Robust volcano plot: identification of differential metabolites in the presence of outliers
Abstract
Background
The identification of differential metabolites in metabolomics is still a big challenge and plays a prominent role in metabolomics data analyses. Metabolomics datasets often contain outliers because of analytical, experimental, and biological ambiguity, but the currently available differential metabolite identification techniques are sensitive to outliers.
Results
We propose a kernel weight based outlierrobust volcano plot for identifying differential metabolites from noisy metabolomics datasets. Two numerical experiments are used to evaluate the performance of the proposed technique against nine existing techniques, including the ttest and the KruskalWallis test. Artificially generated data with outliers reveal that the proposed method results in a lower misclassification error rate and a greater area under the receiver operating characteristic curve compared with existing methods. An experimentally measured breast cancer dataset to which outliers were artificially added reveals that our proposed method produces only two nonoverlapping differential metabolites whereas the other nine methods produced between seven and 57 nonoverlapping differential metabolites.
Conclusion
Our data analyses show that the performance of the proposed differential metabolite identification technique is better than that of existing methods. Thus, the proposed method can contribute to analysis of metabolomics data with outliers. The R package and user manual of the proposed method are available at https://github.com/nishithkumarpaul/Rvolcano.
Keywords
Metabolomics Differential metabolites Fold change Classical volcano plot Receiver operating characteristic (ROC) curveAbbreviations
 ANOVA
Analysis of variance
 AUC
Area under the ROC curve
 BRIDGE
Bayesian robust inference for differential gene expression
 CVP
Classical volcano plot
 FC
Fold change
 FCROS
Fold change rank ordering statistics
 FNR
False negative rate
 FPR
False positive rates
 GCMS
Gas chromatography mass spectrometry
 GCTOFMS
Gas chromatography with timeofflight mass spectrometry
 KW
Kruskal–Wallis
 LCMS
Liquid chromatography mass spectrometry
 Limma
Linear models for microarray
 MER
Misclassification error rate
 NIH
National institute of health
 pAUC
Partial area under the ROC curve
 ROC
Receiver operating characteristic
 RVP
Robust volcano plot
 SAM
Significant analysis of microarray
 SVM
Support vector machine
 TNR
True negative rate
 TPR
True positive rates
Background
In bioinformatics, molecular omics studies like genomics, transcriptomics, proteomics and metabolomics are playing a prominent role in life sciences, health and biological research [1]. Among these approaches, metabolomics is frequently used to understand biological metabolic status, making a direct link between genotypes and phenotypes [2]. Many metabolomicsbased biomarker discoveries have explored the key metabolites to discriminate between metabolic diseases, such as diabetes, cardiovascular diseases, and cancers [3]. The metabolites showing different concentrations among the given groups (e.g. healthy and disease subjects) is called as differential metabolites. Combinations of these metabolites can be used to identify subjects with a high risk of suffering from diabetes [4]. Thus, one of the most important tasks of metabolomics research is to identify a differential metabolite or a set of differential metabolites which have ability to differentiate patients with a disease from healthy subjects. The accurate identification of differential metabolites, or molecules that reflect a specific phenotype, is a cornerstone of many applications, such as predicting disease status and drug discovery [5, 6, 7, 8].
To generate highthroughput metabolomics data, nuclear magnetic resonance (NMR) and hyphenated mass spectrometry (MS), such as gas chromatographyMS (GCMS) and liquid chromatographyMS (LCMS), are commonly used. These platforms can simultaneously identify and quantify hundreds of metabolites. All these analytical platforms can result in missing values in the observed data and outliers, which are caused by various reasons including analytical, experimental, and human errors, low quality measurements, malfunctioning equipment, and overlapping signals [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]. Thus, subsequent metabolomics data analysis should consider the presence of these problems in the given data.
