A fused lasso latent feature model for analyzing multi-sample aCGH data

PIntMF: Penalized Integrative Matrix Factorization method for multi-omics data

MOTIVATION

It is more and more common to perform multi-omics analyses to explore the genome at diverse levels and not only at a single level. Through integrative statistical methods, multi-omics data have the power to reveal new biological processes, potential biomarkers and subgroups in a cohort. Matrix factorization (MF) is an unsupervised statistical method that allows a clustering of individuals, but also reveals relevant omics variables from the various blocks.

RESULTS

Here, we present PIntMF (Penalized Integrative Matrix Factorization), an MF model with sparsity, positivity and equality constraints. To induce sparsity in the model, we used a classical Lasso penalization on variable and individual matrices. For the matrix of samples, sparsity helps in the clustering, while normalization (matching an equality constraint) of inferred coefficients is added to improve interpretation. Moreover, we added an automatic tuning of the sparsity parameters using the famous glmnet package. We also proposed three criteria to help the user to choose the number of latent variables. PIntMF was compared with other state-of-the-art integrative methods including feature selection techniques in both synthetic and real data. PIntMF succeeds in finding relevant clusters as well as variables in two types of simulated data (correlated and uncorrelated). Next, PIntMF was applied to two real datasets (Diet and cancer), and it revealed interpretable clusters linked to available clinical data. Our method outperforms the existing ones on two criteria (clustering and variable selection). We show that PIntMF is an easy, fast and powerful tool to extract patterns and cluster samples from multi-omics data.

AVAILABILITY AND IMPLEMENTATION

An R package is available at https://github.com/mpierrejean/pintmf.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A Compact Neural Network for Fused Lasso Signal Approximator

The fused lasso signal approximator (FLSA) is a vital optimization problem with extensive applications in signal processing and biomedical engineering. However, the optimization problem is difficult to solve since it is both nonsmooth and nonseparable. The existing numerical solutions implicate the use of several auxiliary variables in order to deal with the nondifferentiable penalty. Thus, the resulting algorithms are both time- and memory-inefficient. This paper proposes a compact neural network to solve the FLSA. The neural network has a one-layer structure with the number of neurons proportionate to the dimension of the given signal, thanks to the utilization of consecutive projections. The proposed neural network is stable in the Lyapunov sense and is guaranteed to converge globally to the optimal solution of the FLSA. Experiments on several applications from signal processing and biomedical engineering confirm the reasonable performance of the proposed neural network.

Where Do We Stand in Regularization for Life Science Studies?

More and more biologists and bioinformaticians turn to machine learning to analyze large amounts of data. In this context, it is crucial to understand which is the most suitable data analysis pipeline for achieving reliable results. This process may be challenging, due to a variety of factors, the most crucial ones being the data type and the general goal of the analysis (e.g., explorative or predictive). Life science data sets require further consideration as they often contain measures with a low signal-to-noise ratio, high-dimensional observations, and relatively few samples. In this complex setting, regularization, which can be defined as the introduction of additional information to solve an ill-posed problem, is the tool of choice to obtain robust models. Different regularization practices may be used depending both on characteristics of the data and of the question asked, and different choices may lead to different results. In this article, we provide a comprehensive description of the impact and importance of regularization techniques in life science studies. In particular, we provide an intuition of what regularization is and of the different ways it can be implemented and exploited. We propose four general life sciences problems in which regularization is fundamental and should be exploited for robustness. For each of these large families of problems, we enumerate different techniques as well as examples and case studies. Lastly, we provide a unified view of how to approach each data type with various regularization techniques.

A Density Peak-Based Method to Detect Copy Number Variations From Next-Generation Sequencing Data

