Bayesian Random Segmentation Models to Identify Shared Copy Number Aberrations for Array CGH Data

Array-based comparative genomic hybridization (aCGH) is a high-resolution high-throughput technique for studying the genetic basis of cancer. The resulting data consists of log fluorescence ratios as a function of the genomic DNA location and provides a cytogenetic representation of the relative DNA copy number variation. Analysis of such data typically involves estimation of the underlying copy number state at each location and segmenting regions of DNA with similar copy number states. Most current methods proceed by modeling a single sample/array at a time, and thus fail to borrow strength across multiple samples to infer shared regions of copy number aberrations. We propose a hierarchical Bayesian random segmentation approach for modeling aCGH data that utilizes information across arrays from a common population to yield segments of shared copy number changes. These changes characterize the underlying population and allow us to compare different population aCGH profiles to assess which regions of the genome have differential alterations. Our method, referred to as BDSAcgh (Bayesian Detection of Shared Aberrations in aCGH), is based on a unified Bayesian hierarchical model that allows us to obtain probabilities of alteration states as well as probabilities of differential alteration that correspond to local false discovery rates. We evaluate the operating characteristics of our method via simulations and an application using a lung cancer aCGH data set.     

An online copy number variant detection method for short sequencing reads

The availability of the next generation sequencing (NGS) technology in today's biomedical research has provided new opportunities in scientific discovery of genetic information. The high-throughput NGS technology, especially DNA-seq, is particularly useful in profiling a genome for the analysis of DNA copy number variants (CNVs). The read count (RC) data resulting from NGS technology are massive and information rich. How to exploit the RC data for accurate CNV detection has become a computational and statistical challenge. We provide a statistical online change point method to help detect CNVs in the sequencing RC data in this paper. This method uses the idea of online searching for change point (or breakpoint) with a Markov chain assumption on the breakpoints loci and an iterative computing process via a Bayesian framework. We illustrate that an online change-point detection method is particularly suitable for identifying CNVs in the RC data. The algorithm is applied to the publicly available NCI-H2347 lung cancer cell line sequencing reads data for locating the breakpoints. Extensive simulation studies have been carried out and results show the good behavior of the proposed algorithm. The algorithm is implemented in R and the codes are available upon request.     

Statistical models for DNA copy number variation detection using read‐depth data from next generation sequencing experiments

In this ‘Big Data’ era, statisticians inevitably encounter data generated from various disciplines. In particular, advances in bio‐technology have enabled scientists to produce enormous datasets in various biological experiments. In the last two decades, we have seen high‐throughput microarray data resulting from various genomic studies. Recently, next generation sequencing (NGS) technology has been playing an important role in the study of genomic features, resulting in vast amount of NGS data. One frequent application of NGS technology is in the study of DNA copy number variants (CNVs). The resulting NGS read count data are then used by researchers to formulate their various scientific approaches to accurately detect CNVs. Computational and statistical approaches to the detection of CNVs using NGS data are, however, very limited at present. In this review paper, we will focus on read‐depth analysis in CNV detection and give a brief summary of currently used statistical analysis methods in searching for CNVs using NGS data. In addition, based on the review, we discuss the challenges we face and future research directions. The ultimate goal of this review paper is to give a timely exposition of the surveyed statistical methods to researchers in related fields.     

Bayesian Nonparametric Hidden Markov Models with application to the analysis of copy-number-variation in mammalian genomes

We consider the development of Bayesian Nonparametric methods for product partition models such as Hidden Markov Models and change point models. Our approach uses a Mixture of Dirichlet Process (MDP) model for the unknown sampling distribution (likelihood) for the observations arising in each state and a computationally efficient data augmentation scheme to aid inference. The method uses novel MCMC methodology which combines recent retrospective sampling methods with the use of slice sampler variables. The methodology is computationally efficient, both in terms of MCMC mixing properties, and robustness to the length of the time series being investigated. Moreover, the method is easy to implement requiring little or no user-interaction. We apply our methodology to the analysis of genomic copy number variation.     

