Cross-platform analysis of longitudinal data in metabolomics

Metabolic profiling is considered to be a very promising tool for diagnostic purposes, for assessing nutritional status and response to drugs. However, it is also evident that human metabolic profiles have a complex nature, influenced by many external factors. This, together with the understanding of the difficulty to assign people to distinct groups and a general move in clinical science towards personalized medicine, raises the interest to explore individual and variable metabolic features for each individual separately in longitudinal study design. In the current paper we have analyzed a set of metabolic profiles of a selection of six urine samples per person from a set of healthy individuals by (1)H NMR and reversed-phase UPLC-MS. We have demonstrated that the method for recovery of individual metabolic phenotypes can give complementary information to another established method for analysis of longitudinal data--multilevel component analysis. We also show that individual metabolic signatures can be found not only in (1)H NMR data, as has been demonstrated before, but also even more strongly in LC-MS data.     

Analysis of longitudinal multinomial outcome data

Analysis of categorical outcomes in a longitudinal study has been an important statistical issue. Continuous outcome in a similar study design is commonly handled by the mixed effects model. The longitudinal binary or Poisson-like outcome analysis is often handled by the generalized estimation equation (GEE) method. Neither method is appropriate for analyzing a multinomial outcome in a longitudinal study, although the cross-sectional multinomial outcome is often analyzed by generalized linear models. One reason that these methods are not used is that the correlation structure of two multinomial variables can not be easily specified. In addition, methods that rely upon GEE or mixed effects models are unsuitable in instances when the focus of a longitudinal study is on the rate of moving from one category to another. In this research, a longitudinal model that has three categories in the outcome variable will be examined. A continuous-time Markov chain model will be used to examine the transition from one category to another. This model permits an unbalanced number of measurements collected on individuals and an uneven duration between pairs of consecutive measurements. In this study, the explicit expression for the transition probability is derived that provides an algebraic form of the likelihood function and hence allows the implementation of the maximum likelihood method. Using this approach, the instantaneous transition rate that is assumed to be a function of the linear combination of independent variables can be estimated. For a comparison between two groups, the odds ratios of occurrence at a particular category and their confidence intervals can be calculated. Empirical studies will be performed to compare the goodness of fit of the proposed method with other available methods. An example will also be used to demonstrate the application of this method.     

Multilevel pharmacokinetics-driven modeling of metabolomics data

Introduction

Multilevel modeling is a quantitative statistical method to investigate variability and relationships between variables of interest, taking into account population structure and dependencies. It can be used for prediction, data reduction and causal inference from experiments and observational studies allowing for more efficient elucidation of knowledge.

Objectives

In this study we introduced the concept of multilevel pharmacokinetics (PK)-driven modelling for large-sample, unbalanced and unadjusted metabolomics data comprising nucleoside and creatinine concentration measurements in urine of healthy and cancer patients.

Methods

A Bayesian multilevel model was proposed to describe the nucleoside and creatinine concentration ratio considering age, sex and health status as covariates. The predictive performance of the proposed model was summarized via area under the ROC, sensitivity and specificity using external validation.

Results

Cancer was associated with an increase in methylthioadenosine/creatinine excretion rate by a factor of 1.42 (1.09–2.03) which constituted the highest increase among all nucleosides. Age influenced nucleosides/creatinine excretion rates for all nucleosides in the same direction which was likely caused by a decrease in creatinine clearance with age. There was a small evidence of sex-related differences for methylthioadenosine. The individual a posteriori prediction of patient classification as area under the ROC with 5th and 95th percentile was 0.57(0.5–0.67) with sensitivity and specificity of 0.59(0.42–0.76) and 0.57(0.45–0.7), respectively suggesting limited usefulness of 13 nucleosides/creatinine urine concentration measurements in predicting disease in this population.

Conclusion

Bayesian multilevel pharmacokinetics-driven modeling in metabolomics may be useful in understanding the data and may constitute a new tool for searching towards potential candidates of disease indicators.

     

Analysis of longitudinal count data with serial correlation

We propose a state space model for analyzing equally or unequally spaced longitudinal count data with serial correlation. With a log link function, the mean of the Poisson response variable is a nonlinear function of the fixed and random effects. The random effects are assumed to be generated from a Gaussian first order autoregression (AR(1)). In this case, the mean of the observations has a log normal distribution. We use a combination of linear and nonlinear methods to take advantage of the Gaussian process embedded in a nonlinear function. The state space model uses a modified Kalman filter recursion to estimate the mean and variance of the AR(1) random error given the previous observations. The marginal likelihood is approximated by numerically integrating out the AR(1) random error. Simulation studies with different sets of parameters show that the state space model performs well. The model is applied to Epileptic Seizure data and Primary Care Visits Data. Missing and unequally spaced observations are handled naturally with this model.     

