Real Metabolomics Dataset Research Articles

Weighted scaling approach for metabolomics data analysis

Systematic variation is a common issue in metabolomics data analysis. Therefore, different scaling and normalization techniques are used to preprocess the data for metabolomics data analysis. Although several scaling methods are available in the literature, however, choice of scaling, transformation and/or normalization technique influences the further statistical analysis. It is challenged to choose the appropriate scaling technique for downstream analysis to get accurate results or to make proper decision. Moreover, the existing scaling techniques are sensitive to outliers or extreme values. To fill the gap, our objective is to introduce a robust scaling approach that is not influenced by outliers as well as provides more accurate results for downstream analysis. Here, we introduced a new weighted scaling approach that is robust against outliers; however, no additional outlier detection/treatment step is needed in data preprocessing and also compared it with the conventional scaling and normalization techniques through artificial and real metabolomics datasets. We evaluated the performance of the proposed method in comparison to the other existing conventional scaling techniques using metabolomics data analysis in both the absence and presence of different percentages of outliers. Results show that in most cases, the proposed scaling technique is a better performer than the traditional scaling methods in both the absence and presence of outliers. The proposed method improves the further downstream metabolomics analysis. The R function of the proposed robust scaling method is available at https://github.com/nishithkumarpaul/robustScaling/blob/main/wscaling.R

BUDDY: molecular formula discovery via bottom-up MS/MS interrogation.

A substantial fraction of metabolic features remains undetermined in mass spectrometry (MS)-based metabolomics, and molecular formula annotation is the starting point for unraveling their chemical identities. Here we present bottom-up tandem MS (MS/MS) interrogation, a method for de novo formula annotation. Our approach prioritizes MS/MS-explainable formula candidates, implements machine-learned ranking and offers false discovery rate estimation. Compared with the mathematically exhaustive formula enumeration, our approach shrinks the formula candidate space by 42.8% on average. Method benchmarking on annotation accuracy was systematically carried out on reference MS/MS libraries and real metabolomics datasets. Applied on 155,321 recurrent unidentified spectra, our approach confidently annotated >5,000 novel molecular formulae absent from chemical databases. Beyond the level of individual metabolic features, we combined bottom-up MS/MS interrogation with global optimization to refine formula annotations while revealing peak interrelationships. This approach allowed the systematic annotation of 37 fatty acid amide molecules in human fecal data. All bioinformatics pipelines are available in a standalone software, BUDDY ( https://github.com/HuanLab/BUDDY ).

Resampling for estimation of parameters uncertainty in genetic algorithm based model fitting

Resampling methods draw samples from the observed data to draw certain conclusions about the population of interest.The study is the employment of resampling to the calculation of parameters uncertainty in hard model fitting of chemical and spectrochemical data, assisted by genetic algorithm. Four data sets are investigated including: a simulated two steps of complexometric spectrophotometric titration data, a real data from IgG purification by ion exchange chromatography, one 1H NMR spectrum from a real metabolomics data set, and a simulated metabolomics 1H NMR spectrum. In the first data, the logarithm of formation constants in the first and second steps were 4.500 and 7.200, respectively. The mean of estimated parameters and standard deviations using the proposed method were obtained as 4.504 ± 0.005 and 7.205 ± 0.017 by removing around half of the samples while for NGLM algorithm and Hessian matrix were 4.503 ± 0.005 and 7.203 ± 0.018. In the second data, desorption coefficient (kdes,0), equilibrium coefficient (Keq,0), and a constant parameter that describes ion exchange characteristics (β) were well estimated with root mean square error (RMSE) of 0.031 mg mL−1. In the third and last data sets, parameters including chemical shifts and intensity of each metabolite were well calculated with low relative error of 4.23 × 10−4. The estimated uncertainty of parameters were different. In some cases, the means of estimated parameters were dependent of the number of eliminated samples in resampling. Effect of number of variables in data and model deficiency on the results from resampling was investigated. Due to the complexity of the mentioned datasets, use of resampling and GA is useful and important strategy for acquiring parameter mean and uncertainty, when we are not able to determine the Hessian matrix.

NormAE: Deep Adversarial Learning Model to Remove Batch Effects in Liquid Chromatography Mass Spectrometry-Based Metabolomics Data.

Untargeted metabolomics based on liquid chromatography-mass spectrometry is affected by nonlinear batch effects, which cover up biological effects, result in nonreproducibility, and are difficult to be calibrate. In this study, we propose a novel deep learning model, called Normalization Autoencoder (NormAE), which is based on nonlinear autoencoders (AEs) and adversarial learning. An additional classifier and ranker are trained to provide adversarial regularization during the training of the AE model, latent representations are extracted by the encoder, and then the decoder reconstructs the data without batch effects. The NormAE method was tested on two real metabolomics data sets. After calibration by NormAE, the quality control samples (QCs) for both data sets gathered most closely in a PCA score plot (average distances decreased from 56.550 and 52.476 to 7.383 and 14.075, respectively) and obtained the highest average correlation coefficients (from 0.873 and 0.907 to 0.997 for both). Additionally, NormAE significantly improved biomarker discovery (median number of differential peaks increased from 322 and 466 to 1140 and 1622, respectively). NormAE was compared with four commonly used batch effect removal methods. The results demonstrated that using NormAE produces the best calibration results.

