A novel approach for nontargeted data analysis for metabolomics. Large-scale profiling of tomato fruit volatiles

To take full advantage of the power of functional genomics technologies and in particular those for metabolomics, both the analytical approach and the strategy chosen for data analysis need to be as unbiased and comprehensive as possible. Existing approaches to analyze metabolomic data still do not allow a fast and unbiased comparative analysis of the metabolic composition of the hundreds of genotypes that are often the target of modern investigations. We have now developed a novel strategy to analyze such metabolomic data. This approach consists of (1) full mass spectral alignment of gas chromatography (GC)-mass spectrometry (MS) metabolic profiles using the MetAlign software package, (2) followed by multivariate comparative analysis of metabolic phenotypes at the level of individual molecular fragments, and (3) multivariate mass spectral reconstruction, a method allowing metabolite discrimination, recognition, and identification. This approach has allowed a fast and unbiased comparative multivariate analysis of the volatile metabolite composition of ripe fruits of 94 tomato (Lycopersicon esculentum Mill.) genotypes, based on intensity patterns of >20,000 individual molecular fragments throughout 198 GC-MS datasets. Variation in metabolite composition, both between- and within-fruit types, was found and the discriminative metabolites were revealed. In the entire genotype set, a total of 322 different compounds could be distinguished using multivariate mass spectral reconstruction. A hierarchical cluster analysis of these metabolites resulted in clustering of structurally related metabolites derived from the same biochemical precursors. The approach chosen will further enhance the comprehensiveness of GC-MS-based metabolomics approaches and will therefore prove a useful addition to nontargeted functional genomics research.     

Capturing genomic signatures of DNA sequence variation using a standard anonymous microarray platform

Comparative genomics, using the model organism approach, has provided powerful insights into the structure and evolution of whole genomes. Unfortunately, only a small fraction of Earth's biodiversity will have its genome sequenced in the foreseeable future. Most wild organisms have radically different life histories and evolutionary genomics than current model systems. A novel technique is needed to expand comparative genomics to a wider range of organisms. Here, we describe a novel approach using an anonymous DNA microarray platform that gathers genomic samples of sequence variation from any organism. Oligonucleotide probe sequences placed on a custom 44 K array were 25 bp long and designed using a simple set of criteria to maximize their complexity and dispersion in sequence probability space. Using whole genomic samples from three known genomes (mouse, rat and human) and one unknown (Gonystylus bancanus), we demonstrate and validate its power, reliability, transitivity and sensitivity. Using two separate statistical analyses, a large numbers of genomic ‘indicator’ probes were discovered. The construction of a genomic signature database based upon this technique would allow virtual comparisons and simple queries could generate optimal subsets of markers to be used in large-scale assays, using simple downstream techniques. Biologists from a wide range of fields, studying almost any organism, could efficiently perform genomic comparisons, at potentially any phylogenetic level after performing a small number of standardized DNA microarray hybridizations. Possibilities for refining and expanding the approach are discussed.     

Multivariate t linear mixed models for irregularly observed multiple repeated measures with missing outcomes

Missing outcomes or irregularly timed multivariate longitudinal data frequently occur in clinical trials or biomedical studies. The multivariate t linear mixed model (MtLMM) has been shown to be a robust approach to modeling multioutcome continuous repeated measures in the presence of outliers or heavy‐tailed noises. This paper presents a framework for fitting the MtLMM with an arbitrary missing data pattern embodied within multiple outcome variables recorded at irregular occasions. To address the serial correlation among the within‐subject errors, a damped exponential correlation structure is considered in the model. Under the missing at random mechanism, an efficient alternating expectation‐conditional maximization (AECM) algorithm is used to carry out estimation of parameters and imputation of missing values. The techniques for the estimation of random effects and the prediction of future responses are also investigated. Applications to an HIV‐AIDS study and a pregnancy study involving analysis of multivariate longitudinal data with missing outcomes as well as a simulation study have highlighted the superiority of MtLMMs on the provision of more adequate estimation, imputation and prediction performances.     