Analysis of longitudinal data with unmeasured confounders.

Confounding in longitudinal or clustered data creates special problems and opportunities because the relationship between the confounder and covariate of interest may differ across and within individuals or clusters. A well-known example of such confounding in longitudinal data is the presence of cohort and period effects in models of aging in epidemiologic research. We first formulate a data-generating model with confounding and derive the distribution of the response variable unconditional on the confounder. We then examine the properties of the regression coefficient for some analytic approaches when the confounder is omitted from the fitted model. The expected value of the regression coefficient differs in across- and within-individual regression. In the multivariate case, within- and between-individual information is combined and weighted according to the assumed covariance structure. We assume compound symmetry in the fitted covariance matrix and derive the variance, bias, and mean squared error of the slope estimate as a function of the fitted within-individual correlation. We find that even in this simplest multivariate case, the trade-off between bias and variance depends on a large number of parameters. It is generally preferable to fit correlations somewhat above the true correlation to minimize the effect of between-individual confounders or cohort effects. Period effects can lead to situations where it is advantageous to fit correlations that are below the true correlation. The results highlight the trade-offs inherent in the choice of method for analysis of longitudinal data, and show that an appropriate choice can be made only after determining whether within- or between-individual confounding is the major concern.     

The origin of correlations in metabolomics data

A phenomenon observed earlier in the development of metabolomics as a systems biology methodology, consists of a small but significant number of metabolites whose levels are highly correlated between biological replicates. Contrary to initial interpretations, these correlations are not necessarily only between neighboring metabolites in the metabolic network. Most metabolites that participate in common reactions are not correlated in this way, while some non-neighboring metabolites are highly correlated. Here we investigate the origin of such correlations using metabolic control analysis and computer simulation of biochemical networks. A series of cases is identified which lead to high correlation between metabolite pairs in replicate measurement. These are (1) chemical equilibrium, (2) mass conservation, (3) asymmetric control distribution, and (4) unusually high variance in the expression of a single gene. The importance of identifying metabolite correlations within a physiological state and changes of correlation between different states is discussed in the context of systems biology.     

Genetic algorithm based two-mode clustering of metabolomics data

Metabolomics and other omics tools are generally characterized by large data sets with many variables obtained under different environmental conditions. Clustering methods and more specifically two-mode clustering methods are excellent tools for analyzing this type of data. Two-mode clustering methods allow for analysis of the behavior of subsets of metabolites under different experimental conditions. In addition, the results are easily visualized. In this paper we introduce a two-mode clustering method based on a genetic algorithm that uses a criterion that searches for homogeneous clusters. Furthermore we introduce a cluster stability criterion to validate the clusters and we provide an extended knee plot to select the optimal number of clusters in both experimental and metabolite modes. The genetic algorithm-based two-mode clustering gave biological relevant results when it was applied to two real life metabolomics data sets. It was, for instance, able to identify a catabolic pathway for growth on several of the carbon sources. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. J. A. Hageman and R. A. van den Berg contributed equally to this paper.     

Toward supportive data collection tools for plant metabolomics

Over recent years, a number of initiatives have proposed standard reporting guidelines for functional genomics experiments. Associated with these are data models that may be used as the basis of the design of software tools that store and transmit experiment data in standard formats. Central to the success of such data handling tools is their usability. Successful data handling tools are expected to yield benefits in time saving and in quality assurance. Here, we describe the collection of datasets that conform to the recently proposed data model for plant metabolomics known as ArMet (architecture for metabolomics) and illustrate a number of approaches to robust data collection that have been developed in collaboration between software engineers and biologists. These examples also serve to validate ArMet from the data collection perspective by demonstrating that a range of software tools, supporting data recording and data upload to central databases, can be built using the data model as the basis of their design.     

Untargeted metabolomics suffers from incomplete raw data processing

Introduction

Untargeted metabolomics is a powerful tool for biological discoveries. To analyze the complex raw data, significant advances in computational approaches have been made, yet it is not clear how exhaustive and reliable the data analysis results are.

