Missing value imputation.

Often, for biological and technical reasons (e.g., inaccurate peak detection, values under the limit of quantification, etc.), some features cannot be identified or quantified in some metabolomics and proteomics samples [19, 20]. To address this problem, several methods have been developed and compared to identify the best approaches for data imputation in this context [19–21]. POMAShiny workflow offers a missing value imputation panel composed of different operations divided into three sequential steps: 1) distinction between zeros and missing values, 2) removal of features with a high percentage of missing values, and 3) imputation of remaining missing values.

First, if the data contain zeros or a combination of zeros and missing values, users can distinguish between them by using the algorithm provided by POMAShiny. For example, if the data contain both endogenous and exogenous compounds, the exogenous ones could be a real zero if they are not in the sample (absence), while the endogenous ones are unlikely to be real zeros (since they should always be in the sample, at least in very low concentrations). In that case, users could consider zeros as real zeros and impute only the missing values in the data. However, if users do not know the exact nature of the zeros in the data, or the difference between zeros and missing values, the authors recommend considering all zeros as missing values.

Second, users are able to remove features of the data with more than a specific percentage of missing values in all the study groups (20% allowed by default). Finally, several imputation methods for dealing with the remaining missing values after the two previous steps are provided in POMAShiny. The available methods are the imputation by zero, the half minimum imputation, the imputation by median, the imputation by mean, the imputation by minimum and the k-nearest neighbours imputation (where missing values are imputed using the k-nearest neighbours algorithm [22]).

Normalization.

It is generally accepted that some factors can introduce variability in metabolomics and proteomics data. Even if the data have been generated under identical experimental conditions, this introduced variability can have a critical influence on the final statistical results, making normalization a key step in the workflow [23]. These factors include: 1) differences in orders of magnitude between measured feature concentrations, 2) differences in the fold changes in feature concentration due to the induced variability, 3) large fluctuations in the concentration of some features under identical experimental conditions, 4) technical variability, and 5) heteroscedasticity [24]. POMAShiny provides six different normalization methods widely used in this field and compared in different studies [24, 25]. Here, the normalization process comprises both the transformation and scaling of the data in a single step. The methods available for this purpose are autoscaling, level scaling, log scaling, log transformation, vast scaling, and log pareto scaling.

Outlier detection.

The last step provided in this panel is outlier detection and data cleaning. Outliers are defined as observations that are not concordant with those of the vast majority of the remaining data points [20]. Outliers in metabolomics and proteomics can be separated into biological and analytical outliers [26]. On the one hand, the first group reflects random and induced biological variations that make some observations different from others. On the other hand, the second group reflects different kinds of problems during the analytical process (e.g., sampling, storage) [26]. These values can have an enormous influence on the resultant statistical analysis, making it difficult to meet all required assumptions in the most commonly applied statistical tests as well as all required assumptions in many regression techniques and predictive modelling approaches. Therefore, outlier detection procedures are a critical point on which all subsequent analysis will depend (both inference and predictive statistics).

POMAShiny allows the analysis of outliers by different plots and tables as well as the possibility of removing statistical outliers from the analysis using different customizable parameters (see Fig 2).

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Fig 2. Screenshot of the “Outlier detection” panel showing the Euclidean distances in principal coordinate space between samples and their respective group centroid.

ST000284 example data were used to create this plot.

https://doi.org/10.1371/journal.pcbi.1009148.g002

Here, we propose an ad hoc multivariate outlier detection method based on the Euclidean distances among observations and their distances to each group centroid in a two-dimensional space (maximum, manhattan, canberra and minkowski distances are also available). Once the distances are computed, the classical univariate outlier detection formula Q₃ + x * IQR is used to detect multivariate group-dependent outliers using the computed distances to each group centroid (x; the higher this value, the less sensitive the method is to outliers) (Fig 2).

PDF report.

In an effort to facilitate the EDA process, POMAShiny includes a function to automatically generate a PDF report with a complete EDA, including all plots mentioned above. Users can generate the PDF report by clicking the “Exploratory report” button in the data upload panel.