Copy number variation (CNV) is a common type of structural variations in human genome and confers biological meanings to human complex diseases. Detection of CNVs is an important step for a systematic analysis of CNVs in medical research of complex diseases. The recent development of next-generation sequencing (NGS) platforms provides unprecedented opportunities for the detection of CNVs at a base-level resolution. However, due to the intrinsic characteristics behind NGS data, accurate detection of CNVs is still a challenging task. In this article, we propose a new density peak-based method, called dpCNV, for the detection of CNVs from NGS data. The algorithm of dpCNV is designed based on density peak clustering algorithm. It extracts two features, i.e., local density and minimum distance, from sequencing read depth (RD) profile and generates a two-dimensional data. Based on the generated data, a two-dimensional null distribution is constructed to test the significance of each genome bin and then the significant genome bins are declared as CNVs. We test the performance of the dpCNV method on a number of simulated datasets and make comparison with several existing methods. The experimental results demonstrate that our proposed method outperforms others in terms of sensitivity and F1-score. We further apply it to a set of real sequencing samples and the results demonstrate the validity of dpCNV. Therefore, we expect that dpCNV can be used as a supplementary to existing methods and may become a routine tool in the field of genome mutation analysis.

Statistical Considerations on NGS Data for Inferring Copy Number Variations

The next-generation sequencing (NGS) technology has revolutionized research in genetics and genomics, resulting in massive NGS data and opening more fronts to answer unresolved issues in genetics. NGS data are usually stored at three levels: image files, sequence tags, and alignment reads. The sizes of these types of data usually range from several hundreds of gigabytes to several terabytes. Biostatisticians and bioinformaticians are typically working with the aligned NGS read count data (hence the last level of NGS data) for data modeling and interpretation.To horn in on the use of NGS technology, researchers utilize it to profile the whole genome to study DNA copy number variations (CNVs) for an individual subject (or patient) as well as groups of subjects (or patients). The resulting aligned NGS read count data are then modeled by proper mathematical and statistical approaches so that the loci of CNVs can be accurately detected. In this book chapter, a summary of most popularly used statistical methods for detecting CNVs using NGS data is given. The goal is to provide readers with a comprehensive resource of available statistical approaches for inferring DNA copy number variations using NGS data.

Robust Recurrent CNV Detection in the Presence of Inter-Subject Variability

The study of recurrent copy number variations (CNVs) plays an important role in understanding the onset and evolution of complex diseases such as cancer. Array-based comparative genomic hybridization (aCGH) is a widely used microarray based technology for identifying CNVs. However, due to high noise levels and inter-sample variability, detecting recurrent CNVs from aCGH data remains a challenging topic. This paper proposes a novel method for identification of the recurrent CNVs. In the proposed method, the noisy aCGH data is modeled as the superposition of three matrices: a full-rank matrix of weighted piece-wise generating signals accounting for the clean aCGH data, a Gaussian noise matrix to model the inherent experimentation errors and other sources of error, and a sparse matrix to capture the sparse inter-sample (sample-specific) variations. We demonstrated the ability of our method to separate accurately recurrent CNVs from sample-specific variations and noise in both simulated (artificial) data and real data. The proposed method produced more accurate results than current state-of-the-art methods used in recurrent CNV detection and exhibited robustness to noise and sample-specific variations.

WaveDec: A Wavelet Approach to Identify Both Shared and Individual Patterns of Copy-Number Variations

Copy-number variations (CNVs) are associated with complex diseases and particular tumor types. Array-based comparative genomic hybridization (aCGH) is a common approach for the detection of CNVs. Traditional CNV detection methods for multiple aCGH samples mainly use batch samples to find common variations, not accounting for the individual characteristics of each sample. Accurately differentiating both the commonly shared and the individual CNV patterns is pivotal to identify cell populations, or to distinguish cell growth (as in cancer) from invasion of new cells. Our preliminary results have now demonstrated that both the shared and individual CNV patterns have distinctive characteristics after wavelet transform.

METHODS

To exploit these characteristics, we propose to formulate a quadratic data-separation problem within the wavelet space to discriminate the shared and individual CNVs from raw data. We have elaborated a numerical solution and shown that the solution can be obtained by solving decoupled subproblems. By this approach, computational costs can be limited, enabling efficient application in the analysis of large sequencing datasets.

RESULTS

The advantages of our proposed method, called WaveDec, have been demonstrated by comparison with popular CNV-detection methods using synthetic and empirical aCGH data. The performance of WaveDec was further validated by experiments with single-cell-sequencing data.

CONCLUSION

WaveDec can successfully differentiate shared and individual patterns, and performs well even in data contaminated with high levels of noise.

SIGNIFICANCE

Both the shared and individual patterns can be uniquely characterized as well as effectively decomposed within the wavelet space.