Bayesian Hidden Markov Modeling of Array CGH Data

Genomic alterations have been linked to the development and progression of cancer. The technique of comparative genomic hybridization (CGH) yields data consisting of fluorescence intensity ratios of test and reference DNA samples. The intensity ratios provide information about the number of copies in DNA. Practical issues such as the contamination of tumor cells in tissue specimens and normalization errors necessitate the use of statistics for learning about the genomic alterations from array CGH data. As increasing amounts of array CGH data become available, there is a growing need for automated algorithms for characterizing genomic profiles. Specifically, there is a need for algorithms that can identify gains and losses in the number of copies based on statistical considerations, rather than merely detect trends in the data.We adopt a Bayesian approach, relying on the hidden Markov model to account for the inherent dependence in the intensity ratios. Posterior inferences are made about gains and losses in copy number. Localized amplifications (associated with oncogene mutations) and deletions (associated with mutations of tumor suppressors) are identified using posterior probabilities. Global trends such as extended regions of altered copy number are detected. Because the posterior distribution is analytically intractable, we implement a Metropolis-within-Gibbs algorithm for efficient simulation-based inference. Publicly available data on pancreatic adenocarcinoma, glioblastoma multiforme, and breast cancer are analyzed, and comparisons are made with some widely used algorithms to illustrate the reliability and success of the technique.     

RECONSTRUCTING DNA COPY NUMBER BY PENALIZED ESTIMATION AND IMPUTATION

Recent advances in genomics have underscored the surprising ubiquity of DNA copy number variation (CNV). Fortunately, modern genotyping platforms also detect CNVs with fairly high reliability. Hidden Markov models and algorithms have played a dominant role in the interpretation of CNV data. Here we explore CNV reconstruction via estimation with a fused-lasso penalty as suggested by Tibshirani and Wang [Biostatistics 9 (2008) 18-29]. We mount a fresh attack on this difficult optimization problem by the following: (a) changing the penalty terms slightly by substituting a smooth approximation to the absolute value function, (b) designing and implementing a new MM (majorization-minimization) algorithm, and (c) applying a fast version of Newton's method to jointly update all model parameters. Together these changes enable us to minimize the fused-lasso criterion in a highly effective way.We also reframe the reconstruction problem in terms of imputation via discrete optimization. This approach is easier and more accurate than parameter estimation because it relies on the fact that only a handful of possible copy number states exist at each SNP. The dynamic programming framework has the added bonus of exploiting information that the current fused-lasso approach ignores. The accuracy of our imputations is comparable to that of hidden Markov models at a substantially lower computational cost.     

A Bayesian approach for locating change points in a compound Poisson process with application to detecting DNA copy number variations

This work examines the problem of locating changes in the distribution of a Compound Poisson Process where the variables being summed are iid normal and the number of variable follows the Poisson distribution. A Bayesian approach is developed to identify the location of significant changes in any of the parameters of the distribution, and a sliding window algorithm is used to identify multiple change points. These results can be applied in any field of study where an interest in locating changes not only in the parameter of a normally distributed data set but also in the rate of their occurrence. It has direct application to the study of DNA copy number variations in cancer research, where it is known that the distances between the genes can affect their intensity level.     

Bayesian covariance estimation and inference in latent Gaussian process models

This paper describes inference methods for functional data under the assumption that the functional data of interest are smooth latent functions, characterized by a Gaussian process, which have been observed with noise over a finite set of time points. The methods we propose are completely specified in a Bayesian environment that allows for all inferences to be performed through a simple Gibbs sampler. Our main focus is in estimating and describing uncertainty in the covariance function. However, these models also encompass functional data estimation, functional regression where the predictors are latent functions, and an automatic approach to smoothing parameter selection. Furthermore, these models require minimal assumptions on the data structure as the time points for observations do not need to be equally spaced, the number and placement of observations are allowed to vary among functions, and special treatment is not required when the number of functional observations is less than the dimensionality of those observations. We illustrate the effectiveness of these models in estimating latent functional data, capturing variation in the functional covariance estimate, and in selecting appropriate smoothing parameters in both a simulation study and a regression analysis of medfly fertility data.     