The automatically generated PDF report provides information about the number of samples, features, covariates and the main study groups, as well as information on the percentage of total missing values in the data and the specific number of missing values per feature. Moreover, information on the number of zeros and features without variability is also provided. All the information provided in the PDF report is given in tables, plots and text format. A section with boxplots and density plots before and after missing value imputation and normalization (k-NN and log pareto scaling methods by default) is also included, providing users with valuable information about the preprocessing effect on the data. Furthermore, an outlier analysis, highly correlated features (r> 0.97), clustered heatmap and a PCA scores plot are also provided.

A POMAShiny PDF report helps users to have a quick and accurate description of the data. An example of this report is included as a vignette in the POMA package and it is also available at POMA’s GitHub repository.

Univariate analysis.

POMAShiny offers four widely used methodologies for performing classical parametric and non-parametric univariate tests. On the one hand, T-test (two-group analysis) and ANOVA (> 2 group analysis) methods are available to perform parametric tests. In the ANOVA tab, an ANCOVA (analysis of covariance) model is also computed if covariates are included in the target file. On the other hand, the Mann-Whitney U test (two-group analysis) and Kruskal-Wallis test (>2 group analysis) are available for non-parametric analysis. Each of these methodologies offers customizable parameters to adjust the analysis to users and data requirements. Due to the large number of tests performed in these types of analyses, the FDR (false discovery rate) method is used to compute adjusted p-values.

Limma.

Limma (linear models for microarray data) is a univariate method created for the statistical analysis of gene expression experiments as microarrays [30]. In recent years, this approach has become the main choice for many researchers to explore and identify differential expressed genes between two conditions. Due to the many similarities between metabolomics, proteomics and microarray data (often hundreds of features and small sample sizes, quantitative data, etc.), limma can be used in metabolomics and proteomics data sets when they meet the requirements (e.g., feature normal distributions). POMAShiny allows users to perform limma models easily and include covariates in the model, if necessary. If covariates are provided in the target file (e.g., batch effects, sex, age), two limma models—with and without covariates—are computed automatically, including the covariates in the model in the order in which they are provided in the target file (the further to the left, the more importance in the model). An interactive volcano plot based on the limma results is also generated in this tab.

Multivariate analysis.

Multivariate methods focus analyses on the observation of more than one feature at a time, taking into account the different relationships between features. These methods can provide information about the structure of the data and different internal relationships that would not be observed with univariate statistics. However, the interpretation of these analyses can be more complex.

The most frequently used multivariate methodologies in metabolomics and proteomics statistical analysis are PCA, for unsupervised analysis, and PLS (partial least squares), for supervised analysis [31]. POMAShiny provides a collection of three different multivariate approaches powered by the mixOmics Bioconductor package [32]. The provided methods are PCA, PLS-DA (partial least squares discriminant analysis), and sPLS-DA (sparse partial least squares discriminant analysis).

PCA is an unsupervised method for dimension reduction that is done by calculating the data covariance matrix and performing eigenvalue decomposition on this covariance matrix without considering sample groups. In contrast, PLS-DA is a supervised method that uses the multiple linear regression method to find the direction of maximum covariance between the data and sample group [33]. sPLS-DA has been presented elsewhere [34] as an extension of sPLS (sparse partial least squares) [35] designed for classification problems. Note that while PCA is often used in exploratory data analysis, PLS-DA and sPLS-DA are used for classification and feature selection purposes, respectively. Several tuning parameters are available in all multivariate methods provided in POMAShiny. Users can define the number of components to compute, numerous graphical parameters, the number of features to select (in sPLS-DA), the VIP (variable importance in the projection) cut-off (in PLS-DA) and the cross-validation method to use, including both leave-one-out (LOO) and k-fold cross-validation.

Cluster analysis.

Cluster analysis is also composed of multivariate methods, however this section is separated from multivariate methods to make POMAShiny structure clearer and more intuitive. The cluster analysis provided in POMAShiny allows users to explore different clusters in the data using the k-means algorithm [36]. k-means is an unsupervised method aimed at assigning all samples of the study to k clusters based on the sample means. By default, the optimal number of clusters (k) is determined through the popular “elbow method”. Alternatively, users can define a specific number of clusters.

To provide a multivariate visualization of computed clusters, POMAShiny projects these clusters in the first two dimensions of a multidimensional scaling (MDS) plot [37]. Many user-customizable parameters are offered to define the distance used in MDS calculation. POMAShiny provides a table with the assigned cluster to each sample and an interactive MDS plot with computed clusters. This feature serves the users both in terms of cluster analysis and in calculating a classic MDS, integrating two useful functionalities within the same tab. As mentioned before, this method can also be useful in EDA.