Genomic region detection via Spatial Convex Clustering

Several modern genomic technologies, such as DNA-Methylation arrays, measure spatially registered probes that number in the hundreds of thousands across multiple chromosomes. The measured probes are by themselves less interesting scientifically; instead scientists seek to discover biologically interpretable genomic regions comprised of contiguous groups of probes which may act as biomarkers of disease or serve as a dimension-reducing pre-processing step for downstream analyses. In this paper, we introduce an unsupervised feature learning technique which maps technological units (probes) to biological units (genomic regions) that are common across all subjects. We use ideas from fusion penalties and convex clustering to introduce a method for Spatial Convex Clustering, or SpaCC. Our method is specifically tailored to detecting multi-subject regions of methylation, but we also test our approach on the well-studied problem of detecting segments of copy number variation. We formulate our method as a convex optimization problem, develop a massively parallelizable algorithm to find its solution, and introduce automated approaches for handling missing values and determining tuning parameters. Through simulation studies based on real methylation and copy number variation data, we show that SpaCC exhibits significant performance gains relative to existing methods. Finally, we illustrate SpaCC's advantages as a pre-processing technique that reduces large-scale genomics data into a smaller number of genomic regions through several cancer epigenetics case studies on subtype discovery, network estimation, and epigenetic-wide association.

Detection of Copy Number Variation Regions Using the DNA-Sequencing Data from Multiple Profiles with Correlated Structure

In this article, we investigate the problem of detecting boundaries of DNA copy number variation (CNV) regions using the DNA-sequencing data from multiple subject samples. Genomic features along the linear realization of the actual genome are correlated, especially within vicinity of a locus, so are the sequencing reads along the genome. It is then crucial to take the correlated structure of such high-throughput genomic data into consideration when modeling DNA-sequencing data for CNV detection from statistical and computational viewpoints. We use the framework of a fused Lasso latent feature model to solve the problem, and propose a modified information criterion for selecting the tuning parameter when search for common CNVs is shared by multiple subjects. Simulation studies and application on multiple subjects' next-generation sequencing data, downloaded from the 1000 Genome Project, showed that the proposed approach can effectively identify individual CNVs of a single subject profile and common CNVs shared by multiple subjects.

Sparse partial least squares with group and subgroup structure

Integrative analysis of high dimensional omics datasets has been studied by many authors in recent years. By incorporating prior known relationships among the variables, these analyses have been successful in elucidating the relationships between different sets of omics data. In this article, our goal is to identify important relationships between genomic expression and cytokine data from a human immunodeficiency virus vaccine trial. We proposed a flexible partial least squares technique, which incorporates group and subgroup structure in the modelling process. Our new method accounts for both grouping of genetic markers (eg, gene sets) and temporal effects. The method generalises existing sparse modelling techniques in the partial least squares methodology and establishes theoretical connections to variable selection methods for supervised and unsupervised problems. Simulation studies are performed to investigate the performance of our methods over alternative sparse approaches. Our R package sgspls is available at https://github.com/matt-sutton/sgspls.

Nonconvex Penalty Based Low-Rank Representation and Sparse Regression for eQTL Mapping

This paper addresses the problem of accounting for confounding factors and expression quantitative trait loci (eQTL) mapping in the study of SNP-gene associations. The existing convex penalty based algorithm has limited capacity to keep main information of matrix in the process of reducing matrix rank. We present an algorithm, which use nonconvex penalty based low-rank representation to account for confounding factors and make use of sparse regression for eQTL mapping (NCLRS). The efficiency of the presented algorithm is evaluated by comparing the results of 18 synthetic datasets given by NCLRS and presented algorithm, respectively. The experimental results or biological dataset show that our approach is an effective tool to account for non-genetic effects than currently existing methods.

Penalized weighted low-rank approximation for robust recovery of recurrent copy number variations

BACKGROUND

Copy number variation (CNV) analysis has become one of the most important research areas for understanding complex disease. With increasing resolution of array-based comparative genomic hybridization (aCGH) arrays, more and more raw copy number data are collected for multiple arrays. It is natural to realize the co-existence of both recurrent and individual-specific CNVs, together with the possible data contamination during the data generation process. Therefore, there is a great need for an efficient and robust statistical model for simultaneous recovery of both recurrent and individual-specific CNVs.