Models for surveillance data under reporting delay: applications to US veteran first-time suicide attempters

Surveillance data provide a vital source of information for assessing the spread of a health problem or disease of interest and for planning for future health-care needs. However, the use of surveillance data requires proper adjustments of the reported caseload due to underreporting caused by reporting delays within a limited observation period. Although methods are available to address this classic statistical problem, they are largely focused on inference for the reporting delay distribution, with inference about caseload of disease incidence based on estimates for the delay distribution. This approach limits the complexity of models for disease incidence to provide reliable estimates and projections of incidence. Also, many of the available methods lack robustness since they require parametric distribution assumptions. We propose a new approach to overcome such limitations by allowing for separate models for the incidence and the reporting delay in a distribution-free fashion, but with joint inference for both modeling components, based on functional response models. In addition, we discuss inference about projections of future disease incidence to help identify significant shifts in temporal trends modeled based on the observed data. This latter issue on detecting ‘change points’ is not sufficiently addressed in the literature, despite the fact that such warning signs of potential outbreak are critically important for prevention purposes. We illustrate the approach with both simulated and real data, with the latter involving data for suicide attempts from the Veteran Healthcare Administration.     

A Bayesian mixture model for differential gene expression

Summary.  We propose model-based inference for differential gene expression, using a nonparametric Bayesian probability model for the distribution of gene intensities under various conditions. The probability model is a mixture of normal distributions. The resulting inference is similar to a popular empirical Bayes approach that is used for the same inference problem. The use of fully model-based inference mitigates some of the necessary limitations of the empirical Bayes method. We argue that inference is no more difficult than posterior simulation in traditional nonparametric mixture-of-normal models. The approach proposed is motivated by a microarray experiment that was carried out to identify genes that are differentially expressed between normal tissue and colon cancer tissue samples. Additionally, we carried out a small simulation study to verify the methods proposed. In the motivating case-studies we show how the nonparametric Bayes approach facilitates the evaluation of posterior expected false discovery rates. We also show how inference can proceed even in the absence of a null sample of known non-differentially expressed scores. This highlights the difference from alternative empirical Bayes approaches that are based on plug-in estimates.     

A Bayesian Approach to Modelling Reticulation Events with Application to the Ribosomal Protein Gene rps11 of Flowering Plants

Traditional phylogenetic inference assumes that the history of a set of taxa can be explained by a tree. This assumption is often violated as some biological entities can exchange genetic material giving rise to non‐treelike events often called reticulations. Failure to consider these events might result in incorrectly inferred phylogenies. Phylogenetic networks provide a flexible tool which allows researchers to model the evolutionary history of a set of organisms in the presence of reticulation events. In recent years, a number of methods addressing phylogenetic network parameter estimation have been introduced. Some of them are based on the idea that a phylogenetic network can be defined as a directed acyclic graph. Based on this definition, we propose a Bayesian approach to the estimation of phylogenetic network parameters which allows for different phylogenies to be inferred at different parts of a multiple DNA alignment. The algorithm is tested on simulated data and applied to the ribosomal protein gene rps11 data from five flowering plants, where reticulation events are suspected to be present. The proposed approach can be applied to a wide variety of problems which aim at exploring the possibility of reticulation events in the history of a set of taxa.     

Bayesian factor models for multivariate categorical data obtained from questionnaires

Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often have an interesting theoretical interpretation in real problems. However, standard factor analysis is only applicable when the variables are scaled, which is often inappropriate, for example, in data obtained from questionnaires in the field of psychology, where the variables are often categorical. In this framework, we propose a factor model for the analysis of multivariate ordered and non-ordered polychotomous data. The inference procedure is done under the Bayesian approach via Markov chain Monte Carlo methods. Two Monte Carlo simulation studies are presented to investigate the performance of this approach in terms of estimation bias, precision and assessment of the number of factors. We also illustrate the proposed method to analyze participants'' responses to the Motivational State Questionnaire dataset, developed to study emotions in laboratory and field settings.     

On a variance stabilizing model and its application to genomic data

In this paper, we propose a model based on a class of symmetric distributions, which avoids the transformation of data, stabilizes the variance of the observations, and provides robust estimation of parameters and high flexibility for modeling different types of data. Probabilistic and statistical aspects of this new model are developed throughout the article, which include mathematical properties, estimation of parameters and inference. The obtained results are illustrated by means of real genomic data.     

Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling

ABSTRACT

We introduce a score-type statistic to test for a non-zero regression coefficient when the relevant term involves a nuisance parameter present only under the alternative. Despite the non-regularity and complexity of the problem and unlike the previous approaches, the proposed test statistic does not require the nuisance to be estimated. It is simple to implement by relying on the conventional distributions, such as Normal or t, and it justified in the setting of probabilistic coherence. We focus on testing for the existence of a breakpoint in segmented regression, and illustrate the methodology with an analysis on data of DNA copy number aberrations and gene expression profiles from 97 breast cancer patients; moreover some simulations reveal that the proposed test is more powerful than its competitors previously discussed in literature.     

