High-dimensional Omics Data Research Articles

Relationship between gene regulation network structure and prediction accuracy in high dimensional regression

The least absolute shrinkage and selection operator (lasso) and principal component regression (PCR) are popular methods of estimating traits from high-dimensional omics data, such as transcriptomes. The prediction accuracy of these estimation methods is highly dependent on the covariance structure, which is characterized by gene regulation networks. However, the manner in which the structure of a gene regulation network together with the sample size affects prediction accuracy has not yet been sufficiently investigated. In this study, Monte Carlo simulations are conducted to investigate the prediction accuracy for several network structures under various sample sizes. When the gene regulation network is a random graph, a sufficiently large number of observations are required to ensure good prediction accuracy with the lasso. The PCR provided poor prediction accuracy regardless of the sample size. However, a real gene regulation network is likely to exhibit a scale-free structure. In such cases, the simulation indicates that a relatively small number of observations, such as N=300, is sufficient to allow the accurate prediction of traits from a transcriptome with the lasso.

Machine learning for precision medicine forecasts and challenges when incorporating non omics and omics data

Precision Medicine has emerged as a preventive, diagnostic and treatment tool to approach human diseases in a personalized manner. Since precision medicine incorporates omics data and knowledge in personal health records, people who live in industrially polluted areas have an advantage in the medicinal field. Integration of non-omics data and related biological knowledge in term omics data is a reality. The heterogenic characteristics of non-omics data and high dimensional omics data makes the integration challengeable. Hard data analytics problems create better opportunities in analytics. This review cut across the boundaries of machine learning models for the eventual development of a successful precision medicine forecast model, different strategies for the integration of non-omics data and omics data, limitations and challenges in data integration, and future directions for the precision medicine forecasts. The literature also discusses non-omics data, diseases associated with air pollutants, and omics data. This information gives insight to the integrated data analytics and their application in future project implications. It intends to motivate researchers and precision medicine forecast model developers in a global integrative analytical approach.

Correspondence-Aware Manifold Learning for Microscopic and Spatial Omics Imaging: A Novel Data Fusion Method Bringing Mass Spectrometry Imaging to a Cellular Resolution.

High-dimensional molecular measurements are transforming the field of pathology into a data-driven discipline. While hematoxylin and eosin (H&E) stainings are still the gold standard to diagnose diseases, the integration of microscopic and molecular information is becoming crucial to advance our understanding of tissue heterogeneity. To this end, we propose a data fusion method that integrates spatial omics and microscopic data obtained from the same tissue slide. Through correspondence-aware manifold learning, we can visualize the biological trends observed in the high-dimensional omics data at microscopic resolution. While data fusion enables the detection of elements that would not be detected taking into account the separate data modalities individually, out-of-sample prediction makes it possible to predict molecular trends outside of the measured tissue area. The proposed dimensionality reduction-based data fusion paradigm will therefore be helpful in deciphering molecular heterogeneity by bringing molecular measurements such as mass spectrometry imaging (MSI) to the cellular resolution.

Cancer classification based on chromatin accessibility profiles with deep adversarial learning model.

Given the complexity and diversity of the cancer genomics profiles, it is challenging to identify distinct clusters from different cancer types. Numerous analyses have been conducted for this propose. Still, the methods they used always do not directly support the high-dimensional omics data across the whole genome (Such as ATAC-seq profiles). In this study, based on the deep adversarial learning, we present an end-to-end approach ClusterATAC to leverage high-dimensional features and explore the classification results. On the ATAC-seq dataset and RNA-seq dataset, ClusterATAC has achieved excellent performance. Since ATAC-seq data plays a crucial role in the study of the effects of non-coding regions on the molecular classification of cancers, we explore the clustering solution obtained by ClusterATAC on the pan-cancer ATAC dataset. In this solution, more than 70% of the clustering are single-tumor-type-dominant, and the vast majority of the remaining clusters are associated with similar tumor types. We explore the representative non-coding loci and their linked genes of each cluster and verify some results by the literature search. These results suggest that a large number of non-coding loci affect the development and progression of cancer through its linked genes, which can potentially advance cancer diagnosis and therapy.