RESULT

We develop a penalized weighted low-rank approximation method (WPLA) for robust recovery of recurrent CNVs. In particular, we formulate multiple aCGH arrays into a realization of a hidden low-rank matrix with some random noises and let an additional weight matrix account for those individual-specific effects. Thus, we do not restrict the random noise to be normally distributed, or even homogeneous. We show its performance through three real datasets and twelve synthetic datasets from different types of recurrent CNV regions associated with either normal random errors or heavily contaminated errors.

CONCLUSION

Our numerical experiments have demonstrated that the WPLA can successfully recover the recurrent CNV patterns from raw data under different scenarios. Compared with two other recent methods, it performs the best regarding its ability to simultaneously detect both recurrent and individual-specific CNVs under normal random errors. More importantly, the WPLA is the only method which can effectively recover the recurrent CNVs region when the data is heavily contaminated.

Genome instability model of metastatic neuroblastoma tumorigenesis by a dictionary learning algorithm

Background

Metastatic neuroblastoma (NB) occurs in pediatric patients as stage 4S or stage 4 and it is characterized by heterogeneous clinical behavior associated with diverse genotypes. Tumors of stage 4 contain several structural copy number aberrations (CNAs) rarely found in stage 4S. To date, the NB tumorigenesis is not still elucidated, although it is evident that genomic instability plays a critical role in the genesis of the tumor. Here we propose a mathematical approach to decipher genomic data and we provide a new model of NB metastatic tumorigenesis.

Method

We elucidate NB tumorigenesis using Enhanced Fused Lasso Latent Feature Model (E-FLLat) modeling the array comparative chromosome hybridization (aCGH) data of 190 metastatic NBs (63 stage 4S and 127 stage 4). This model for aCGH segmentation, based on the minimization of functional dictionary learning (DL), combines several penalties tailored to the specificities of aCGH data. In DL, the original signal is approximated by a linear weighted combination of atoms: the elements of the learned dictionary.

Results

The hierarchical structures for stage 4S shows at the first level of the oncogenetic tree several whole chromosome gains except to the unbalanced gains of 17q, 2p and 2q. Conversely, the high CNA complexity found in stage 4 tumors, requires two different trees. Both stage 4 oncogenetic trees are marked diverged, up to five sublevels and the 17q gain is the most common event at the first level (2/3 nodes). Moreover the 11q deletion, one of the major unfavorable marker of disease progression, occurs before 3p loss indicating that critical chromosome aberrations appear at early stages of tumorigenesis. Finally, we also observed a significant (p = 0.025) association between patient age and chromosome loss in stage 4 cases.

Conclusion

These results led us to propose a genome instability progressive model in which NB cells initiate with a DNA synthesis uncoupled from cell division, that leads to stage 4S tumors, primarily characterized by numerical aberrations, or stage 4 tumors with high levels of genome instability resulting in complex chromosome rearrangements associated with high tumor aggressiveness and rapid disease progression.

Electronic supplementary material

The online version of this article (doi:10.1186/s12920-015-0132-y) contains supplementary material, which is available to authorized users.

Dictionary learning improves subtyping of breast cancer aCGH data

The advent of Comparative Genomic Hybridization (CGH) data led to the development of new mathematical models and computational methods to automatically infer chromosomal alterations. In this work we tackle a standard clustering problem exploiting the good representation properties of a novel method based on dictionary learning. The identified dictionary atoms, which show co-occuring shared alterations among samples, can be easily interpreted by domain experts. We compare a state-of-the-art approach with an original method on a breast cancer dataset.

