Quantifying evidence for candidate gene polymorphisms: Bayesian analysis combining sequence-specific and quantitative trait loci colocation information

Prioritizing covariates in the planning of future studies in the meta-analytic framework

Science can be seen as a sequential process where each new study augments evidence to the existing knowledge. To have the best prospects to make an impact in this process, a new study should be designed optimally taking into account the previous studies and other prior information. We propose a formal approach for the covariate prioritization, that is the decision about the covariates to be measured in a new study. The decision criteria can be based on conditional power, change of the p-value, change in lower confidence limit, Kullback-Leibler divergence, Bayes factors, Bayesian false discovery rate or difference between prior and posterior expectation. The criteria can be also used for decisions on the sample size. As an illustration, we consider covariate prioritization based on genome-wide association studies for C-reactive protein levels and make suggestions on the genes to be studied further.

Impact of prior specifications in a shrinkage-inducing Bayesian model for quantitative trait mapping and genomic prediction

BACKGROUND

In quantitative trait mapping and genomic prediction, Bayesian variable selection methods have gained popularity in conjunction with the increase in marker data and computational resources. Whereas shrinkage-inducing methods are common tools in genomic prediction, rigorous decision making in mapping studies using such models is not well established and the robustness of posterior results is subject to misspecified assumptions because of weak biological prior evidence.

METHODS

Here, we evaluate the impact of prior specifications in a shrinkage-based Bayesian variable selection method which is based on a mixture of uniform priors applied to genetic marker effects that we presented in a previous study. Unlike most other shrinkage approaches, the use of a mixture of uniform priors provides a coherent framework for inference based on Bayes factors. To evaluate the robustness of genetic association under varying prior specifications, Bayes factors are compared as signals of positive marker association, whereas genomic estimated breeding values are considered for genomic selection. The impact of specific prior specifications is reduced by calculation of combined estimates from multiple specifications. A Gibbs sampler is used to perform Markov chain Monte Carlo estimation (MCMC) and a generalized expectation-maximization algorithm as a faster alternative for maximum a posteriori point estimation. The performance of the method is evaluated by using two publicly available data examples: the simulated QTLMAS XII data set and a real data set from a population of pigs.

RESULTS

Combined estimates of Bayes factors were very successful in identifying quantitative trait loci, and the ranking of Bayes factors was fairly stable among markers with positive signals of association under varying prior assumptions, but their magnitudes varied considerably. Genomic estimated breeding values using the mixture of uniform priors compared well to other approaches for both data sets and loss of accuracy with the generalized expectation-maximization algorithm was small as compared to that with MCMC.

CONCLUSIONS

Since no error-free method to specify priors is available for complex biological phenomena, exploring a wide variety of prior specifications and combining results provides some solution to this problem. For this purpose, the mixture of uniform priors approach is especially suitable, because it comprises a wide and flexible family of distributions and computationally intensive estimation can be carried out in a reasonable amount of time.

Statistical analysis of genomic data

In this chapter we describe methods for statistical analysis of GWAS data with the goal of quantifying evidence for genomic effects associated with trait variation, while avoiding spurious associations due to evidence not being well quantified or due to population structure.Single marker analysis and imputation are discussed in Sect. 1, and a Bayesian multi-locus analysis using the BayesQTLBIC R package (1, 2) is described in Sect. 2. The multi-locus analysis, applied in a genomic window, enables local inference of the QTL genetic architecture and is an alternative to imputation. Multi-locus analysis with BayesQTLBIC, including calculation of posterior probabilities for alternative models, posterior probabilities for number of QTL, marginal probabilities for markers, and Bayes factors for individual chromosomes, is demonstrated for simulated QTL data. Methods for correcting the population structure and the possible effects of population structure on power are discussed in Sect. 3. Section 4 considers analysis combining information from linkage and linkage disequilibrium when sampling from a pedigree. Section 5 considers combining information from two different studies-showing that data from an existing QTL mapping family can be profitably used in combination with an association study-prior odds are higher for candidate genes mapping into a QTL region in the QTL mapping family, and, optionally, the number of markers genotyped in an association study can be reduced. Examples using R and the R packages BayesQTLBIC, ncdf are given.