101 Exploring the 3D spatial organization of the genome

Knowledge about the 3D organization of the genome will offer great insights into how cells retrieve and process the genetic information. Knowing the spatial probability distributions of individual genes will provide insights into gene regulatory and replication processes, and fill in the missing links between epigenomics, functional genomics, and structural biology. We will discuss an approach to determine 3D genome structures and structure–function maps of genomes by integrating divers types of data. To address the challenge of modeling highly variable genome structures, we discuss a population-based modeling approach, where we construct a large population of 3D genome structures that together are entirely consistent with all available experimental data including data from genome-wide chromosome conformation capture and imaging experiments. We interpret the result in terms of probabilities of a sample drawn from a population of heterogeneous structures. We will discuss results on the 3D spatial organization of genomes in human lymphoblastoid cells and budding yeast.     

A Bayesian functional data model for surveys collected under informative sampling with application to mortality estimation using NHANES

Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in multivariate settings. In addition, we make use of a variety of Bayesian modeling techniques to ensure that the model is fit in a computationally efficient manner. We illustrate the value of our approach through two simulation studies as well as an example of mortality estimation using NHANES data.     

Subspace projection approaches to classification and visualization of neural network-level encoding patterns

Recent advances in large-scale ensemble recordings allow monitoring of activity patterns of several hundreds of neurons in freely behaving animals. The emergence of such high-dimensional datasets poses challenges for the identification and analysis of dynamical network patterns. While several types of multivariate statistical methods have been used for integrating responses from multiple neurons, their effectiveness in pattern classification and predictive power has not been compared in a direct and systematic manner. Here we systematically employed a series of projection methods, such as Multiple Discriminant Analysis (MDA), Principal Components Analysis (PCA) and Artificial Neural Networks (ANN), and compared them with non-projection multivariate statistical methods such as Multivariate Gaussian Distributions (MGD). Our analyses of hippocampal data recorded during episodic memory events and cortical data simulated during face perception or arm movements illustrate how low-dimensional encoding subspaces can reveal the existence of network-level ensemble representations. We show how the use of regularization methods can prevent these statistical methods from over-fitting of training data sets when the trial numbers are much smaller than the number of recorded units. Moreover, we investigated the extent to which the computations implemented by the projection methods reflect the underlying hierarchical properties of the neural populations. Based on their ability to extract the essential features for pattern classification, we conclude that the typical performance ranking of these methods on under-sampled neural data of large dimension is MDA>PCA>ANN>MGD.     

Assessment of Genetic Heterogeneity in Structured Plant Populations Using Multivariate Whole-Genome Regression Models

Plant breeding populations exhibit varying levels of structure and admixture; these features are likely to induce heterogeneity of marker effects across subpopulations. Traditionally, structure has been dealt with as a potential confounder, and various methods exist to “correct” for population stratification. However, these methods induce a mean correction that does not account for heterogeneity of marker effects. The animal breeding literature offers a few recent studies that consider modeling genetic heterogeneity in multibreed data, using multivariate models. However, these methods have received little attention in plant breeding where population structure can have different forms. In this article we address the problem of analyzing data from heterogeneous plant breeding populations, using three approaches: (a) a model that ignores population structure [A-genome-based best linear unbiased prediction (A-GBLUP)], (b) a stratified (i.e., within-group) analysis (W-GBLUP), and (c) a multivariate approach that uses multigroup data and accounts for heterogeneity (MG-GBLUP). The performance of the three models was assessed on three different data sets: a diversity panel of rice (Oryza sativa), a maize (Zea mays L.) half-sib panel, and a wheat (Triticum aestivum L.) data set that originated from plant breeding programs. The estimated genomic correlations between subpopulations varied from null to moderate, depending on the genetic distance between subpopulations and traits. Our assessment of prediction accuracy features cases where ignoring population structure leads to a parsimonious more powerful model as well as others where the multivariate and stratified approaches have higher predictive power. In general, the multivariate approach appeared slightly more robust than either the A- or the W-GBLUP.     