Objectives

Assessment of the quality of raw data processing in untargeted metabolomics.

Methods

Five published untargeted metabolomics studies, were reanalyzed.

Results

Omissions of at least 50 relevant compounds from the original results as well as examples of representative mistakes were reported for each study.

Conclusion

Incomplete raw data processing shows unexplored potential of current and legacy data.

     

Reflections on univariate and multivariate analysis of metabolomics data

Metabolomics experiments usually result in a large quantity of data. Univariate and multivariate analysis techniques are routinely used to extract relevant information from the data with the aim of providing biological knowledge on the problem studied. Despite the fact that statistical tools like the t test, analysis of variance, principal component analysis, and partial least squares discriminant analysis constitute the backbone of the statistical part of the vast majority of metabolomics papers, it seems that many basic but rather fundamental questions are still often asked, like: Why do the results of univariate and multivariate analyses differ? Why apply univariate methods if you have already applied a multivariate method? Why if I do not see something univariately I see something multivariately? In the present paper we address some aspects of univariate and multivariate analysis, with the scope of clarifying in simple terms the main differences between the two approaches. Applications of the t test, analysis of variance, principal component analysis and partial least squares discriminant analysis will be shown on both real and simulated metabolomics data examples to provide an overview on fundamental aspects of univariate and multivariate methods.     

Modeling nonstationary longitudinal data

An important theme of longitudinal data analysis in the past two decades has been the development and use of explicit parametric models for the data's variance-covariance structure. A variety of these models have been proposed, of which most are second-order stationary. A few are flexible enough to accommodate nonstationarity, i.e., nonconstant variances and/or correlations that are not a function solely of elapsed time between measurements. We review five nonstationary models that we regard as most useful: (1) the unstructured covariance model, (2) unstructured antedependence models, (3) structured antedependence models, (4) autoregressive integrated moving average and similar models, and (5) random coefficients models. We evaluate the relative strengths and limitations of each model, emphasizing when it is inappropriate or unlikely to be useful. We present three examples to illustrate the fitting and comparison of the models and to demonstrate that nonstationary longitudinal data can be modeled effectively and, in some cases, quite parsimoniously. In these examples, the antedependence models generally prove to be superior and the random coefficients models prove to be inferior. We conclude that antedependence models should be given much greater consideration than they have historically received.     

Analysis of clustered and longitudinal binary data subject to response misclassification

Misclassified clustered and longitudinal data arise in studies where the response indicates a condition identified through an imperfect diagnostic procedure. Examples include longitudinal studies that use an imperfect diagnostic test to assess whether or not an individual has been infected with a specific virus. This article presents methods to implement both population-averaged and cluster-specific analyses of such data when the misclassification rates are known. The methods exploit the fact that the class of generalized linear models enjoys a closure property in the case of misclassified responses. Data from longitudinal studies of infectious disease will illustrate the findings.     

FELLA: an R package to enrich metabolomics data

Background

Pathway enrichment techniques are useful for understanding experimental metabolomics data. Their purpose is to give context to the affected metabolites in terms of the prior knowledge contained in metabolic pathways. However, the interpretation of a prioritized pathway list is still challenging, as pathways show overlap and cross talk effects.

Results

We introduce FELLA, an R package to perform a network-based enrichment of a list of affected metabolites. FELLA builds a hierarchical representation of an organism biochemistry from the Kyoto Encyclopedia of Genes and Genomes (KEGG), containing pathways, modules, enzymes, reactions and metabolites. In addition to providing a list of pathways, FELLA reports intermediate entities (modules, enzymes, reactions) that link the input metabolites to them. This sheds light on pathway cross talk and potential enzymes or metabolites as targets for the condition under study. FELLA has been applied to six public datasets –three from Homo sapiens, two from Danio rerio and one from Mus musculus– and has reproduced findings from the original studies and from independent literature.

Conclusions

The R package FELLA offers an innovative enrichment concept starting from a list of metabolites, based on a knowledge graph representation of the KEGG database that focuses on interpretability. Besides reporting a list of pathways, FELLA suggests intermediate entities that are of interest per se. Its usefulness has been shown at several molecular levels on six public datasets, including human and animal models. The user can run the enrichment analysis through a simple interactive graphical interface or programmatically. FELLA is publicly available in Bioconductor under the GPL-3 license.