Designing a GWAS: power, sample size, and data structure

In this chapter we describe a novel Bayesian approach to designing GWAS studies with the goal of ensuring robust detection of effects of genomic loci associated with trait variation.The goal of GWAS is to detect loci associated with variation in traits of interest. Finding which of 500,000-1,000,000 loci has a practically significant effect is a difficult statistical problem, like finding a needle in a haystack. We address this problem by designing experiments to detect effects with a given Bayes factor, where the Bayes factor is chosen sufficiently large to overcome the low prior odds for genomic associations. Methods are given for various possible data structures including random population samples, case-control designs, transmission disequilibrium tests, sib-based transmission disequilibrium tests, and other family-based designs including designs for plants with clonal replication. We also consider the problem of eliciting prior information from experts, which is necessary to quantify prior odds for loci. We advocate a "subjective" Bayesian approach, where the prior distribution is considered as a mathematical representation of our prior knowledge, while also giving generic formulae that allow conservative computations based on low prior information, e.g., equivalent to the information in a single sample point. Examples using R and the R packages ldDesign are given throughout.

Experimental designs for robust detection of effects in genome-wide case-control studies

In genome-wide association studies hundreds of thousands of loci are scanned in thousands of cases and controls, with the goal of identifying genomic loci underpinning disease. This is a challenging statistical problem requiring strong evidence. Only a small proportion of the heritability of common diseases has so far been explained. This "dark matter of the genome" is a subject of much discussion. It is critical to have experimental design criteria that ensure that associations between genomic loci and phenotypes are robustly detected. To ensure associations are robustly detected we require good power (e.g., 0.8) and sufficiently strong evidence [i.e., a high Bayes factor (e.g., 10(6), meaning the data are 1 million times more likely if the association is real than if there is no association)] to overcome the low prior odds for any given marker in a genome scan to be associated with a causal locus. Power calculations are given for determining the sample sizes necessary to detect effects with the required power and Bayes factor for biallelic markers in linkage disequilibrium with causal loci in additive, dominant, and recessive genetic models. Significantly stronger evidence and larger sample sizes are required than indicated by traditional hypothesis tests and power calculations. Many reported putative effects are not robustly detected and many effects including some large moderately low-frequency effects may remain undetected. These results may explain the dark matter in the genome. The power calculations have been implemented in R and will be available in the R package ldDesign.

Genetic analysis of complex traits via Bayesian variable selection: the utility of a mixture of uniform priors

A new estimation-based Bayesian variable selection approach is presented for genetic analysis of complex traits based on linear or logistic regression. By assigning a mixture of uniform priors (MU) to genetic effects, the approach provides an intuitive way of specifying hyperparameters controlling the selection of multiple influential loci. It aims at avoiding the difficulty of interpreting assumptions made in the specifications of priors. The method is compared in two real datasets with two other approaches, stochastic search variable selection (SSVS) and a re-formulation of Bayes B utilizing indicator variables and adaptive Student's t-distributions (IAt). The Markov Chain Monte Carlo (MCMC) sampling performance of the three methods is evaluated using the publicly available software OpenBUGS (model scripts are provided in the Supplementary material). The sensitivity of MU to the specification of hyperparameters is assessed in one of the data examples.

Genetic architecture of plasma adiponectin overlaps with the genetics of metabolic syndrome-related traits

OBJECTIVE

Adiponectin, a hormone secreted by adipose tissue, is of particular interest in metabolic syndrome, because it is inversely correlated with obesity and insulin sensitivity. However, it is not known to what extent the genetics of plasma adiponectin and the genetics of obesity and insulin sensitivity are interrelated. We aimed to evaluate the heritability of plasma adiponectin and its genetic correlation with the metabolic syndrome and metabolic syndrome-related traits and the association between these traits and 10 ADIPOQ single nucleotide polymorphisms (SNPs).

