A bayesian mixed regression based prediction of quantitative traits from molecular marker and gene expression data

Both molecular marker and gene expression data were considered alone as well as jointly to serve as additive predictors for two pathogen-activity-phenotypes in real recombinant inbred lines of soybean. For unobserved phenotype prediction, we used a bayesian hierarchical regression modeling, where the number of possible predictors in the model was controlled by different selection strategies tested. Our initial findings were submitted for DREAM5 (the 5th Dialogue on Reverse Engineering Assessment and Methods challenge) and were judged to be the best in sub-challenge B3 wherein both functional genomic and genetic data were used to predict the phenotypes. In this work we further improve upon this previous work by considering various predictor selection strategies and cross-validation was used to measure accuracy of in-data and out-data predictions. The results from various model choices indicate that for this data use of both data types (namely functional genomic and genetic) simultaneously improves out-data prediction accuracy. Adequate goodness-of-fit can be easily achieved with more complex models for both phenotypes, since the number of potential predictors is large and the sample size is not small. We also further studied gene-set enrichment (for continuous phenotype) in the biological process in question and chromosomal enrichment of the gene set. The methodological contribution of this paper is in exploration of variable selection techniques to alleviate the problem of over-fitting. Different strategies based on the nature of covariates were explored and all methods were implemented under the bayesian hierarchical modeling framework with indicator-based covariate selection. All the models based in careful variable selection procedure were found to produce significant results based on permutation test.     

Genetic markers applied in regression tree prediction models

Classification and regression tree (CART) modelling was used to determine infectious hypodermal and haematopoietic necrosis virus (IHHNV) resistance and susceptibility in Penaeus stylirostris. In a previous study, eight random amplified polymorphic DNA (RAPD) markers and viral load values using real-time quantitative PCR were obtained and used as the training data set in order to create numerous regression tree models. Specifically, the genetic markers were used as categorical predictor variables and viral load values as the dependent response variable. To determine which model has the highest predictive accuracy for future samples, RAPD fingerprint data was generated from new Penaues stylirostris IHHNV resistant and susceptible individuals and used to test the regression models. The best performing tree was a four terminal node tree with three genetic markers as significant variables. Marker-assisted breeding practices may benefit from the creation of regression tree models that apply genetic markers as predictive factors. To our knowledge this is the first study to use RAPD markers as predictors within a CART prediction model to determine viral susceptibility.     

Bias in random forest variable importance measures: Illustrations,sources and a solution

Background  

Variable importance measures for random forests have been receiving increased attention as a means of variable selection in many classification tasks in bioinformatics and related scientific fields, for instance to select a subset of genetic markers relevant for the prediction of a certain disease. We show that random forest variable importance measures are a sensible means for variable selection in many applications, but are not reliable in situations where potential predictor variables vary in their scale of measurement or their number of categories. This is particularly important in genomics and computational biology, where predictors often include variables of different types, for example when predictors include both sequence data and continuous variables such as folding energy, or when amino acid sequence data show different numbers of categories.     

Exploratory Bayesian model selection for serial genetics data

Characterizing the process by which molecular and cellular level changes occur over time will have broad implications for clinical decision making and help further our knowledge of disease etiology across many complex diseases. However, this presents an analytic challenge due to the large number of potentially relevant biomarkers and the complex, uncharacterized relationships among them. We propose an exploratory Bayesian model selection procedure that searches for model simplicity through independence testing of multiple discrete biomarkers measured over time. Bayes factor calculations are used to identify and compare models that are best supported by the data. For large model spaces, i.e., a large number of multi-leveled biomarkers, we propose a Markov chain Monte Carlo (MCMC) stochastic search algorithm for finding promising models. We apply our procedure to explore the extent to which HIV-1 genetic changes occur independently over time.     

Variable selection for discriminant analysis with Markov random field priors for the analysis of microarray data

MOTIVATION: Discriminant analysis is an effective tool for the classification of experimental units into groups. Here, we consider the typical problem of classifying subjects according to phenotypes via gene expression data and propose a method that incorporates variable selection into the inferential procedure, for the identification of the important biomarkers. To achieve this goal, we build upon a conjugate normal discriminant model, both linear and quadratic, and include a stochastic search variable selection procedure via an MCMC algorithm. Furthermore, we incorporate into the model prior information on the relationships among the genes as described by a gene-gene network. We use a Markov random field (MRF) prior to map the network connections among genes. Our prior model assumes that neighboring genes in the network are more likely to have a joint effect on the relevant biological processes. RESULTS: We use simulated data to assess performances of our method. In particular, we compare the MRF prior to a situation where independent Bernoulli priors are chosen for the individual predictors. We also illustrate the method on benchmark datasets for gene expression. Our simulation studies show that employing the MRF prior improves on selection accuracy. In real data applications, in addition to identifying markers and improving prediction accuracy, we show how the integration of existing biological knowledge into the prior model results in an increased ability to identify genes with strong discriminatory power and also aids the interpretation of the results.     