     

Differential metabolomics software for capillary electrophoresis-mass spectrometry data analysis

In metabolomics, the rapid identification of quantitative differences between multiple biological samples remains a major challenge. While capillary electrophoresis–mass spectrometry (CE–MS) is a powerful tool to simultaneously quantify charged metabolites, reliable and easy-to-use software that is well suited to analyze CE–MS metabolic profiles is still lacking. Optimized software tools for CE–MS are needed because of the sometimes large variation in migration time between runs and the wider variety of peak shapes in CE–MS data compared with LC–MS or GC–MS. Therefore, we implemented a stand-alone application named JDAMP (Java application for Differential Analysis of Metabolite Profiles), which allows users to identify the metabolites that vary between two groups. The main features include fast calculation modules and a file converter using an original compact file format, baseline subtraction, dataset normalization and alignment, visualization on 2D plots (m/z and time axis) with matching metabolite standards, and the detection of significant differences between metabolite profiles. Moreover, it features an easy-to-use graphical user interface that requires only a few mouse-actions to complete the analysis. The interface also enables the analyst to evaluate the semiautomatic processes and interactively tune options and parameters depending on the input datasets. The confirmation of findings is available as a list of overlaid electropherograms, which is ranked using a novel difference-evaluation function that accounts for peak size and distortion as well as statistical criteria for accurate difference-detection. Overall, the JDAMP software complements other metabolomics data processing tools and permits easy and rapid detection of significant differences between multiple complex CE–MS profiles.     

Proposed minimum reporting standards for data analysis in metabolomics

The goal of this group is to define the reporting requirements associated with the statistical analysis (including univariate, multivariate, informatics, machine learning etc.) of metabolite data with respect to other measured/collected experimental data (often called meta-data). These definitions will embrace as many aspects of a complete metabolomics study as possible at this time. In chronological order this will include: Experimental Design, both in terms of sample collection/matching, and data acquisition scheduling of samples through whichever spectroscopic technology used; Deconvolution (if required); Pre-processing, for example, data cleaning, outlier detection, row/column scaling, or other transformations; Definition and parameterization of subsequent visualizations and Statistical/Machine learning Methods applied to the dataset; If required, a clear definition of the Model Validation Scheme used (including how data are split into training/validation/test sets); Formal indication on whether the data analysis has been Independently Tested (either by experimental reproduction, or blind hold out test set). Finally, data interpretation and the visual representations and hypotheses obtained from the data analyses.     

MetaboLights: towards a new COSMOS of metabolomics data management

Exciting funding initiatives are emerging in Europe and the US for metabolomics data production, storage, dissemination and analysis. This is based on a rich ecosystem of resources around the world, which has been build during the past ten years, including but not limited to resources such as MassBank in Japan and the Human Metabolome Database in Canada. Now, the European Bioinformatics Institute has launched MetaboLights, a database for metabolomics experiments and the associated metadata (http://www.ebi.ac.uk/metabolights). It is the first comprehensive, cross-species, cross-platform metabolomics database maintained by one of the major open access data providers in molecular biology. In October, the European COSMOS consortium will start its work on Metabolomics data standardization, publication and dissemination workflows. The NIH in the US is establishing 6?C8 metabolomics services cores as well as a national metabolomics repository. This communication reports about MetaboLights as a new resource for Metabolomics research, summarises the related developments and outlines how they may consolidate the knowledge management in this third large omics field next to proteomics and genomics.     

Stability of exploratory multivariate data modeling in longitudinal data

Exploratory data-driven multivariate analysis provides a means of investigating underlying structure in complex data. To explore the stability of multivariate data modeling, we have applied a common method of multivariate modeling (factor analysis) to the Genetic Analysis Workshop 13 (GAW13) Framingham Heart Study data. Given the longitudinal nature of the data, multivariate models were generated independently for a number of different time points (corresponding to cross-sectional clinic visits for the two cohorts), and compared. In addition, each multivariate model was used to generate factor scores, which were then used as a quantitative trait in variance component-based linkage analysis to investigate the stability of linkage signals over time. We found surprisingly good correlation between factor models (i.e., predicted factor structures), maximum LOD scores, and locations of maximum LOD scores (0.81< rho <0.94 for factor scores; rho >0.99 for peak locations; and 0.67< rho <0.93 for peak LOD scores). Furthermore, the regions implicated by linkage analysis with these factor scores have also been observed in other studies, further validating our exploratory modeling.