Alternating proximal regularized dictionary learning

We present an algorithm for dictionary learning that is based on the alternating proximal algorithm studied by Attouch, Bolte, Redont, and Soubeyran (2010), coupled with a reliable and efficient dual algorithm for computation of the related proximity operators. This algorithm is suitable for a general dictionary learning model composed of a Bregman-type data fit term that accounts for the goodness of the representation and several convex penalization terms on the coefficients and atoms, explaining the prior knowledge at hand. As Attouch et al. recently proved, an alternating proximal scheme ensures better convergence properties than the simpler alternating minimization. We take care of the issue of inexactness in the computation of the involved proximity operators, giving a sound stopping criterion for the dual inner algorithm, which keeps under control the related errors, unavoidable for such a complex penalty terms, providing ultimately an overall effective procedure. Thanks to the generality of the proposed framework, we give an application in the context of genome-wide data understanding, revising the model proposed by Nowak, Hastie, Pollack, and Tibshirani (2011). The aim is to extract latent features (atoms) and perform segmentation on array-based comparative genomic hybridization (aCGH) data. We improve several important aspects that increase the quality and interpretability of the results. We show the effectiveness of the proposed model with two experiments on synthetic data, which highlight the enhancements over the original model.

Principles and methods of integrative genomic analyses in cancer

Combined analyses of molecular data, such as DNA copy-number alteration, mRNA and protein expression, point to biological functions and molecular pathways being deregulated in multiple cancers. Genomic, metabolomic and clinical data from various solid cancers and model systems are emerging and can be used to identify novel patient subgroups for tailored therapy and monitoring. The integrative genomics methodologies that are used to interpret these data require expertise in different disciplines, such as biology, medicine, mathematics, statistics and bioinformatics, and they can seem daunting. The objectives, methods and computational tools of integrative genomics that are available to date are reviewed here, as is their implementation in cancer research.

Piecewise-constant and low-rank approximation for identification of recurrent copy number variations

MOTIVATION

The post-genome era sees urgent need for more novel approaches to extracting useful information from the huge amount of genetic data. The identification of recurrent copy number variations (CNVs) from array-based comparative genomic hybridization (aCGH) data can help understand complex diseases, such as cancer. Most of the previous computational methods focused on single-sample analysis or statistical testing based on the results of single-sample analysis. Finding recurrent CNVs from multi-sample data remains a challenging topic worth further study.

RESULTS

We present a general and robust method to identify recurrent CNVs from multi-sample aCGH profiles. We express the raw dataset as a matrix and demonstrate that recurrent CNVs will form a low-rank matrix. Hence, we formulate the problem as a matrix recovering problem, where we aim to find a piecewise-constant and low-rank approximation (PLA) to the input matrix. We propose a convex formulation for matrix recovery and an efficient algorithm to globally solve the problem. We demonstrate the advantages of PLA compared with alternative methods using synthesized datasets and two breast cancer datasets. The experimental results show that PLA can successfully reconstruct the recurrent CNV patterns from raw data and achieve better performance compared with alternative methods under a wide range of scenarios.

AVAILABILITY AND IMPLEMENTATION

The MATLAB code is available at http://bioinformatics.ust.hk/pla.zip.

Novel multisample scheme for inferring phylogenetic markers from whole genome tumor profiles

Computational cancer phylogenetics seeks to enumerate the temporal sequences of aberrations in tumor evolution, thereby delineating the evolution of possible tumor progression pathways, molecular subtypes, and mechanisms of action. We previously developed a pipeline for constructing phylogenies describing evolution between major recurring cell types computationally inferred from whole-genome tumor profiles. The accuracy and detail of the phylogenies, however, depend on the identification of accurate, high-resolution molecular markers of progression, i.e., reproducible regions of aberration that robustly differentiate different subtypes and stages of progression. Here, we present a novel hidden Markov model (HMM) scheme for the problem of inferring such phylogenetically significant markers through joint segmentation and calling of multisample tumor data. Our method classifies sets of genome-wide DNA copy number measurements into a partitioning of samples into normal (diploid) or amplified at each probe. It differs from other similar HMM methods in its design specifically for the needs of tumor phylogenetics, by seeking to identify robust markers of progression conserved across a set of copy number profiles. We show an analysis of our method in comparison to other methods on both synthetic and real tumor data, which confirms its effectiveness for tumor phylogeny inference and suggests avenues for future advances.