Matrix heterogeneity affects population size of the harvest mice: Bayesian estimation of matrix resistance and model validation

It has been increasingly recognized that landscape matrices are an important factor determining patch connectivity and hence the population size of organisms living in highly fragmented landscapes. However, most previous studies estimated the effect of matrix heterogeneity using prior information regarding dispersal or habitat preferences of a focal organism. Here we estimated matrix resistance of harvest mice in agricultural landscapes using a novel pattern‐oriented modeling with Bayesian estimation and no prior information, and then conducted model validation using data sets independent from those used for model construction. First, we investigated the distribution patterns of harvest mice for approximately 400 habitat patches, and estimated matrix resistance for different matrix types using statistical models incorporating patch size, patch environment, and patch connectivity. We used Bayesian estimation with a Markov chain Monte Carlo algorithm, and searched for appropriate matrix resistance that best explained the distribution pattern. Patch connectivity as well as patch quality was an important determinant of local population size for the harvest mice. Moreover, matrix resistance was far from uniform, with rice and crop fields exhibiting low resistance and forests, creeks, roads and residential areas showing much higher resistance. The deviance explained by this model (heterogeneous matrix model) was much larger than that obtained by the model with no consideration of matrix heterogeneity (homogeneous matrix model). Second, we obtained distribution data from five additional landscapes that were more fragmented than that used for model construction, and used them for model validation. The heterogeneous matrix model well predicted the population size for four out of five landscapes. In contrast, the homogeneous model considerably overestimated population sizes in all cases. Our approach is widely applicable to species living in fragmented landscapes, especially those for which prior information regarding movement or dispersal is difficult to obtain.     

A compound decision approach to covariance matrix estimation

Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is suboptimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings are common in modern genomics, where covariance matrix estimation is frequently employed as a method for inferring gene networks. To achieve estimation accuracy in these settings, existing methods typically either assume that the population covariance matrix has some particular structure, for example, sparsity, or apply shrinkage to better estimate the population eigenvalues. In this paper, we study a new approach to estimating high-dimensional covariance matrices. We first frame covariance matrix estimation as a compound decision problem. This motivates defining a class of decision rules and using a nonparametric empirical Bayes g-modeling approach to estimate the optimal rule in the class. Simulation results and gene network inference in an RNA-seq experiment in mouse show that our approach is comparable to or can outperform a number of state-of-the-art proposals.     

Coreferentiality: a new method for the hypothesis-based analysis of phenotypes characterized by multivariate data

Many multifactorial biologic effects, particularly in the context of complex human diseases, are still poorly understood. At the same time, the systematic acquisition of multivariate data has become increasingly easy. The use of such data to analyze and model complex phenotypes, however, remains a challenge. Here, a new analytic approach is described, termed coreferentiality, together with an appropriate statistical test. Coreferentiality is the indirect relation of two variables of functional interest in respect to whether they parallel each other in their respective relatedness to multivariate reference data, which can be informative for a complex effect or phenotype. It is shown that the power of coreferentiality testing is comparable to multiple regression analysis, sufficient even when reference data are informative only to a relatively small extent of 2.5%, and clearly exceeding the power of simple bivariate correlation testing. Thus, coreferentiality testing uses the increased power of multivariate analysis, however, in order to address a more straightforward interpretable bivariate relatedness. Systematic application of this approach could substantially improve the analysis and modeling of complex phenotypes, particularly in the context of human study where addressing functional hypotheses by direct experimentation is often difficult.     

Modeling Mutual Exclusivity of Cancer Mutations

In large collections of tumor samples, it has been observed that sets of genes that are commonly involved in the same cancer pathways tend not to occur mutated together in the same patient. Such gene sets form mutually exclusive patterns of gene alterations in cancer genomic data. Computational approaches that detect mutually exclusive gene sets, rank and test candidate alteration patterns by rewarding the number of samples the pattern covers and by punishing its impurity, i.e., additional alterations that violate strict mutual exclusivity. However, the extant approaches do not account for possible observation errors. In practice, false negatives and especially false positives can severely bias evaluation and ranking of alteration patterns. To address these limitations, we develop a fully probabilistic, generative model of mutual exclusivity, explicitly taking coverage, impurity, as well as error rates into account, and devise efficient algorithms for parameter estimation and pattern ranking. Based on this model, we derive a statistical test of mutual exclusivity by comparing its likelihood to the null model that assumes independent gene alterations. Using extensive simulations, the new test is shown to be more powerful than a permutation test applied previously. When applied to detect mutual exclusivity patterns in glioblastoma and in pan-cancer data from twelve tumor types, we identify several significant patterns that are biologically relevant, most of which would not be detected by previous approaches. Our statistical modeling framework of mutual exclusivity provides increased flexibility and power to detect cancer pathways from genomic alteration data in the presence of noise. A summary of this paper appears in the proceedings of the RECOMB 2014 conference, April 2–5.     