Identifying Significant Metabolic Pathways Using Multi-Block Partial Least-Squares Analysis.

In metabolomics, identification of metabolic pathways altered by disease, genetics, or environmental perturbations is crucial to uncover the underlying biological mechanisms. A number of pathway analysis methods are currently available, which are generally based on equal-probability, topological-centrality, or model-separability methods. In brief, prior identification of significant metabolites is needed for the first two types of methods, while each pathway is modeled separately in the model-separability-based methods. In these methods, interactions between metabolic pathways are not taken into consideration. The current study aims to develop a novel metabolic pathway identification method based on multi-block partial least squares (MB-PLS) analysis by including all pathways into a global model to facilitate biological interpretation. The detected metabolites are first assigned to pathway blocks based on their roles in metabolism as defined by the KEGG pathway database. The metabolite intensity or concentration data matrix is then reconstructed as data blocks according to the metabolite subsets. Then, a MB-PLS model is built on these data blocks. A new metric, named the pathway importance in projection (PIP), is proposed for evaluation of the significance of each metabolic pathway for group separation. A simulated dataset was generated by imposing artificial perturbation on four pre-defined pathways of the healthy control group of a colorectal cancer study. Performance of the proposed method was evaluated and compared with seven other commonly used methods using both an actual metabolomics dataset and the simulated dataset. For the real metabolomics dataset, most of the significant pathways identified by the proposed method were found to be consistent with the published literature. For the simulated dataset, the significant pathways identified by the proposed method are highly consistent with the pre-defined pathways. The experimental results demonstrate that the proposed method is effective for identification of significant metabolic pathways, which may facilitate biological interpretation of metabolomics data.

Evaluation of Classifier Performance for Multiclass Phenotype Discrimination in Untargeted Metabolomics.

Statistical classification is a critical component of utilizing metabolomics data for examining the molecular determinants of phenotypes. Despite this, a comprehensive and rigorous evaluation of the accuracy of classification techniques for phenotype discrimination given metabolomics data has not been conducted. We conducted such an evaluation using both simulated and real metabolomics datasets, comparing Partial Least Squares-Discriminant Analysis (PLS-DA), Sparse PLS-DA, Random Forests, Support Vector Machines (SVM), Artificial Neural Network, k-Nearest Neighbors (k-NN), and Naïve Bayes classification techniques for discrimination. We evaluated the techniques on simulated data generated to mimic global untargeted metabolomics data by incorporating realistic block-wise correlation and partial correlation structures for mimicking the correlations and metabolite clustering generated by biological processes. Over the simulation studies, covariance structures, means, and effect sizes were stochastically varied to provide consistent estimates of classifier performance over a wide range of possible scenarios. The effects of the presence of non-normal error distributions, the introduction of biological and technical outliers, unbalanced phenotype allocation, missing values due to abundances below a limit of detection, and the effect of prior-significance filtering (dimension reduction) were evaluated via simulation. In each simulation, classifier parameters, such as the number of hidden nodes in a Neural Network, were optimized by cross-validation to minimize the probability of detecting spurious results due to poorly tuned classifiers. Classifier performance was then evaluated using real metabolomics datasets of varying sample medium, sample size, and experimental design. We report that in the most realistic simulation studies that incorporated non-normal error distributions, unbalanced phenotype allocation, outliers, missing values, and dimension reduction, classifier performance (least to greatest error) was ranked as follows: SVM, Random Forest, Naïve Bayes, sPLS-DA, Neural Networks, PLS-DA and k-NN classifiers. When non-normal error distributions were introduced, the performance of PLS-DA and k-NN classifiers deteriorated further relative to the remaining techniques. Over the real datasets, a trend of better performance of SVM and Random Forest classifier performance was observed.

Partial Least Squares with Structured Output for Modelling the Metabolomics Data Obtained from Complex Experimental Designs: A Study into the Y-Block Coding.

Partial least squares (PLS) is one of the most commonly used supervised modelling approaches for analysing multivariate metabolomics data. PLS is typically employed as either a regression model (PLS-R) or a classification model (PLS-DA). However, in metabolomics studies it is common to investigate multiple, potentially interacting, factors simultaneously following a specific experimental design. Such data often cannot be considered as a “pure” regression or a classification problem. Nevertheless, these data have often still been treated as a regression or classification problem and this could lead to ambiguous results. In this study, we investigated the feasibility of designing a hybrid target matrix Y that better reflects the experimental design than simple regression or binary class membership coding commonly used in PLS modelling. The new design of Y coding was based on the same principle used by structural modelling in machine learning techniques. Two real metabolomics datasets were used as examples to illustrate how the new Y coding can improve the interpretability of the PLS model compared to classic regression/classification coding.

Local false discovery rate estimation using feature reliability in LC/MS metabolomics data.