A systems biology approach to discovering pathway signaling dysregulation in metastasis.

Total metastatic burden is the primary cause of death for many cancer patients. While the process of metastasis has been studied widely, much remains to be understood. Moreover, few agents have been developed that specifically target the major steps of the metastatic cascade. Many individual genes and pathways have been implicated in metastasis but a holistic view of how these interact and cooperate to regulate and execute the process remains somewhat rudimentary. It is unclear whether all of the signaling features that regulate and execute metastasis are yet fully understood. Novel features of a complex system such as metastasis can often be discovered by taking a systems-based approach. We introduce the concepts of systems modeling and define some of the central challenges facing the application of a multidisciplinary systems-based approach to understanding metastasis and finding actionable targets therein. These challenges include appreciating the unique properties of the high-dimensional omics data often used for modeling, limitations in knowledge of the system (metastasis), tumor heterogeneity and sampling bias, and some of the issues key to understanding critical features of molecular signaling in the context of metastasis. We also provide a brief introduction to integrative modeling that focuses on both the nodes and edges of molecular signaling networks. Finally, we offer some observations on future directions as they relate to developing a systems-based model of the metastatic cascade.

Structured sparsity regularization for analyzing high-dimensional omics data.

The development of new molecular and cell technologies is having a significant impact on the quantity of data generated nowadays. The growth of omics databases is creating a considerable potential for knowledge discovery and, concomitantly, is bringing new challenges to statistical learning and computational biology for health applications. Indeed, the high dimensionality of these data may hamper the use of traditional regression methods and parameter estimation algorithms due to the intrinsic non-identifiability of the inherent optimization problem. Regularized optimization has been rising as a promising and useful strategy to solve these ill-posed problems by imposing additional constraints in the solution parameter space. In particular, the field of statistical learning with sparsity has been significantly contributing to building accurate models that also bring interpretability to biological observations and phenomena. Beyond the now-classic elastic net, one of the best-known methods that combine lasso with ridge penalizations, we briefly overview recent literature on structured regularizers and penalty functions that have been applied in biomedical data to build parsimonious models in a variety of underlying contexts, from survival to generalized linear models. These methods include functions of $\ell _k$-norms and network-based penalties that take into account the inherent relationships between the features. The successful application to omics data illustrates the potential of sparse structured regularization for identifying disease's molecular signatures and for creating high-performance clinical decision support systems towards more personalized healthcare. Supplementary information: Supplementary data are available at Briefings in Bioinformatics online.

Single-center versus multi-center data sets for molecular prognostic modeling: a simulation study

BackgroundPrognostic models based on high-dimensional omics data generated from clinical patient samples, such as tumor tissues or biopsies, are increasingly used for prognosis of radio-therapeutic success. The model development process requires two independent discovery and validation data sets. Each of them may contain samples collected in a single center or a collection of samples from multiple centers. Multi-center data tend to be more heterogeneous than single-center data but are less affected by potential site-specific biases. Optimal use of limited data resources for discovery and validation with respect to the expected success of a study requires dispassionate, objective decision-making. In this work, we addressed the impact of the choice of single-center and multi-center data as discovery and validation data sets, and assessed how this impact depends on the three data characteristics signal strength, number of informative features and sample size.MethodsWe set up a simulation study to quantify the predictive performance of a model trained and validated on different combinations of in silico single-center and multi-center data. The standard bioinformatical analysis workflow of batch correction, feature selection and parameter estimation was emulated. For the determination of model quality, four measures were used: false discovery rate, prediction error, chance of successful validation (significant correlation of predicted and true validation data outcome) and model calibration.ResultsIn agreement with literature about generalizability of signatures, prognostic models fitted to multi-center data consistently outperformed their single-center counterparts when the prediction error was the quality criterion of interest. However, for low signal strengths and small sample sizes, single-center discovery sets showed superior performance with respect to false discovery rate and chance of successful validation.ConclusionsWith regard to decision making, this simulation study underlines the importance of study aims being defined precisely a priori. Minimization of the prediction error requires multi-center discovery data, whereas single-center data are preferable with respect to false discovery rate and chance of successful validation when the expected signal or sample size is low. In contrast, the choice of validation data solely affects the quality of the estimator of the prediction error, which was more precise on multi-center validation data.