Sufficient dimension reduction via bayesian mixture modeling

Dimension reduction is central to an analysis of data with many predictors. Sufficient dimension reduction aims to identify the smallest possible number of linear combinations of the predictors, called the sufficient predictors, that retain all of the information in the predictors about the response distribution. In this article, we propose a Bayesian solution for sufficient dimension reduction. We directly model the response density in terms of the sufficient predictors using a finite mixture model. This approach is computationally efficient and offers a unified framework to handle categorical predictors, missing predictors, and Bayesian variable selection. We illustrate the method using both a simulation study and an analysis of an HIV data set.     

Bayesian variable selection for latent class models

In this article, we develop a latent class model with class probabilities that depend on subject-specific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection uncertainty. We propose a Bayesian variable selection approach and implement a stochastic search Gibbs sampler for posterior computation to obtain model-averaged estimates of quantities of interest such as marginal inclusion probabilities of predictors. Our methods are illustrated through simulation studies and application to data on weight gain during pregnancy, where it is of interest to identify important predictors of latent weight gain classes.     

Y-chromosomal Markers Suitable for Noninvasive Studies of Guenon Hybridization

We examine previously-published TSPY sequence data to identify synapomorphies useful for tracking Y-chromosomal gene flow between hybridizing guenon species. We then describe a set of PCR primers and protocols that amplify many of these variable sites from feces. Such Y-chromosomal markers are potentially very useful to conservation studies because they may offer an early sign of introgression as a threat to the genetic integrity of a rare species. Moreover, the ability to survey these markers from feces greatly expands the utility of noninvasive studies.     

Robust Bayesian variable selection for gene–environment interactions

Gene–environment (G× E) interactions have important implications to elucidate the etiology of complex diseases beyond the main genetic and environmental effects. Outliers and data contamination in disease phenotypes of G× E studies have been commonly encountered, leading to the development of a broad spectrum of robust regularization methods. Nevertheless, within the Bayesian framework, the issue has not been taken care of in existing studies. We develop a fully Bayesian robust variable selection method for G× E interaction studies. The proposed Bayesian method can effectively accommodate heavy-tailed errors and outliers in the response variable while conducting variable selection by accounting for structural sparsity. In particular, for the robust sparse group selection, the spike-and-slab priors have been imposed on both individual and group levels to identify important main and interaction effects robustly. An efficient Gibbs sampler has been developed to facilitate fast computation. Extensive simulation studies, analysis of diabetes data with single-nucleotide polymorphism measurements from the Nurses' Health Study, and The Cancer Genome Atlas melanoma data with gene expression measurements demonstrate the superior performance of the proposed method over multiple competing alternatives.     

Stochastic search variable selection for identifying multiple quantitative trait loci

In this article, we utilize stochastic search variable selection methodology to develop a Bayesian method for identifying multiple quantitative trait loci (QTL) for complex traits in experimental designs. The proposed procedure entails embedding multiple regression in a hierarchical normal mixture model, where latent indicators for all markers are used to identify the multiple markers. The markers with significant effects can be identified as those with higher posterior probability included in the model. A simple and easy-to-use Gibbs sampler is employed to generate samples from the joint posterior distribution of all unknowns including the latent indicators, genetic effects for all markers, and other model parameters. The proposed method was evaluated using simulated data and illustrated using a real data set. The results demonstrate that the proposed method works well under typical situations of most QTL studies in terms of number of markers and marker density.     

Data-Mining Discovery of Pattern and Process in Ecological Systems

ABSTRACT Most ecologists use statistical methods as their main analytical tools when analyzing data to identify relationships between a response and a set of predictors; thus, they treat all analyses as hypothesis tests or exercises in parameter estimation. However, little or no prior knowledge about a system can lead to creation of a statistical model or models that do not accurately describe major sources of variation in the response variable. We suggest that under such circumstances data mining is more appropriate for analysis. In this paper we 1) present the distinctions between data-mining (usually exploratory) analyses and parametric statistical (confirmatory) analyses, 2) illustrate 3 strengths of data-mining tools for generating hypotheses from data, and 3) suggest useful ways in which data mining and statistical analyses can be integrated into a thorough analysis of data to facilitate rapid creation of accurate models and to guide further research.     

Prediction of hybrid biomass in Arabidopsis thaliana by selected parental SNP and metabolic markers

A recombinant inbred line (RIL) population, derived from two Arabidopsis thaliana accessions, and the corresponding testcrosses with these two original accessions were used for the development and validation of machine learning models to predict the biomass of hybrids. Genetic and metabolic information of the RILs served as predictors. Feature selection reduced the number of variables (genetic and metabolic markers) in the models by more than 80% without impairing the predictive power. Thus, potential biomarkers have been revealed. Metabolites were shown to bear information on inherited macroscopic phenotypes. This proof of concept could be interesting for breeders. The example population exhibits substantial mid-parent biomass heterosis. The results of feature selection could therefore be used to shed light on the origin of heterosis. In this respect, mainly dominance effects were detected.     