False discovery rate (FDR) control is an important tool of statistical inference in feature selection. In mass spectrometry-based metabolomics data, features can be measured at different levels of reliability and false features are often detected in untargeted metabolite profiling as chemical and/or bioinformatics noise. The traditional false discovery rate methods treat all features equally, which can cause substantial loss of statistical power to detect differentially expressed features. We propose a reliability index for mass spectrometry-based metabolomics data with repeated measurements, which is quantified using a composite measure. We then present a new method to estimate the local false discovery rate (lfdr) that incorporates feature reliability. In simulations, our proposed method achieved better balance between sensitivity and controlling false discovery, as compared to traditional lfdr estimation. We applied our method to a real metabolomics dataset and were able to detect more differentially expressed metabolites that were biologically meaningful.

Biological network inference using low order partial correlation

Biological network inference is a major challenge in systems biology. Traditional correlation-based network analysis results in too many spurious edges since correlation cannot distinguish between direct and indirect associations. To address this issue, Gaussian graphical models (GGM) were proposed and have been widely used. Though they can significantly reduce the number of spurious edges, GGM are insufficient to uncover a network structure faithfully due to the fact that they only consider the full order partial correlation. Moreover, when the number of samples is smaller than the number of variables, further technique based on sparse regularization needs to be incorporated into GGM to solve the singular covariance inversion problem. In this paper, we propose an efficient and mathematically solid algorithm that infers biological networks by computing low order partial correlation (LOPC) up to the second order. The bias introduced by the low order constraint is minimal compared to the more reliable approximation of the network structure achieved. In addition, the algorithm is suitable for a dataset with small sample size but large number of variables. Simulation results show that LOPC yields far less spurious edges and works well under various conditions commonly seen in practice. The application to a real metabolomics dataset further validates the performance of LOPC and suggests its potential power in detecting novel biomarkers for complex disease.

Genome-wide association studies with high-dimensional phenotypes

High-dimensional phenotypes hold promise for richer findings in association studies, but testing of several phenotype traits aggravates the grand challenge of association studies, that of multiple testing. Several methods have recently been proposed for testing jointly all traits in a high-dimensional vector of phenotypes, with prospect of increased power to detect small effects that would be missed if tested individually. However, the methods have rarely been compared to the extent of enabling assessment of their relative merits and setting up guidelines on which method to use, and how to use it. We compare the methods on simulated data and with a real metabolomics data set comprising 137 highly correlated variables and approximately 550,000 SNPs. Applying the methods to genome-wide data with hundreds of thousands of markers inevitably requires division of the problem into manageable parts facilitating parallel processing, parts corresponding to individual genetic variants, pathways, or genes, for example. Here we utilize a straightforward formulation according to which the genome is divided into blocks of nearby correlated genetic markers, tested jointly for association with the phenotypes. This formulation is computationally feasible, reduces the number of tests, and lets the methods take advantage of combining information over several correlated variables not only on the phenotype side, but also on the genotype side. Our experiments show that canonical correlation analysis has higher power than alternative methods, while remaining computationally tractable for routine use in the GWAS setting, provided the number of samples is sufficient compared to the numbers of phenotype and genotype variables tested. Sparse canonical correlation analysis and regression models with latent confounding factors show promising performance when the number of samples is small compared to the dimensionality of the data.

A novel kernel Fisher discriminant analysis: Constructing informative kernel by decision tree ensemble for metabolomics data analysis

Large amounts of data from high-throughput metabolomics experiments become commonly more and more complex, which brings an enormous amount of challenges to existing statistical modeling. Thus there is a need to develop statistically efficient approach for mining the underlying metabolite information contained by metabolomics data under investigation. In the work, we developed a novel kernel Fisher discriminant analysis (KFDA) algorithm by constructing an informative kernel based on decision tree ensemble. The constructed kernel can effectively encode the similarities of metabolomics samples between informative metabolites/biomarkers in specific parts of the measurement space. Simultaneously, informative metabolites or potential biomarkers can be successfully discovered by variable importance ranking in the process of building kernel. Moreover, KFDA can also deal with nonlinear relationship in the metabolomics data by such a kernel to some extent. Finally, two real metabolomics datasets together with a simulated data were used to demonstrate the performance of the proposed approach through the comparison of different approaches.

A new strategy of exploring metabolomics data using Monte Carlo tree

Large amounts of data from high-throughput metabolomics experiments have become commonly more and more complex, which brings a number of challenges to existing statistical modeling. Thus there is a need to develop a statistically efficient approach for mining the underlying metabolite information contained by metabolomics data under investigation. In this work, we provide a new strategy based on Monte Carlo cross validation coupled with the classification tree algorithm, which is termed as the MCTree approach. The MCTree approach inherently provides a feasible way to uncover the predictive structure of metabolomics data by the establishment of many cross-predictive models. With the help of the sample proximity matrix such obtained, it seems to be able to give some interesting insights into metabolomics data. Simultaneously, informative metabolites or potential biomarkers can be successfully discovered by means of variable importance ranking in the MCTree approach. Two real metabolomics datasets are finally used to demonstrate the performance of the proposed approach.