Comparative Analysis of CNV Calling Algorithms: Literature Survey and a Case Study Using Bovine High-Density SNP Data

Copy number variations (CNVs) are gains and losses of genomic sequence between two individuals of a species when compared to a reference genome. The data from single nucleotide polymorphism (SNP) microarrays are now routinely used for genotyping, but they also can be utilized for copy number detection. Substantial progress has been made in array design and CNV calling algorithms and at least 10 comparison studies in humans have been published to assess them. In this review, we first survey the literature on existing microarray platforms and CNV calling algorithms. We then examine a number of CNV calling tools to evaluate their impacts using bovine high-density SNP data. Large incongruities in the results from different CNV calling tools highlight the need for standardizing array data collection, quality assessment and experimental validation. Only after careful experimental design and rigorous data filtering can the impacts of CNVs on both normal phenotypic variability and disease susceptibility be fully revealed.

Multiple samples aCGH analysis for rare CNVs detection

Background

DNA copy number variations (CNV) constitute an important source of genetic variability. The standard method used for CNV detection is array comparative genomic hybridization (aCGH).

Results

We propose a novel multiple sample aCGH analysis methodology aiming in rare CNVs detection. In contrast to the majority of previous approaches, which deal with cancer datasets, we focus on constitutional genomic abnormalities identified in a diverse spectrum of diseases in human. Our method is tested on exon targeted aCGH array of 366 patients affected with developmental delay/intellectual disability, epilepsy, or autism. The proposed algorithms can be applied as a post–processing filtering to any given segmentation method.

Conclusions

Thanks to the additional information obtained from multiple samples, we could efficiently detect significant segments corresponding to rare CNVs responsible for pathogenic changes. The robust statistical framework applied in our method enables to eliminate the influence of widespread technical artifact termed ‘waves’.

Breakpoint analysis of transcriptional and genomic profiles uncovers novel gene fusions spanning multiple human cancer types

Gene fusions, like BCR/ABL1 in chronic myelogenous leukemia, have long been recognized in hematologic and mesenchymal malignancies. The recent finding of gene fusions in prostate and lung cancers has motivated the search for pathogenic gene fusions in other malignancies. Here, we developed a “breakpoint analysis” pipeline to discover candidate gene fusions by tell-tale transcript level or genomic DNA copy number transitions occurring within genes. Mining data from 974 diverse cancer samples, we identified 198 candidate fusions involving annotated cancer genes. From these, we validated and further characterized novel gene fusions involving ROS1 tyrosine kinase in angiosarcoma (CEP85L/ROS1), SLC1A2 glutamate transporter in colon cancer (APIP/SLC1A2), RAF1 kinase in pancreatic cancer (ATG7/RAF1) and anaplastic astrocytoma (BCL6/RAF1), EWSR1 in melanoma (EWSR1/CREM), CDK6 kinase in T-cell acute lymphoblastic leukemia (FAM133B/CDK6), and CLTC in breast cancer (CLTC/VMP1). Notably, while these fusions involved known cancer genes, all occurred with novel fusion partners and in previously unreported cancer types. Moreover, several constituted druggable targets (including kinases), with therapeutic implications for their respective malignancies. Lastly, breakpoint analysis identified new cell line models for known rearrangements, including EGFRvIII and FIP1L1/PDGFRA. Taken together, we provide a robust approach for gene fusion discovery, and our results highlight a more widespread role of fusion genes in cancer pathogenesis.

Gene fusions represent an important class of cancer genes, created by rearrangements of the genome that bring together two different genes. Because they are unique to cancer cells, gene fusions are ideal diagnostic markers and therapeutic targets. While gene fusions were once thought restricted mainly to blood cancers, recent discoveries suggest they are more widespread. Here, we have developed an approach for mining DNA microarray data to detect the tell-tale signatures of gene fusions, as “breakpoints” occurring within the encoding DNA or expressed transcripts. We apply this approach to a large collection of nearly 1,000 human cancer specimens. From this analysis, we discover and verify twelve new gene fusions occurring in diverse cancer types. We verify that some of these rearrangements recur in other samples of the same cancer type (supporting a causal role) and that the cancers show dependency on the fusion for cancer cell growth. Notably, some of these fusions (e.g. CEP85L/ROS1 in angiosarcoma) represent the first for that cancer type and thus provide important new biological insight. Some are also good drug targets (including rearrangements of ROS1, RAF1, and CDK6 kinases), with clear implications for therapy.

