Bayesian joint selection of genes and pathways: applications in multiple myeloma genomics

A Bayesian Hierarchical Framework for Pathway Analysis in Genome-Wide Association Studies

BACKGROUND

Pathway analysis allows joint consideration of multiple SNPs belonging to multiple genes, which in turn belong to a biologically defined pathway. This type of analysis is usually more powerful than single-SNP analyses for detecting joint effects of variants in a pathway.

METHODS

We develop a Bayesian hierarchical model by fully modeling the 3-level hierarchy, namely, SNP-gene-pathway that is naturally inherent in the structure of the pathways, unlike the currently used ad hoc ways of combining such information. We model the effects at each level conditional on the effects of the levels preceding them within the generalized linear model framework. To deal with the high dimensionality, we regularize the regression coefficients through an appropriate choice of priors. The model is fit using a combination of iteratively weighted least squares and expectation-maximization algorithms to estimate the posterior modes and their standard errors. A normal approximation is used for inference.

RESULTS

We conduct simulations to study the proposed method and find that our method has higher power than some standard approaches in several settings for identifying pathways with multiple modest-sized variants. We illustrate the method by analyzing data from two genome-wide association studies on breast and renal cancers.

CONCLUSION

Our method can be helpful in detecting pathway association.

Accounting for grouped predictor variables or pathways in high-dimensional penalized Cox regression models

BACKGROUND

The standard lasso penalty and its extensions are commonly used to develop a regularized regression model while selecting candidate predictor variables on a time-to-event outcome in high-dimensional data. However, these selection methods focus on a homogeneous set of variables and do not take into account the case of predictors belonging to functional groups; typically, genomic data can be grouped according to biological pathways or to different types of collected data. Another challenge is that the standard lasso penalisation is known to have a high false discovery rate.

RESULTS

We evaluated different penalizations in a Cox model to select grouped variables in order to further penalize variables that, in addition to having a low effect, belong to a group with a low overall effect; and to favor the selection of variables that, in addition to having a large effect, belong to a group with a large overall effect. We considered the case of prespecified and disjoint groups and proposed diverse weights for the adaptive lasso method. In particular we proposed the product Max Single Wald by Single Wald weighting (MSW*SW) which takes into account the information of the group to which it belongs and of this biomarker. Through simulations, we compared the selection and prediction ability of our approach with the standard lasso, the composite Minimax Concave Penalty (cMCP), the group exponential lasso (gel), the Integrative L1-Penalized Regression with Penalty Factors (IPF-Lasso), and the Sparse Group Lasso (SGL) methods. In addition, we illustrated the methods using gene expression data of 614 breast cancer patients.

CONCLUSIONS

The adaptive lasso with the MSW*SW weighting method incorporates both the information in the grouping structure and the individual variable. It outperformed the competitors by reducing the false discovery rate without severely increasing the false negative rate.

Structured Genome-Wide Association Studies with Bayesian Hierarchical Variable Selection

It becomes increasingly important in using genome-wide association studies (GWAS) to select important genetic information associated with qualitative or quantitative traits. Currently, the discovery of biological association among SNPs motivates various strategies to construct SNP-sets along the genome and to incorporate such set information into selection procedure for a higher selection power, while facilitating more biologically meaningful results. The aim of this paper is to propose a novel Bayesian framework for hierarchical variable selection at both SNP-set (group) level and SNP (within group) level. We overcome a key limitation of existing posterior updating scheme in most Bayesian variable selection methods by proposing a novel sampling scheme to explicitly accommodate the ultrahigh-dimensionality of genetic data. Specifically, by constructing an auxiliary variable selection model under SNP-set level, the new procedure utilizes the posterior samples of the auxiliary model to subsequently guide the posterior inference for the targeted hierarchical selection model. We apply the proposed method to a variety of simulation studies and show that our method is computationally efficient and achieves substantially better performance than competing approaches in both SNP-set and SNP selection. Applying the method to the Alzheimers Disease Neuroimaging Initiative (ADNI) data, we identify biologically meaningful genetic factors under several neuroimaging volumetric phenotypes. Our method is general and readily to be applied to a wide range of biomedical studies.

Overlapping group screening for detection of gene-gene interactions: application to gene expression profiles with survival trait

Background

The development of a disease is a complex process that may result from joint effects of multiple genes. In this article, we propose the overlapping group screening (OGS) approach to determining active genes and gene-gene interactions incorporating prior pathway information. The OGS method is developed to overcome the challenges in genome-wide data analysis that the number of the genes and gene-gene interactions is far greater than the sample size, and the pathways generally overlap with one another. The OGS method is further proposed for patients’ survival prediction based on gene expression data.

Results

Simulation studies demonstrate that the performance of the OGS approach in identifying the true main and interaction effects is good and the survival prediction accuracy of OGS with the Lasso penalty is better than the ordinary Lasso method. In real data analysis, we identify several significant genes and/or epistasis interactions that are associated with clinical survival outcomes of diffuse large B-cell lymphoma (DLBCL) and non-small-cell lung cancer (NSCLC) by utilizing prior pathway information from the KEGG pathway and the GO biological process databases, respectively.

Conclusions

The OGS approach is useful for selecting important genes and epistasis interactions in the ultra-high dimensional feature space. The prediction ability of OGS with the Lasso penalty is better than existing methods. The OGS approach is generally applicable to various types of outcome data (quantitative, qualitative, censored event time data) and regression models (e.g. linear, logistic, and Cox’s regression models).

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2372-2) contains supplementary material, which is available to authorized users.