Multiset sparse partial least squares path modeling for high dimensional omics data analysis

BackgroundRecent technological developments have enabled the measurement of a plethora of biomolecular data from various omics domains, and research is ongoing on statistical methods to leverage these omics data to better model and understand biological pathways and genetic architectures of complex phenotypes. Current reviews report that the simultaneous analysis of multiple (i.e. three or more) high dimensional omics data sources is still challenging and suitable statistical methods are unavailable. Often mentioned challenges are the lack of accounting for the hierarchical structure between omics domains and the difficulty of interpretation of genomewide results. This study is motivated to address these challenges. We propose multiset sparse Partial Least Squares path modeling (msPLS), a generalized penalized form of Partial Least Squares path modeling, for the simultaneous modeling of biological pathways across multiple omics domains. msPLS simultaneously models the effect of multiple molecular markers, from multiple omics domains, on the variation of multiple phenotypic variables, while accounting for the relationships between data sources, and provides sparse results. The sparsity in the model helps to provide interpretable results from analyses of hundreds of thousands of biomolecular variables.ResultsWith simulation studies, we quantified the ability of msPLS to discover associated variables among high dimensional data sources. Furthermore, we analysed high dimensional omics datasets to explore biological pathways associated with Marfan syndrome and with Chronic Lymphocytic Leukaemia. Additionally, we compared the results of msPLS to the results of Multi-Omics Factor Analysis (MOFA), which is an alternative method to analyse this type of data.ConclusionsmsPLS is an multiset multivariate method for the integrative analysis of multiple high dimensional omics data sources. It accounts for the relationship between multiple high dimensional data sources while it provides interpretable results through its sparse solutions. The biomarkers found by msPLS in the omics datasets can be interpreted in terms of biological pathways associated with the pathophysiology of Marfan syndrome and of Chronic Lymphocytic Leukaemia. Additionally, msPLS outperforms MOFA in terms of variation explained in the chronic lymphocytic leukaemia dataset while it identifies the two most important clinical markers for Chronic Lymphocytic LeukaemiaAvailabilityhttp://uva.csala.me/mspls.https://github.com/acsala/2018_msPLS

Multi-kernel linear mixed model with adaptive lasso for prediction analysis on high-dimensional multi-omics data.

The use of human genome discoveries and other established factors to build an accurate risk prediction model is an essential step toward precision medicine. While multi-layer high-dimensional omics data provide unprecedented data resources for prediction studies, their corresponding analytical methods are much less developed. We present a multi-kernel penalized linear mixed model with adaptive lasso (MKpLMM), a predictive modeling framework that extends the standard linear mixed models widely used in genomic risk prediction, for multi-omics data analysis. MKpLMM can capture not only the predictive effects from each layer of omics data but also their interactions via using multiple kernel functions. It adopts a data-driven approach to select predictive regions as well as predictive layers of omics data, and achieves robust selection performance. Through extensive simulation studies, the analyses of PET-imaging outcomes from the Alzheimer's Disease Neuroimaging Initiative study, and the analyses of 64 drug responses, we demonstrate that MKpLMM consistently outperforms competing methods in phenotype prediction. The R-package is available at https://github.com/YaluWen/OmicPred. Supplementary data are available at Bioinformatics online.

Integration of Machine Learning Methods to Dissect Genetically Imputed Transcriptomic Profiles in Alzheimer's Disease.