Accounting for non-genetic factors by low-rank representation and sparse regression for eQTL mapping

MOTIVATION

Expression quantitative trait loci (eQTL) studies investigate how gene expression levels are affected by DNA variants. A major challenge in inferring eQTL is that a number of factors, such as unobserved covariates, experimental artifacts and unknown environmental perturbations, may confound the observed expression levels. This may both mask real associations and lead to spurious association findings.

RESULTS

In this article, we introduce a LOw-Rank representation to account for confounding factors and make use of Sparse regression for eQTL mapping (LORS). We integrate the low-rank representation and sparse regression into a unified framework, in which single-nucleotide polymorphisms and gene probes can be jointly analyzed. Given the two model parameters, our formulation is a convex optimization problem. We have developed an efficient algorithm to solve this problem and its convergence is guaranteed. We demonstrate its ability to account for non-genetic effects using simulation, and then apply it to two independent real datasets. Our results indicate that LORS is an effective tool to account for non-genetic effects. First, our detected associations show higher consistency between studies than recently proposed methods. Second, we have identified some new hotspots that can not be identified without accounting for non-genetic effects.

AVAILABILITY

The software is available at: http://bioinformatics.med.yale.edu/software.aspx.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Multisample aCGH data analysis via total variation and spectral regularization

DNA copy number variation (CNV) accounts for a large proportion of genetic variation. One commonly used approach to detecting CNVs is array-based comparative genomic hybridization (aCGH). Although many methods have been proposed to analyze aCGH data, it is not clear how to combine information from multiple samples to improve CNV detection. In this paper, we propose to use a matrix to approximate the multisample aCGH data and minimize the total variation of each sample as well as the nuclear norm of the whole matrix. In this way, we can make use of the smoothness property of each sample and the correlation among multiple samples simultaneously in a convex optimization framework. We also developed an efficient and scalable algorithm to handle large-scale data. Experiments demonstrate that the proposed method outperforms the state-of-the-art techniques under a wide range of scenarios and it is capable of processing large data sets with millions of probes.

Reconstructing DNA copy number by joint segmentation of multiple sequences

BACKGROUND

Variations in DNA copy number carry information on the modalities of genome evolution and mis-regulation of DNA replication in cancer cells. Their study can help localize tumor suppressor genes, distinguish different populations of cancerous cells, and identify genomic variations responsible for disease phenotypes. A number of different high throughput technologies can be used to identify copy number variable sites, and the literature documents multiple effective algorithms. We focus here on the specific problem of detecting regions where variation in copy number is relatively common in the sample at hand. This problem encompasses the cases of copy number polymorphisms, related samples, technical replicates, and cancerous sub-populations from the same individual.

RESULTS

We present a segmentation method named generalized fused lasso (GFL) to reconstruct copy number variant regions. GFL is based on penalized estimation and is capable of processing multiple signals jointly. Our approach is computationally very attractive and leads to sensitivity and specificity levels comparable to those of state-of-the-art specialized methodologies. We illustrate its applicability with simulated and real data sets.

CONCLUSIONS

The flexibility of our framework makes it applicable to data obtained with a wide range of technology. Its versatility and speed make GFL particularly useful in the initial screening stages of large data sets.

Genetic association studies of copy-number variation: should assignment of copy number states precede testing?

Recently, structural variation in the genome has been implicated in many complex diseases. Using genomewide single nucleotide polymorphism (SNP) arrays, researchers are able to investigate the impact not only of SNP variation, but also of copy-number variants (CNVs) on the phenotype. The most common analytic approach involves estimating, at the level of the individual genome, the underlying number of copies present at each location. Once this is completed, tests are performed to determine the association between copy number state and phenotype. An alternative approach is to carry out association testing first, between phenotype and raw intensities from the SNP array at the level of the individual marker, and then aggregate neighboring test results to identify CNVs associated with the phenotype. Here, we explore the strengths and weaknesses of these two approaches using both simulations and real data from a pharmacogenomic study of the chemotherapeutic agent gemcitabine. Our results indicate that pooled marker-level testing is capable of offering a dramatic increase in power (> 12-fold) over CNV-level testing, particularly for small CNVs. However, CNV-level testing is superior when CNVs are large and rare; understanding these tradeoffs is an important consideration in conducting association studies of structural variation.