Correlation analysis.

Correlation analysis is usually one of the preferred options for evaluating the strength of relationships between different features [38].

POMAShiny provides different approaches to conducting an accurate correlation analysis. First, POMAShiny provides a highly customizable and interactive scatterplot of pairwise correlation between features (Fig 3). Here, users can select two different features and explore them in a very comfortable way, as they are able to remove some points of the plot by clicking on them, drawing a smooth line based on a linear model, and exploring pairwise correlations within each study group and among factorial covariates (if they are provided). A downloadable table with all pairwise correlations between features is also provided. Moreover, POMAShiny provides a global correlation plot (or correlogram) and a network correlation plot. For all of the above methods and options, the three most common methods for calculating correlation coefficients—Pearson, Spearman and Kendall—are available.

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Fig 3. Screenshot of the “Correlation Analysis” panel showing an interactive scatterplot of pairwise correlation between acetoacetate and epinephrine in the three different study groups “CRC”, “Healthy” and “Polyp”.

ST000284 example data were used to create these plots.

https://doi.org/10.1371/journal.pcbi.1009148.g003

Lastly, POMAShiny provides an alternative method for correlation network visualization in this tab. Estimation of Gaussian graphical models (GGMs) through the glasso R package [39] is also provided here. Thus, users can define the regularization parameter to estimate a sparse inverse correlation matrix using LASSO [40] and visualize the resultant GGM in a network plot.

Regularized regression.

Regularized regression is a type of regression that shrinks the coefficient estimates towards zero, providing less complex and flexible models but avoiding the risk of overfitting. POMAShiny offers three different regularization strategies: LASSO, ridge regression and elasticnet.

LASSO (least absolute shrinkage and selection operator) is a regression analysis method that sets some coefficients to zero, providing more compact and interpretable models [40, 41]. Because of that, LASSO is a very good approach for the statistical analysis of metabolomics and proteomics data, both in terms of feature selection and prediction model performance.

POMAShiny provides a function based on the glmnet R package [42] that allows users to create LASSO logistic regression models (two-group analysis) both for feature selection and prediction model purposes. If the purpose is not predictive, users can set the test set parameter to zero and the function will return interactive plots and tables referring to the LASSO model created using all samples of the study. Otherwise, if the purpose is to build a predictive model, users can select the proportion of samples that will be used as a test set. In the second case, POMAShiny will fit a LASSO model without using the test set and using it only to perform an external validation, providing users with numerous real prediction metrics (accuracy, accuracy confidence intervals, sensitivity, specificity, etc.). Alternatively, users can also perform elasticnet (defining a penalty parameter) and ridge regression models in the same tab. For all regularized regression strategies provided in POMAShiny, the lambda parameter is chosen automatically through internal k-fold cross-validation.

Random forest.

In recent years, machine learning algorithms such as random forest have become very common in the analysis of omics data. These algorithms are constantly used both to rank the importance of features and to create prediction models. POMAShiny provides a classification random forest algorithm [43] designed for the creation of prediction models to classify between two or more groups. This feature allows users to easily split data into train and test sets, where a train set is used to create the model and a test set is used only to perform an external validation. POMAShiny’s random forest tab provides different tables and interactive plots with model metrics and the importance of features in the classification. In addition, the classification algorithm provided by POMAShiny returns the model confusion matrix and errors calculated using the test set, providing a real measure of model accuracy.

Odds ratio.

Odds ratio (OR) calculation can be very helpful in visualizing and exploring the individual feature effects on the study outcome. POMAShiny includes an option to calculate OR based on a logistic regression model (two-group analysis). By changing the function parameters, users can easily define those features that will be included in the model and the ability to include study covariates in the model.

Rank products.

The rank product is a statistical non-parametric test based on ranks of fold changes. This method has been used for several years to detect differentially expressed genes in microarray experiments [44]. However, in recent years this methodology has also become popular in other omics fields such as transcriptomics, metabolomics and proteomics [45]. POMAShiny includes an option to calculate rank products both for paired and unpaired samples with a set of customizable parameters. This function provides both tables and interactive plots showing the upregulated and downregulated features, respectively.