Systemic analysis: Individual typological characteristics of the human body

Statistical analysis of the distribution of the mean somatometric, functional, and psychophysiological parameters in the total sample of subjects with the use of the χ² and λ tests and low, medium, and high habitual physical activity (HPA) levels (LHPA, MHPA, and HHPA, respectively) at different ontogenetic stages (junior and senior school students and young adults of both sexes) showed wide quantitative and qualitative ranges of psychophysiological individuality in a healthy population and demonstrated that it is reasonable to distinguish three typological groups or functional constitutional types (FT-1 corresponding to LHPA; FT-2, to MHPA; and FT-3, to HHPA). Typical first- and second-order parameters, as well as the results of third-order tests characterizing the current state, were determined for each FT. In order to comprehensively assess the constitutional type (synthetic constitution) of the subjects with low, medium, and high HPAs, the integrated analysis of the set of their characteristics was performed using the principles of polythetic (multi-variate) classification. The results obtained using multivariate statistical methods confirmed the basic postulate of the concept of typological variability of physiological individuality that a healthy human population is qualitatively heterogeneous in morphological, functional, and psychophysiological traits. The integrated physiological and statistical analyses of the results provided a scientific basis for three functional constitutional types (FT-1, FT-2, and FT-3) corresponding to three synthetic constitutional types (C 0-1, C 00, and C 01). These data indicate that the systemic (constitutional) approach to the estimation of individual typological characteristics confirm a high informativeness of partial constitution (FT-1, FT-2, and FT-3) in the human biological organization, and the set of characters selected for analysis allows the synthetic constitutional types to be adequately differentiated on a formal basis.     

Mapping and analysis of quantitative trait loci in experimental populations

Simple statistical methods for the study of quantitative trait loci (QTL), such as analysis of variance, have given way to methods that involve several markers and high-resolution genetic maps. As a result, the mapping community has been provided with statistical and computational tools that have much greater power than ever before for studying and locating multiple and interacting QTL. Apart from their immediate practical applications, the lessons learnt from this evolution of QTL methodology might also be generally relevant to other types of functional genomics approach that are aimed at the dissection of complex phenotypes, such as microarray assessment of gene expression.     

A composite likelihood approach to latent multivariate Gaussian modeling of SNP data with application to genetic association testing

Many statistical tests have been proposed for case-control data to detect disease association with multiple single nucleotide polymorphisms (SNPs) in linkage disequilibrium. The main reason for the existence of so many tests is that each test aims to detect one or two aspects of many possible distributional differences between cases and controls, largely due to the lack of a general and yet simple model for discrete genotype data. Here we propose a latent variable model to represent SNP data: the observed SNP data are assumed to be obtained by discretizing a latent multivariate Gaussian variate. Because the latent variate is multivariate Gaussian, its distribution is completely characterized by its mean vector and covariance matrix, in contrast to much more complex forms of a general distribution for discrete multivariate SNP data. We propose a composite likelihood approach for parameter estimation. A direct application of this latent variable model is to association testing with multiple SNPs in a candidate gene or region. In contrast to many existing tests that aim to detect only one or two aspects of many possible distributional differences of discrete SNP data, we can exclusively focus on testing the mean and covariance parameters of the latent Gaussian distributions for cases and controls. Our simulation results demonstrate potential power gains of the proposed approach over some existing methods.     