Four types of statistical procedure have primarily been used to identify differential metabolites: (i) classical parametric approaches, such as Student’s ttest [21], classical volcano plot (CVP) [22] and fold change rank ordering statistics (FCROS) [23], (ii) classical nonparametric approaches, such as significance analysis of microarrays (SAM) [24], and the Wilcoxon [25] and KruskalWallis (KW) [26] tests, (iii) Bayesian parametric approaches, such as Bayesian robust inference for differential gene expression (BRIDGE) [27], empirical Bayes methods for microarrays (EBarrays) [28], and linear models for microarrays (Limma) [29], and (iv) Bayesian nonparametric approaches [30, 31]. In classical procedures, differential metabolites are identified using pvalues (significance levels) that are estimated based on the distribution of a test statistic or a permutation, whereas in Bayesian procedures, differential metabolites are identified using posterior probabilities. However, most of the aforementioned techniques are not robust against outliers [27, 32]. Thus, they may produce misleading results in the presence of outlying samples or irregular concentrations of metabolites. Moreover, outlying samples or irregular concentrations of metabolites may violate the normality assumption in metabolomics datasets. Several nonparametric approaches (Wilcoxon and KW test) and some Bayesian approaches (BRIDGE and Robust limma) are robust against outliers; however, increases in the number of outliers in these techniques reduce the accuracy of differential metabolite identification. One of the easiest ways to overcome this problem is to delete the outlying metabolites or outlying samples from the dataset. However, the deleted metabolites may be important metabolites in some cases, while deleting samples and metabolites can make the dataset much smaller or even vanish.
Comparatively, CVP [22] is a good technique for identifying differential metabolites because it can control the false discovery rate [33]. The volcano plot is based on pvalues from a ttest and foldchange (FC) values [34], both of which depend on classical location and scatter, and thus volcano plot is affected by outliers. Therefore, in this paper, we develop an outlierrobust volcano plot by unifying CVP and a kernel weight function to overcome the problem of outliers. The advantage of the proposed method compared to existing methods is that it performs considerably better in the presence of outliers. We introduced a kernel weight function, which plays a key role in the performance of the proposed method. Robust volcano plot ensures robustness by producing smaller weights for outlying observations from the kernel weight function. Appropriate selection of the tuning parameter for the kernel function also improves the performance of the proposed method, as discussed later.
Since metabolomics dataset frequently contains outliers and all of the existing differential metabolite identification techniques are more or less influenced by outliers; as a result, outliers reduce the accuracy of differential metabolite identification. Therefore, in this paper we develop a kernel weight based outlierrobust volcano plot for detecting differential metabolites from metabolomics datasets in the presence of outliers. To measure the performance of the proposed method in comparison with other techniques, we consider nine existing differential metabolite identification techniques: three classical parametric approaches (ttest, FCROS, CVP), three nonparametric approaches (Wilcoxon test, KW test, SAM) and three Bayesian approaches (BRIDGE, Limma, EBarrays). We also evaluate the performance of the proposed method using both artificially generated and experimentally measured metabolomics datasets in the absence and presence of outliers. Every metabolite identification method has a specific cutoff and its choices are sensitive to determine the metabolite identification which has large effect on the statistical analyses. In this paper, the cutoff of ttest, SAM, Wilcoxon test and KW test have been taken as Bonferroni corrected pvalue < 0.05. According to Dembélé et al. [23] we declared those metabolites as differential whose fvalue is close to 0 or 1 and if fvalue is close to 0.5 we took those metabolites as non differential. For CVP, a metabolite was said to be differential if pvalue < 0.05 and  log_{2} (foldchange)  > 1. For Bayesian approaches we took the cutoff of Bonferroni corrected posterior probabilities > 0.95.
Methods
In this paper, a kernel weight based outlierrobust volcano plot is developed for detecting differential metabolites. To reduce the family wise error rate when comparing the performance of the proposed method with existing differential metabolite identification techniques, the pvalues are adjusted using Bonferroni correction. The algorithm for outlierrobust volcano plot is given below.
Outlierrobust volcano plot (proposed)
We extend volcano plot by introducing a kernel weight function behind CVP. Classical volcano plot identifies differential metabolites using the ttest and foldchange (FC) methods, and plots log_{2} (foldchange) on the Xaxis against log_{10} (pvalue) from the ttest on the Yaxis. Because the tstatistic depends on mean and variance and foldchange depends on mean, CVP is heavily influenced by outliers. Therefore, we use the kernel weighted average and variance instead of the classical mean and variance in the tstatistic and foldchange functions, and also plot log_{ 2 } foldchange on the Xaxis and log_{10} (pvalue) from the ttest on the Yaxis. We refer to this procedure as robust volcano plot (RVP).
