Variable Selection Accuracy Research Articles

Network-guided regression for detecting associations between DNA methylation and gene expression.

High-throughput profiling in biological research has resulted in the availability of a wealth of data cataloguing the genetic, epigenetic and transcriptional states of cells. These data could yield discoveries that may lead to breakthroughs in the diagnosis and treatment of human disease, but require statistical methods designed to find the most relevant patterns from millions of potential interactions. Aberrant DNA methylation is often a feature of cancer, and has been proposed as a therapeutic target. However, the relationship between DNA methylation and gene expression remains poorly understood. We propose Network-sparse Reduced-Rank Regression (NsRRR), a multivariate regression framework capable of using prior biological knowledge expressed as gene interaction networks to guide the search for associations between gene expression and DNA methylation signatures. We use simulations to show the advantage of our proposed model in terms of variable selection accuracy over alternative models that do not use prior network information. We discuss an application of NsRRR to The Cancer Genome Atlas datasets on primary ovarian tumours. R code implementing the NsRRR model is available at http://www2.imperial.ac.uk/∼gmontana giovanni.montana@kcl.ac.uk Supplementary data are available at Bioinformatics online.

NETWORK-REGULARIZED HIGH-DIMENSIONAL COX REGRESSION FOR ANALYSIS OF GENOMIC DATA.

We consider estimation and variable selection in high-dimensional Cox regression when a prior knowledge of the relationships among the covariates, described by a network or graph, is available. A limitation of the existing methodology for survival analysis with high-dimensional genomic data is that a wealth of structural information about many biological processes, such as regulatory networks and pathways, has often been ignored. In order to incorporate such prior network information into the analysis of genomic data, we propose a network-based regularization method for high-dimensional Cox regression; it uses an ℓ1-penalty to induce sparsity of the regression coefficients and a quadratic Laplacian penalty to encourage smoothness between the coefficients of neighboring variables on a given network. The proposed method is implemented by an efficient coordinate descent algorithm. In the setting where the dimensionality p can grow exponentially fast with the sample size n, we establish model selection consistency and estimation bounds for the proposed estimators. The theoretical results provide insights into the gain from taking into account the network structural information. Extensive simulation studies indicate that our method outperforms Lasso and elastic net in terms of variable selection accuracy and stability. We apply our method to a breast cancer gene expression study and identify several biologically plausible subnetworks and pathways that are associated with breast cancer distant metastasis.

An efficient Monte Carlo EM algorithm for Bayesian lasso

The lasso is a popular technique of simultaneous estimation and variable selection in many research areas. The marginal posterior mode of the regression coefficients is equivalent to estimates given by the non-Bayesian lasso when the regression coefficients have independent Laplace priors. Because of its flexibility of statistical inferences, the Bayesian approach is attracting a growing body of research in recent years. Current approaches are primarily to either do a fully Bayesian analysis using Markov chain Monte Carlo (MCMC) algorithm or use Monte Carlo expectation maximization (MCEM) methods with an MCMC algorithm in each E-step. However, MCMC-based Bayesian method has much computational burden and slow convergence. Tan et al. [An efficient MCEM algorithm for fitting generalized linear mixed models for correlated binary data. J Stat Comput Simul. 2007;77:929–943] proposed a non-iterative sampling approach, the inverse Bayes formula (IBF) sampler, for computing posteriors of a hierarchical model in the structure of MCEM. Motivated by their paper, we develop this IBF sampler in the structure of MCEM to give the marginal posterior mode of the regression coefficients for the Bayesian lasso, by adjusting the weights of importance sampling, when the full conditional distribution is not explicit. Simulation experiments show that the computational time is much reduced with our method based on the expectation maximization algorithm and our algorithms and our methods behave comparably with other Bayesian lasso methods not only in prediction accuracy but also in variable selection accuracy and even better especially when the sample size is relatively large.

Weighted Elastic Net Model for Mass Spectrometry Imaging Processing

In proteomics study, Imaging Mass Spectrometry (IMS) is an emerging and very promis- ing new technique for protein analysis from intact biological tissues. Though it has shown great potential and is very promising for rapid mapping of protein localization and the detection of size- able differences in protein expression, challenges remain in data processing due to the difficulty of high dimensionality and the fact that the number of input variables in prediction model is signifi- cantly larger than the number of observations. To obtain a complete overview of IMS data and find trace features based on both spectral and spatial patterns, one faces a global optimization problem. In this paper, we propose a weighted elastic net (WEN) model based on IMS data processing needs of using both the spectral and spatial information for biomarker selection and classification. Prop- erties including variable selection accuracy of the WEN model are discussed. Experimental IMS data analysis results show that such a model not only reduces the number of side features but also helps new biomarkers discovery.

An Introspective Comparison of Random Forest-Based Classifiers for the Analysis of Cluster-Correlated Data by Way of RF++

Many mass spectrometry-based studies, as well as other biological experiments produce cluster-correlated data. Failure to account for correlation among observations may result in a classification algorithm overfitting the training data and producing overoptimistic estimated error rates and may make subsequent classifications unreliable. Current common practice for dealing with replicated data is to average each subject replicate sample set, reducing the dataset size and incurring loss of information. In this manuscript we compare three approaches to dealing with cluster-correlated data: unmodified Breiman's Random Forest (URF), forest grown using subject-level averages (SLA), and RF++ with subject-level bootstrapping (SLB). RF++, a novel Random Forest-based algorithm implemented in C++, handles cluster-correlated data through a modification of the original resampling algorithm and accommodates subject-level classification. Subject-level bootstrapping is an alternative sampling method that obviates the need to average or otherwise reduce each set of replicates to a single independent sample. Our experiments show nearly identical median classification and variable selection accuracy for SLB forests and URF forests when applied to both simulated and real datasets. However, the run-time estimated error rate was severely underestimated for URF forests. Predictably, SLA forests were found to be more severely affected by the reduction in sample size which led to poorer classification and variable selection accuracy. Perhaps most importantly our results suggest that it is reasonable to utilize URF for the analysis of cluster-correlated data. Two caveats should be noted: first, correct classification error rates must be obtained using a separate test dataset, and second, an additional post-processing step is required to obtain subject-level classifications. RF++ is shown to be an effective alternative for classifying both clustered and non-clustered data. Source code and stand-alone compiled versions of command-line and easy-to-use graphical user interface (GUI) versions of RF++ for Windows and Linux as well as a user manual (Supplementary File S2) are available for download at: http://sourceforge.org/projects/rfpp/ under the GNU public license.