Kriging with nonparametric variance function estimation

A method for fitting regression models to data that exhibit spatial correlation and heteroskedasticity is proposed. It is well known that ignoring a nonconstant variance does not bias least-squares estimates of regression parameters; thus, data analysts are easily lead to the false belief that moderate heteroskedasticity can generally be ignored. Unfortunately, ignoring nonconstant variance when fitting variograms can seriously bias estimated correlation functions. By modeling heteroskedasticity and standardizing by estimated standard deviations, our approach eliminates this bias in the correlations. A combination of parametric and nonparametric regression techniques is used to iteratively estimate the various components of the model. The approach is demonstrated on a large data set of predicted nitrogen runoff from agricultural lands in the Midwest and Northern Plains regions of the U.S.A. For this data set, the model comprises three main components: (1) the mean function, which includes farming practice variables, local soil and climate characteristics, and the nitrogen application treatment, is assumed to be linear in the parameters and is fitted by generalized least squares; (2) the variance function, which contains a local and a spatial component whose shapes are left unspecified, is estimated by local linear regression; and (3) the spatial correlation function is estimated by fitting a parametric variogram model to the standardized residuals, with the standardization adjusting the variogram for the presence of heteroskedasticity. The fitting of these three components is iterated until convergence. The model provides an improved fit to the data compared with a previous model that ignored the heteroskedasticity and the spatial correlation.     

Expected estimating equations for missing data, measurement error, and misclassification, with application to longitudinal nonignorable missing data

Summary .   Missing data, measurement error, and misclassification are three important problems in many research fields, such as epidemiological studies. It is well known that missing data and measurement error in covariates may lead to biased estimation. Misclassification may be considered as a special type of measurement error, for categorical data. Nevertheless, we treat misclassification as a different problem from measurement error because statistical models for them are different. Indeed, in the literature, methods for these three problems were generally proposed separately given that statistical modeling for them are very different. The problem is more challenging in a longitudinal study with nonignorable missing data. In this article, we consider estimation in generalized linear models under these three incomplete data models. We propose a general approach based on expected estimating equations (EEEs) to solve these three incomplete data problems in a unified fashion. This EEE approach can be easily implemented and its asymptotic covariance can be obtained by sandwich estimation. Intensive simulation studies are performed under various incomplete data settings. The proposed method is applied to a longitudinal study of oral bone density in relation to body bone density.     

Modeling multivariate survival data by a semiparametric random effects proportional odds model

In this article, the focus is on the analysis of multivariate survival time data with various types of dependence structures. Examples of multivariate survival data include clustered data and repeated measurements from the same subject, such as the interrecurrence times of cancer tumors. A random effect semiparametric proportional odds model is proposed as an alternative to the proportional hazards model. The distribution of the random effects is assumed to be multivariate normal and the random effect is assumed to act additively to the baseline log-odds function. This class of models, which includes the usual shared random effects model, the additive variance components model, and the dynamic random effects model as special cases, is highly flexible and is capable of modeling a wide range of multivariate survival data. A unified estimation procedure is proposed to estimate the regression and dependence parameters simultaneously by means of a marginal-likelihood approach. Unlike the fully parametric case, the regression parameter estimate is not sensitive to the choice of correlation structure of the random effects. The marginal likelihood is approximated by the Monte Carlo method. Simulation studies are carried out to investigate the performance of the proposed method. The proposed method is applied to two well-known data sets, including clustered data and recurrent event times data.     

Quality estimation of multiple sequence alignments by Bayesian hypothesis testing

In this work we present a web-based tool for estimating multiple alignment quality using Bayesian hypothesis testing. The proposed method is very simple, easily implemented and not time consuming with a linear complexity. We evaluated method against a series of different alignments (a set of random and biologically derived alignments) and compared the results with tools based on classical statistical methods (such as sFFT and csFFT). Taking correlation coefficient as an objective criterion of the true quality, we found that Bayesian hypothesis testing performed better on average than the classical methods we tested. This approach may be used independently or as a component of any tool in computational biology which is based on the statistical estimation of alignment quality. AVAILABILITY: http://www.fmi.ch/groups/functional.genomics/tool.htm. SUPPLEMENTARY INFORMATION: Supplementary data are available from http://www.fmi.ch/groups/functional.genomics/tool-Supp.htm.