RESEARCH DESIGN AND METHODS

We made use of a family-based population, the Erasmus Rucphen Family study (1,258 women and 967 men). Heritability analysis was performed using a polygenic model. Genetic correlations were estimated using bivariate heritability analyses. Genetic association analysis was performed using a mixed model.

RESULTS

Plasma adiponectin showed a heritability of 55.1%. Genetic correlations between plasma adiponectin HDL cholesterol and plasma insulin ranged from 15 to 24% but were not significant for fasting glucose, triglycerides, blood pressure, homeostasis model assessment of insulin resistance (HOMA-IR), and C-reactive protein. A significant association with plasma adiponectin was found for ADIPOQ variants rs17300539 and rs182052. A nominally significant association was found with plasma insulin and HOMA-IR and ADIPOQ variant rs17300539 after adjustment for plasma adiponectin.

CONCLUSIONS

The significant genetic correlation between plasma adiponectin and HDL cholesterol and plasma insulin should be taken into account in the interpretation of genome-wide association studies. Association of ADIPOQ SNPs with plasma adiponectin was replicated, and we showed association between one ADIPOQ SNP and plasma insulin and HOMA-IR.

Understanding the use of Bayes factor for testing candidate genes

After quantitative trait loci (QTL) detection, one of the main objectives of research is to identify the causal mutation explaining phenotypic differences. Candidate genes are usually selected according to the physiological mechanism of the trait and their location within the same region of the QTL. After detection of any polymorphism at the candidate gene sequence, it is important to determine whether the detected mutation is the one that causes the phenotypic variation. This is not, however, an easy task, because of the linkage disequilibrium between the genes located in the same region. Several methods have been proposed that consider the neutral marker information in validating the involvement of candidate genes. However, some statistical information may be lost because of the presence of both the QTL and candidate gene effects in the model of analysis. Here, the Bayes factor is suggested as an alternative and a procedure for its calculation between candidate gene and QTL models is presented. The procedure is illustrated with a simulation study and with an example consisting of three SNPs detected at the leptin receptor (LEPR) in an experimental intercross between Iberian and Landrace pigs. The results indicate that the Bayes factor procedure is more powerful than the classical approach.

Quantification of variation in expression networks

Gene expression microarrays allow rapid and easy quantification of transcript accumulation for almost transcripts present in a genome. This technology has been utilized for diverse investigations from studying gene regulation in response to genetic or environmental fluctuation to global expression QTL (eQTL) analyses of natural variation. Typical analysis techniques focus on responses of individual genes in isolation of other genes. However, emerging evidence indicates that genes are organized into regulons, i.e., they respond as groups due to individual transcription factors binding multiple promoters, creating what is commonly called a network. We have developed a set of statistical approaches that allow researchers to test specific network hypothesis using a priori-defined gene networks. When applied to Arabidopsis thaliana this approach has been able to identify natural genetic variation that controls networks. In this chapter we describe approaches to develop and test specific network hypothesis utilizing natural genetic variation. This approach can be expanded to facilitate direct tests of the relationship between phenotypic trait and transcript genetic architecture. Finally, the use of a priori network definitions can be applied to any microarray experiment to directly conduct hypothesis testing at a genomics level.

Mapping in structured populations by resample model averaging

Highly recombinant populations derived from inbred lines, such as advanced intercross lines and heterogeneous stocks, can be used to map loci far more accurately than is possible with standard intercrosses. However, the varying degrees of relatedness that exist between individuals complicate analysis, potentially leading to many false positive signals. We describe a method to deal with these problems that does not require pedigree information and accounts for model uncertainty through model averaging. In our method, we select multiple quantitative trait loci (QTL) models using forward selection applied to resampled data sets obtained by nonparametric bootstrapping and subsampling. We provide model-averaged statistics about the probability of loci or of multilocus regions being included in model selection, and this leads to more accurate identification of QTL than by single-locus mapping. The generality of our approach means it can potentially be applied to any population of unknown structure.