The genetic component of many common traits is associated with the gene expression and several variants act as expression quantitative loci, regulating the gene expression in a tissue specific manner. In this work, we applied tissue-specific cis-eQTL gene expression prediction models on the genotype of 808 samples including controls, subjects with mild cognitive impairment, and patients with Alzheimer's Disease. We then dissected the imputed transcriptomic profiles by means of different unsupervised and supervised machine learning approaches to identify potential biological associations. Our analysis suggests that unsupervised and supervised methods can provide complementary information, which can be integrated for a better characterization of the underlying biological system. In particular, a variational autoencoder representation of the transcriptomic profiles, followed by a support vector machine classification, has been used for tissue-specific gene prioritizations. Interestingly, the achieved gene prioritizations can be efficiently integrated as a feature selection step for improving the accuracy of deep learning classifier networks. The identified gene-tissue information suggests a potential role for inflammatory and regulatory processes in gut-brain axis related tissues. In line with the expected low heritability that can be apportioned to eQTL variants, we were able to achieve only relatively low prediction capability with deep learning classification models. However, our analysis revealed that the classification power strongly depends on the network structure, with recurrent neural networks being the best performing network class. Interestingly, cross-tissue analysis suggests a potentially greater role of models trained in brain tissues also by considering dementia-related endophenotypes. Overall, the present analysis suggests that the combination of supervised and unsupervised machine learning techniques can be used for the evaluation of high dimensional omics data.

Large-Scale Automatic Feature Selection for Biomarker Discovery in High-Dimensional OMICs Data

The identification of biomarker signatures in omics molecular profiling is usually performed to predict outcomes in a precision medicine context, such as patient disease susceptibility, diagnosis, prognosis, and treatment response. To identify these signatures, we have developed a biomarker discovery tool, called BioDiscML. From a collection of samples and their associated characteristics, i.e., the biomarkers (e.g., gene expression, protein levels, clinico-pathological data), BioDiscML exploits various feature selection procedures to produce signatures associated to machine learning models that will predict efficiently a specified outcome. To this purpose, BioDiscML uses a large variety of machine learning algorithms to select the best combination of biomarkers for predicting categorical or continuous outcomes from highly unbalanced datasets. The software has been implemented to automate all machine learning steps, including data pre-processing, feature selection, model selection, and performance evaluation. BioDiscML is delivered as a stand-alone program and is available for download at https://github.com/mickaelleclercq/BioDiscML.

Abstract P1-06-07: Characterization of chromosomal instability in the TNT trial: A randomized phase III trial of carboplatin compared with docetaxel for patients with metastatic or recurrent locally advanced triple negative or BRCA1/2 breast cancer (CRUK/07/012)

