the advantage of using only marginal test statistics and takes about one-quarter to one-fifth of the running time. We applied different methods on two independent cohorts of the same phenotype. Results showed that CAVIARBF, BIMBAM, and PAINTOR selected the same top 3 SNPs; however, CAVIARBF and BIMBAM had better consistency in selecting the top 10 ranked SNPs between the two cohorts. Software is available at https://bitbucket.org/Wenan/caviarbf.

https://www.genetics.org/content/genetics/200/3/719.full.pdf

Fine Mapping Causal Variants with an Approximate Bayesian Method Using Marginal Test Statistics.

Functional annotations have been shown to improve both the discovery power and fine-mapping accuracy in genome-wide association studies. However, the optimal strategy to incorporate the large number of existing annotations is still not clear. In this study, we propose a Bayesian framework to incorporate functional annotations in a systematic manner. We compute the maximum a posteriori solution and use cross validation to find the optimal penalty parameters. By extending our previous fine-mapping method CAVIARBF into this framework, we require only summary statistics as input. We also derived an exact calculation of Bayes factors using summary statistics for quantitative traits, which is necessary when a large proportion of trait variance is explained by the variants of interest, such as in fine mapping expression quantitative trait loci (eQTL). We compared the proposed method with PAINTOR using different strategies to combine annotations. Simulation results show that the proposed method achieves the best accuracy in identifying causal variants among the different strategies and methods compared. We also find that for annotations with moderate effects from a large annotation pool, screening annotations individually and then combining the top annotations can produce overly optimistic results. We applied these methods on two real data sets: a meta-analysis result of lipid traits and a cis-eQTL study of normal prostate tissues. For the eQTL data, incorporating annotations significantly increased the number of potential causal variants with high probabilities.

https://www.genetics.org/content/genetics/204/3/933.full.pdf

Incorporating Functional Annotations for Fine-Mapping Causal Variants in a Bayesian Framework Using Summary Statistics

Kernel machine based association tests (KAT) have been increasingly used in testing the association between an outcome and a set of biological measurements due to its power to combine multiple weak signals of complex relationship with the outcome through the specification of a relevant kernel. Human genetic and microbiome association studies are two important applications of KAT. However, the classic KAT framework relies on large sample theory, and conservativeness has been observed for small sample studies, especially for microbiome association studies. The common approach for addressing the small sample problem relies on computationally intensive resampling methods. Here, we derive an exact test for KAT with continuous traits, which resolve the small sample conservatism of KAT without the need for resampling. The exact test has significantly improved power to detect association for microbiome studies. For binary traits, we propose a similar approximate test, and we show that the approximate test is very powerful for a wide range of kernels including common variant- and microbiome-based kernels, and the approximate test controls the type I error well for these kernels. In contrast, the sequence kernel association tests have slightly inflated genomic inflation factors after small sample adjustment. Extensive simulations and application to a real microbiome association study are used to demonstrate the utility of our method.

/pdf/small-sample-kernel-association-tests-for-human-genetic-and-dcuhj35cs2.pdf

Small Sample Kernel Association Tests for Human Genetic and Microbiome Association Studies.

Recently, Wen and Stephens (Wen and Stephens [2010] Ann Appl Stat 4(3):1158-1182) proposed a linear predictor, called BLIMP, that uses conditional multivariate normal moments to impute genotypes with accuracy similar to current state-of-the-art methods. One novelty is that it regularized the estimated covariance matrix based on a model from population genetics. We extended multivariate moments to impute genotypes in pedigrees. Our proposed method, PedBLIMP, utilizes both the linkage-disequilibrium (LD) information estimated from external panel data and the pedigree structure or identity-by-descent (IBD) information. The proposed method was evaluated on a pedigree design where some individuals were genotyped with dense markers and the rest with sparse markers. We found that incorporating the pedigree/IBD information can improve imputation accuracy compared to BLIMP. Because rare variants usually have low LD with other single-nucleotide polymorphisms (SNPs), incorporating pedigree/IBD information largely improved imputation accuracy for rare variants. We also compared PedBLIMP with IMPUTE2 and GIGI. Results show that when sparse markers are in a certain density range, our method can outperform both IMPUTE2 and GIGI.

/pdf/pedblimp-extending-linear-predictors-to-impute-genotypes-in-18m98fzsot.pdf

Wenan Chen

Papers

Fine Mapping Causal Variants with an Approximate Bayesian Method Using Marginal Test Statistics.

Incorporating Functional Annotations for Fine-Mapping Causal Variants in a Bayesian Framework Using Summary Statistics

Small Sample Kernel Association Tests for Human Genetic and Microbiome Association Studies.

PedBLIMP: Extending Linear Predictors to Impute Genotypes in Pedigrees