An overview of techniques for linking high-dimensional molecular data to time-to-event endpoints by risk prediction models

Analysis of molecular data promises identification of biomarkers for improving prognostic models, thus potentially enabling better patient management. For identifying such biomarkers, risk prediction models can be employed that link high-dimensional molecular covariate data to a clinical endpoint. In low-dimensional settings, a multitude of statistical techniques already exists for building such models, e.g. allowing for variable selection or for quantifying the added value of a new biomarker. We provide an overview of techniques for regularized estimation that transfer this toward high-dimensional settings, with a focus on models for time-to-event endpoints. Techniques for incorporating specific covariate structure are discussed, as well as techniques for dealing with more complex endpoints. Employing gene expression data from patients with diffuse large B-cell lymphoma, some typical modeling issues from low-dimensional settings are illustrated in a high-dimensional application. First, the performance of classical stepwise regression is compared to stage-wise regression, as implemented by a component-wise likelihood-based boosting approach. A second issues arises, when artificially transforming the response into a binary variable. The effects of the resulting loss of efficiency and potential bias in a high-dimensional setting are illustrated, and a link to competing risks models is provided. Finally, we discuss conditions for adequately quantifying the added value of high-dimensional gene expression measurements, both at the stage of model fitting and when performing evaluation.     

Estimating predictors for long- or short-term survivors

Suppose that the response variable in a well-executed clinical or observational study to evaluate a treatment is the time to a certain event, and a set of baseline covariates or predictors was collected for each study patient. Furthermore, suppose that a significant number of study patients had nontrivial, long-term adverse effects from the treatment. A commonly posed question is how to use these covariates from the study to identify future patients who would (or would not) benefit from the treatment. In this article, we present "point" and "interval" estimates for the set of covariate or predictor vectors associated with a specific patient survival status, e.g., long- (or short-) term survival, in the presence of censoring. These estimates can be easily displayed on a two-dimensional plane, even for the case with high-dimensional covariate vectors. These simple numerical and graphical procedures provide useful information for patient management and/or the design of future studies, which are key issues in pharmacogenomics with genetic markers. The new proposal is illustrated with a data set from a cancer study for treating multiple myeloma.     

The chronic fatigue syndrome: a comparative pathway analysis.

In this paper, we introduce a method to detect pathological pathways of a disease. We aim to identify biological processes rather than single genes affected by the chronic fatigue syndrome (CFS). So far, CFS has neither diagnostic clinical signals nor abnormalities that could be diagnosed by laboratory examinations. It is also unclear if the CFS represents one disease or can be subdivided in different categories. We use information from clinical trials, the gene ontology (GO) database as well as gene expression data to identify undirected dependency graphs (UDGs) representing biological processes according to the GO database. The structural comparison of UDGs of sick versus non-sick patients allows us to make predictions about the modification of pathways due to pathogenesis.     

Combining multiple biomarker models in logistic regression

Summary .   In medical research, there is great interest in developing methods for combining biomarkers. We argue that selection of markers should also be considered in the process. Traditional model/variable selection procedures ignore the underlying uncertainty after model selection. In this work, we propose a novel model-combining algorithm for classification in biomarker studies. It works by considering weighted combinations of various logistic regression models; five different weighting schemes are considered in the article. The weights and algorithm are justified using decision theory and risk-bound results. Simulation studies are performed to assess the finite-sample properties of the proposed model-combining method. It is illustrated with an application to data from an immunohistochemical study in prostate cancer.     

Mining mass spectra for diagnosis and biomarker discovery of cerebral accidents

In this paper we try to identify potential biomarkers for early stroke diagnosis using surface-enhanced laser desorption/ionization mass spectrometry coupled with analysis tools from machine learning and data mining. Data consist of 42 specimen samples, i.e., mass spectra divided in two big categories, stroke and control specimens. Among the stroke specimens two further categories exist that correspond to ischemic and hemorrhagic stroke; in this paper we limit our data analysis to discriminating between control and stroke specimens. We performed two suites of experiments. In the first one we simply applied a number of different machine learning algorithms; in the second one we have chosen the best performing algorithm as it was determined from the first phase and coupled it with a number of different feature selection methods. The reason for this was 2-fold, first to establish whether feature selection can indeed improve performance, which in our case it did not seem to confirm, but more importantly to acquire a small list of potentially interesting biomarkers. Of the different methods explored the most promising one was support vector machines which gave us high levels of sensitivity and specificity. Finally, by analyzing the models constructed by support vector machines we produced a small set of 13 features that could be used as potential biomarkers, and which exhibited good performance both in terms of sensitivity, specificity and model stability.