Abstract Background A distinctive trait of triple negative breast cancer (TNBC) is the acquisition of genome wide highly aberrant copy number states, which is more evident in metastatic settings. The level of copy number alterations can be characterized by quantitative estimates of chromosomal instability, such as allelic imbalanced copy number aberrations, telomeric allelic imbalance (NtAI), homologous recombination deficiency (HRD) score, referred here as genomic scars. Several of these scars are reported as being indicative of BRCAness and potential predictive and/or prognostic biomarkers of chemotherapy response, currently mostly demonstrated in neoadjuvant settings in TNBC. Aims Using several genomic scar measures, we aim to capture chromosomal instability and test their predictive and prognostic value in metastatic or recurrent locally advanced triple negative or BRCA1/2 mutated breast cancer in the TNT trial. Methods Patients recruited to TNT (n=376) had ER-/PR-/Her2- breast cancer or were germline BRCA mutation carriers. Genome-wide copy numbers (CN) were derived from FFPE samples including primary tumours and positive lymph nodes (n=183, docetaxel=93, carboplatin=90; BRCA1 mut=25). Genomic scars were generated using ASCAT (Van loo et al., PNAS 2010) CN profiles. HRD scores were established by Myriad Genetics, Inc. assay (n=272). BRCA1-like classifier was applied as described in Schouten et al., Mol Onc 2015. Shannon diversity index was calculated using ASCAT raw CN profiles. Association of genomic scars with PAM50 subtypes and BRCA1 deficiency status were evaluated using Kruskal-Wallis test; p-values were adjusted for multiple comparisons (Dunn's test). Statistical significance was defined as p<0.05. Association of genomic scars with objective tumour response rate (ORR) and Progression Free Survival (PFS) was assessed using logistic regression and restricted mean survival analysis, respectively. Results HRD and NtAI scores were higher in basal like samples compared to non-basal like (median diff. HRD=11.5, p=0.005; NtAI=3, p=0.04). HRD (p=2e-14) and NtAI (p=0.003) scores were also higher in BRCA1 deficient (BRCA1 germline/somatic mutant or BRCA1 methylated) samples compared to non-deficient. Using the BRCA1-like classifier, 42 out of 50 BRCA1 deficient samples and 93 out of 133 BRCA1 non-deficient/undetermined samples were identified as BRCA1-like. The Shannon diversity index, measuring CN heterogeneity, clustered samples into 3 groups. Analysis of ORR showed non-significant trends to preferential response rates with docetaxel in cluster 1 and 3. Membership of cluster 2 predicted higher ORR to carboplatin over docetaxel (interaction p=0.017). PFS indicated a treatment effect in cluster 2, but not in cluster 1 or 3; there was no evidence of interaction between subgroups and treatment (p=0.15). Conclusions Our results suggest that the overall heterogeneity of the copy number landscape is a promising area for seeking predictive/prognostic biomarkers in metastatic TNBC, and combined with other modalities of high-dimensional omics data could provide essential treatment response information. Citation Format: Sipos O, Tovey H, Quist J, Haider S, Nowinski S, Gazinska P, Kernaghan S, Toms C, Timms KM, Lanchbury JS, Linn SC, Pinder SE, Bliss JM, Tutt A, Cheang MC, Grigoriadis A, On behalf of the TNT Trial Management Group and Investigators. Characterization of chromosomal instability in the TNT trial: A randomized phase III trial of carboplatin compared with docetaxel for patients with metastatic or recurrent locally advanced triple negative or BRCA1/2 breast cancer (CRUK/07/012) [abstract]. In: Proceedings of the 2018 San Antonio Breast Cancer Symposium; 2018 Dec 4-8; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2019;79(4 Suppl):Abstract nr P1-06-07.

Bayesian variable selection for parametric survival model with applications to cancer omics data

BackgroundModeling thousands of markers simultaneously has been of great interest in testing association between genetic biomarkers and disease or disease-related quantitative traits. Recently, an expectation-maximization (EM) approach to Bayesian variable selection (EMVS) facilitating the Bayesian computation was developed for continuous or binary outcome using a fast EM algorithm. However, it is not suitable to the analyses of time-to-event outcome in many public databases such as The Cancer Genome Atlas (TCGA).ResultsWe extended the EMVS to high-dimensional parametric survival regression framework (SurvEMVS). A variant of cyclic coordinate descent (CCD) algorithm was used for efficient iteration in M-step, and the extended Bayesian information criteria (EBIC) was employed to make choice on hyperparameter tuning. We evaluated the performance of SurvEMVS using numeric simulations and illustrated the effectiveness on two real datasets. The results of numerical simulations and two real data analyses show the well performance of SurvEMVS in aspects of accuracy and computation. Some potential markers associated with survival of lung or stomach cancer were identified.ConclusionsThese results suggest that our model is effective and can cope with high-dimensional omics data.