The value from eq. (2) is compared with Student’s tvalue with n − 2 degrees of freedom.

Step − 1. Calculate log_{ 2 } (fold change) for the ith metabolite as \( {\log}_2\left({FC}_i\right)={\log}_2\left(\frac{{\overline{X}}_i^D}{{\overline{X}}_i^C}\right), \) where \( {\overline{X}}_i^D=\sum \limits_{j={g}_1+1}^n{w}_j{x}_{ij}/\left(n{g}_1\right) \) represents the weighted average intensity of the ith metabolite for the disease group and \( {\overline{X}}_i^C=\sum \limits_{j=1}^{g_1}{w}_j{x}_{ij}/{g}_1 \) represents the weighted average intensity of the ith metabolite for the control group.

Step − 2. Using the weighted average and weighted variance instead of the classical mean and variance, calculate log_{10}(pvalue) for the ith metabolite from the ttest using eqs. (2), (3) and (4), where \( {S}_{iC}^2=\sum \limits_{j=1}^{g_1}{w}_j{\left({x}_{ij}{\overline{X}}_i^C\right)}^2/\left({g}_11\right) \) and \( {S}_{iD}^2=\sum \limits_{j={g}_1+1}^n{w}_j{\left({x}_{ij}{\overline{X}}_i^D\right)}^2/\left(n{g}_11\right). \)

Step − 3. Draw a scatter plot with log_{2} (foldchange) on the Xaxis and log_{10} (pvalue) from the ttest on the Yaxis. This plot is considered to be an outlierrobust volcano plot (RVP). A metabolite is said to be differential if pvalue < 0.05 and  log_{2} (foldchange)  > 1.
The R package of the proposed method with its user manual is available at https://github.com/nishithkumarpaul/Rvolcano.
Any user can install the “Rvolcano” package in R platform from the GitHub using the following code
library(devtools)
install_github("Rvolcano","nishithkumarpaul")
library(Rvolcano)
To draw the robust volcano plot using the package, the user manual is available at GitHub website.
Dataset description
In this paper, we use an artificially generated dataset and an experimentally measured metabolomics dataset to evaluate the performance of the proposed method in comparison with nine other methods.
Artificial data
In this study, as in [6], we generate an artificial metabolomics dataset using a oneway ANOVA model y_{ ijk } = μ_{ i } + g_{ ij } + ∈_{ ijk }, where y_{ ijk } is the intensity of the i^{th} metabolite, j^{th} group and k^{th} sample, μ_{ i } denotes the overall intensity of metabolite i, g_{ ij } is the j^{th} group effect for the i^{th} metabolite, and ∈_{ ijk } is a random error term. In this linear model, μ_{ i } ~ uniform (10, 20) and ∈_{ ijk } ~ N(0,1). The disease and control group effects for increased concentrations of metabolites are g_{ ij } = N(4, 1) and g_{ ij } = N(2, 1), respectively; for decreased concentrations of metabolites, we use g_{ ij } = N(2, 1) and g_{ ij } = N(4, 1) for the disease and control groups, respectively. Both group effects for nondifferential (equal concentration) metabolites are g_{ ij } = N(0, 1). To create the artificial metabolomics dataset, we designated 130 metabolites as nondifferential and 20 metabolites as differential (having differential concentrations). The dataset contained 70 subjects with 40 subjects in group1 and 30 subjects in group2. To investigate the performance of the proposed method under different conditions, outliers were randomly distributed in the artificially generated data matrix at different rates (5%, 10%, 15%, 20%, and 25%). Note that these outliers can fall anywhere in the data matrix. The outliers for the ith metabolite were taken from a normal distribution with mean 3*μ_{ i } and variance \( {\sigma}_i^2 \), i.e. N (3*μ_{ i }, \( {\sigma}_i^2 \)), where μ_{i} and \( {\sigma}_i^2 \) are the mean and variance of the ith metabolite. In total, 500 artificial datasets were generated for each condition, and the performance of the proposed method was evaluated using these datasets.