Bayesian scale space analysis of temporal changes in satellite images

We consider the detection of land cover changes using pairs of Landsat ETM+ satellite images. The images consist of eight spectral bands and to simplify the multidimensional change detection task, the image pair is first transformed to a one-dimensional image. When the transformation is non-linear, the true change in the images may be masked by complex noise. For example, when changes in the Normalized Difference Vegetation Index is considered, the variance of noise may not be constant over the image and methods based on image thresholding can be ineffective. To facilitate detection of change in such situations, we propose an approach that uses Bayesian statistical modeling and simulation-based inference. In order to detect both large and small scale changes, our method uses a scale space approach that employs multi-level smoothing. We demonstrate the technique using artificial test images and two pairs of real Landsat ETM+satellite images.     

Reverse engineering gene regulatory networks using approximate Bayesian computation

Gene regulatory networks are collections of genes that interact with one other and with other substances in the cell. By measuring gene expression over time using high-throughput technologies, it may be possible to reverse engineer, or infer, the structure of the gene network involved in a particular cellular process. These gene expression data typically have a high dimensionality and a limited number of biological replicates and time points. Due to these issues and the complexity of biological systems, the problem of reverse engineering networks from gene expression data demands a specialized suite of statistical tools and methodologies. We propose a non-standard adaptation of a simulation-based approach known as Approximate Bayesian Computing based on Markov chain Monte Carlo sampling. This approach is particularly well suited for the inference of gene regulatory networks from longitudinal data. The performance of this approach is investigated via simulations and using longitudinal expression data from a genetic repair system in Escherichia coli.     

Variational Bayes with synthetic likelihood

Synthetic likelihood is an attractive approach to likelihood-free inference when an approximately Gaussian summary statistic for the data, informative for inference about the parameters, is available. The synthetic likelihood method derives an approximate likelihood function from a plug-in normal density estimate for the summary statistic, with plug-in mean and covariance matrix obtained by Monte Carlo simulation from the model. In this article, we develop alternatives to Markov chain Monte Carlo implementations of Bayesian synthetic likelihoods with reduced computational overheads. Our approach uses stochastic gradient variational inference methods for posterior approximation in the synthetic likelihood context, employing unbiased estimates of the log likelihood. We compare the new method with a related likelihood-free variational inference technique in the literature, while at the same time improving the implementation of that approach in a number of ways. These new algorithms are feasible to implement in situations which are challenging for conventional approximate Bayesian computation methods, in terms of the dimensionality of the parameter and summary statistic.     

A factor model approach for the joint segmentation with between‐series correlation

We consider the detection of changes in the mean of a set of time series. The breakpoints are allowed to be series specific, and the series are assumed to be correlated. The correlation between the series is supposed to be constant along time but is allowed to take an arbitrary form. We show that such a dependence structure can be encoded in a factor model. Thanks to this representation, the inference of the breakpoints can be achieved via dynamic programming, which remains one the most efficient algorithms. We propose a model selection procedure to determine both the number of breakpoints and the number of factors. This proposed method is implemented in the FASeg R package, which is available on the CRAN. We demonstrate the performances of our procedure through simulation experiments and present an application to geodesic data.     

Bayesian–frequentist hybrid model with application to the analysis of gene copy number changes

Gene copy number (GCN) changes are common characteristics of many genetic diseases. Comparative genomic hybridization (CGH) is a new technology widely used today to screen the GCN changes in mutant cells with high resolution genome-wide. Statistical methods for analyzing such CGH data have been evolving. Existing methods are either frequentist's or full Bayesian. The former often has computational advantage, while the latter can incorporate prior information into the model, but could be misleading when one does not have sound prior information. In an attempt to take full advantages of both approaches, we develop a Bayesian-frequentist hybrid approach, in which a subset of the model parameters is inferred by the Bayesian method, while the rest parameters by the frequentist's. This new hybrid approach provides advantages over those of the Bayesian or frequentist's method used alone. This is especially the case when sound prior information is available on part of the parameters, and the sample size is relatively small. Spatial dependence and false discovery rate are also discussed, and the parameter estimation is efficient. As an illustration, we used the proposed hybrid approach to analyze a real CGH data.