Priority-Lasso: a simple hierarchical approach to the prediction of clinical outcome using multi-omics data

BackgroundThe inclusion of high-dimensional omics data in prediction models has become a well-studied topic in the last decades. Although most of these methods do not account for possibly different types of variables in the set of covariates available in the same dataset, there are many such scenarios where the variables can be structured in blocks of different types, e.g., clinical, transcriptomic, and methylation data. To date, there exist a few computationally intensive approaches that make use of block structures of this kind.ResultsIn this paper we present priority-Lasso, an intuitive and practical analysis strategy for building prediction models based on Lasso that takes such block structures into account. It requires the definition of a priority order of blocks of data. Lasso models are calculated successively for every block and the fitted values of every step are included as an offset in the fit of the next step. We apply priority-Lasso in different settings on an acute myeloid leukemia (AML) dataset consisting of clinical variables, cytogenetics, gene mutations and expression variables, and compare its performance on an independent validation dataset to the performance of standard Lasso models.ConclusionThe results show that priority-Lasso is able to keep pace with Lasso in terms of prediction accuracy. Variables of blocks with higher priorities are favored over variables of blocks with lower priority, which results in easily usable and transportable models for clinical practice.

Using recursive feature elimination in random forest to account for correlated variables in high dimensional data

BackgroundRandom forest (RF) is a machine-learning method that generally works well with high-dimensional problems and allows for nonlinear relationships between predictors; however, the presence of correlated predictors has been shown to impact its ability to identify strong predictors. The Random Forest-Recursive Feature Elimination algorithm (RF-RFE) mitigates this problem in smaller data sets, but this approach has not been tested in high-dimensional omics data sets.ResultsWe integrated 202,919 genotypes and 153,422 methylation sites in 680 individuals, and compared the abilities of RF and RF-RFE to detect simulated causal associations, which included simulated genotype–methylation interactions, between these variables and triglyceride levels. Results show that RF was able to identify strong causal variables with a few highly correlated variables, but it did not detect other causal variables.ConclusionsAlthough RF-RFE decreased the importance of correlated variables, in the presence of many correlated variables, it also decreased the importance of causal variables, making both hard to detect. These findings suggest that RF-RFE may not scale to high-dimensional data.

Data mining and machine learning approaches for the integration of genome-wide association and methylation data: methodology and main conclusions from GAW20

BackgroundMultiple layers of genetic and epigenetic variability are being simultaneously explored in an increasing number of health studies. We summarize here different approaches applied in the Data Mining and Machine Learning group at the GAW20 to integrate genome-wide genotype and methylation array data.ResultsWe provide a non-intimidating introduction to some frequently used methods to investigate high-dimensional molecular data and compare the different approaches tried by group members: random forest, deep learning, cluster analysis, mixed models, and gene-set enrichment analysis. Group contributions were quite heterogeneous regarding investigated data sets (real vs simulated), conducted data quality control and assessed phenotypes (eg, metabolic syndrome vs relative differences of log-transformed triglyceride concentrations before and after fenofibrate treatment). However, some common technical issues were detected, leading to practical recommendations.ConclusionsDifferent sources of correlation were identified by group members, including population stratification, family structure, batch effects, linkage disequilibrium and correlation of methylation values at neighboring cytosine-phosphate-guanine (CpG) sites, and the majority of applied approaches were able to take into account identified correlation structures. The ability to efficiently deal with high-dimensional omics data, and the model free nature of the approaches that did not require detailed model specifications were clearly recognized as the main strengths of applied methods. A limitation of random forest is its sensitivity to highly correlated variables. The parameter setup and the interpretation of results from deep learning methods, in particular deep neural networks, can be extremely challenging. Cluster analysis and mixed models may need some predimension reduction based on existing literature, data filtering, and supplementary statistical methods, and gene-set enrichment analysis requires biological insight.

Penalized co-inertia analysis with applications to -omics data.