Experimentally measured data
In this paper, we considered a wellknown publicly available metabolomics dataset for breast cancer serum data and control serum data containing metabolite abundance level measurements from different subjects. This dataset is available from the National Institute of Health (NIH) data repository and was collected by the University of Hawaii Cancer Center under study ID ST000356. The data were measured using a gas chromatography with timeofflight mass spectrometry (GCTOFMS) instrument and quantified using the ChromaTOF software (v4.33, Leco Co, CA, USA). The dataset contains 134 subjects (103 breast cancer without any treatment and 31 control subjects) and 101 metabolites. Autoscaling was used to reduce the systematic variation in the dataset. To investigate the performance of the proposed method under different conditions, we also modified the dataset by changing 5%, 10%, and 15% of the real values by N(4 × μ_{ i }, σ_{ i }^{ 2 }), where μ_{ i } and σ_{ i }^{ 2 } are the mean and variance of the ith metabolite in the breast cancer data matrix.
Results and discussion
The performance of our proposed method was compared with nine existing methods using both the artificial and experimental datasets.
Performance evaluation based on artificially generated data
Performance evaluation based on experimentally measured data
Literature review of cyclohexanone metabolite associated diseases
Authors  Disease  Title of the paper  Journal name 

Westhoff et al., 2010 [35]  Lung cancer  Differentiation of chronic obstructive pulmonary disease (COPD) including lung cancer from healthy control group by breath analysis using ion mobility spectrometry  International Journal for Ion Mobility Spectrometry 
Wei et al., 2012 [36]  Prostate cancer  Effects of cyclohexanone analogues of curcumin on growth, apoptosis and NFκB activity in PC3 human prostate cancer cells  Oncology letters 
Leung et al. 2012 [37]  Breast cancer  Identification of cyclohexanone derivatives that act as catalytic inhibitors of topoisomerase I: effects on tamoxifenresistant MCF7 cancer cells  Investigational new drugs 
Wang et al., 2014 [26]  Breast cancer  Volatile Organic Metabolites Identify Patients with Breast Cancer, Cyclomastopathy, and Mammary Gland Fibroma  Scientific Report (Nature) 
Mochalski et al., 2014 [38]  Renal disease  Blood and breath profiles of volatile organic compounds in patients with endstage renal disease  BMC Nephrology 
Liu et al., 2014 [39]  Lung cancer  Investigation of volatile organic metabolites in lung cancer pleural effusions by solidphase microextraction and gas chromatography/mass spectrometry  Journal of Chromatography 
Silva et al., 2017 [40]  Breast cancer  Volatile metabolomic signature of human breast cancer cell lines  Scientific Report (Nature) 
Conclusions
Outlying observations weaken the performance of existing differential metabolite identification techniques. In this paper, we have proposed a new outlierrobust differential metabolite identification technique for identifying differential metabolites in the presence of outliers. To investigate the performance of our proposed method, we analyzed artificial data and experimental data in the absence and presence of outliers. We also compared the performance of our proposed method with nine existing differential metabolite identification techniques using the ROC curve, and the average MER, AUC and pAUC values. Both the artificial and experimental data analysis show that our proposed method performed better. The proposed RVP also identified an additional metabolite (cyclohexanone) that was overlooked by CVP, and it has been shown that this metabolite is associated with several cancer diseases. We recommend using the proposed method to identify differential metabolites from noisy metabolomics datasets.
Notes
Acknowledgements
We thank Peter Humphries, PhD, from Edanz Group (www.edanzediting.com/ac) for editing a draft of this manuscript.
Funding
Not applicable
Availability of data and materials
The R package of the proposed method and a detail documented user manual of the package are available at https://github.com/nishithkumarpaul/Rvolcano.
Authors’ contributions
All the authors worked together to develop the robust volcano plot technique. NK analyzed the data, drafted the manuscript, and implemented the statistical analysis. MAH and MS coordinated and supervised the project. All authors read and approved the final manuscript.
Ethics approval and consent to participate
Not applicable
Consent for publication
Not applicable
Competing interests
The authors declare that they have no competing interests.
Supplementary material
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