Co-inertia analysis (CIA) is a multivariate statistical analysis method that can assess relationships and trends in two sets of data. Recently CIA has been used for an integrative analysis of multiple high-dimensional omics data. However, for classical CIA, all elements in the loading vectors are nonzero, presenting a challenge for the interpretation when analyzing omics data. For other multivariate statistical methods such as canonical correlation analysis (CCA), penalized least squares (PLS), various approaches have been proposed to produce sparse loading vectors via l1-penalization/constraint. We propose a novel CIA method that uses l1-penalization to induce sparsity in estimators of loading vectors. Our method simultaneously conducts model fitting and variable selection. Also, we propose another CIA method that incorporates structure/network information such as those from functional genomics, besides using sparsity penalty so that one can get biologically meaningful and interpretable results. Extensive simulations demonstrate that our proposed penalized CIA methods achieve the best or close to the best performance compared to the existing CIA method in terms of feature selection and recovery of true loading vectors. Also, we apply our methods to the integrative analysis of gene expression data and protein abundance data from the NCI-60 cancer cell lines. Our analysis of the NCI-60 cancer cell line data reveals meaningful variables for cancer diseases and biologically meaningful results that are consistent with previous studies. Our algorithms are implemented as an R package which is freely available at: https://www.med.upenn.edu/long-lab/. Supplementary data are available at Bioinformatics online.

Accurate and fast feature selection workflow for high-dimensional omics data.

We are moving into the age of ‘Big Data’ in biomedical research and bioinformatics. This trend could be encapsulated in this simple formula: D = S * F, where the volume of data generated (D) increases in both dimensions: the number of samples (S) and the number of sample features (F). Frequently, a typical omics classification includes redundant and irrelevant features (e.g. genes or proteins) that can result in long computation times; decrease of the model performance and the selection of suboptimal features (genes and proteins) after the classification/regression step. Multiple algorithms and reviews has been published to describe all the existing methods for feature selection, their strengths and weakness. However, the selection of the correct FS algorithm and strategy constitutes an enormous challenge. Despite the number and diversity of algorithms available, the proper choice of an approach for facing a specific problem often falls in a ‘grey zone’. In this study, we select a subset of FS methods to develop an efficient workflow and an R package for bioinformatics machine learning problems. We cover relevant issues concerning FS, ranging from domain’s problems to algorithm solutions and computational tools. Finally, we use seven different proteomics and gene expression datasets to evaluate the workflow and guide the FS process.

Sparse redundancy analysis of high-dimensional genetic and genomic data.

Recent technological developments have enabled the possibility of genetic and genomic integrated data analysis approaches, where multiple omics datasets from various biological levels are combined and used to describe (disease) phenotypic variations. The main goal is to explain and ultimately predict phenotypic variations by understanding their genetic basis and the interaction of the associated genetic factors. Therefore, understanding the underlying genetic mechanisms of phenotypic variations is an ever increasing research interest in biomedical sciences. In many situations, we have a set of variables that can be considered to be the outcome variables and a set that can be considered to be explanatory variables. Redundancy analysis (RDA) is an analytic method to deal with this type of directionality. Unfortunately, current implementations of RDA cannot deal optimally with the high dimensionality of omics data (p≫n). The existing theoretical framework, based on Ridge penalization, is suboptimal, since it includes all variables in the analysis. As a solution, we propose to use Elastic Net penalization in an iterative RDA framework to obtain a sparse solution. We proposed sparse redundancy analysis (sRDA) for high dimensional omics data analysis. We conducted simulation studies with our software implementation of sRDA to assess the reliability of sRDA. Both the analysis of simulated data, and the analysis of 485 512 methylation markers and 18,424 gene-expression values measured in a set of 55 patients with Marfan syndrome show that sRDA is able to deal with the usual high dimensionality of omics data. http://uva.csala.me/rda. a.csala@amc.uva.nl. Supplementary data are available at Bioinformatics online.

Introduction to Bayesian variable selection methods in high-dimensional omics data analysis

With the rapid development of genome sequencing technology and bioinformatics in recent years, it has become possible to measure thousands of omics data which might be associated with the progress of diseases, i.e."high-dimensional data" . This type of omics data have a common feature that the number of variable p is usually greater than the observation cases n, and often has high correlation between independent variables. Therefore, it is a great statistical challenge to identify really meaningful variables from omics data. This paper summarizes the methods of Bayesian variable selection in the analysis of high-dimensional data.