Univariate and Multivariate Analysis in Untargeted Metabolomics

In metabolomics research, untargeted approaches employ univariate and multivariate analysis to comprehensively analyze complex metabolic profiles. Univariate Analysis assesses individual metabolite changes across experimental conditions, employing statistical tests like the T-test and Wilcoxon test to identify significant alterations. This method not only highlights potential biomarkers but also provides insights into specific metabolic pathways affected by diseases or environmental factors. Conversely, Multivariate Analysis integrates data from multiple metabolites, using techniques such as Principal Component Analysis (PCA) and Partial Least Squares Discriminant Analysis (PLS-DA) to uncover broader patterns and interactions within metabolomics datasets. By capturing complex relationships and discriminatory features, multivariate analysis enhances our understanding of metabolic networks and aids in personalized medicine by identifying biomarkers and therapeutic targets tailored to individual metabolic profiles.

Define of Untargeted Metabolomics

Untargeted metabolomics is a comprehensive analytical approach that aims to identify and quantify a wide array of metabolites within a biological sample without prior knowledge of their identities. Unlike targeted metabolomics, which focuses on pre-selected metabolites, untargeted metabolomics provides an unbiased, global overview of the metabolome, encompassing diverse classes of small molecules such as lipids, amino acids, carbohydrates, and nucleotides.

Utilizing advanced technologies like mass spectrometry (MS) and nuclear magnetic resonance (NMR) spectroscopy, untargeted metabolomics generates extensive datasets that capture the dynamic and complex nature of metabolic networks. This approach is pivotal in discovering novel biomarkers, understanding metabolic pathways, and elucidating the metabolic responses to diseases, environmental changes, and therapeutic interventions. By analyzing the entire spectrum of metabolites, untargeted metabolomics offers a holistic view of the biochemical state of an organism, enabling deeper insights into systems biology and precision medicine.

Importance of Univariate and Multivariate Analysis

Univariate and multivariate analyses are indispensable tools in untargeted metabolomics, each offering unique strengths for interpreting complex metabolic data. Univariate analysis evaluates individual metabolites independently across different conditions, using statistical tests like the T-test and Wilcoxon test to identify significant changes. This method is crucial for pinpointing specific biomarkers that exhibit notable variations in response to diseases, treatments, or environmental factors, providing a clear and rigorous framework for initial data exploration. By focusing on individual metabolites, univariate analysis simplifies the interpretation process and ensures statistical robustness, making it an essential starting point for further biochemical and clinical investigations.

In contrast, multivariate analysis considers multiple metabolites simultaneously, uncovering complex interactions and patterns within the data. Techniques such as PCA and PLS-DA reduce the dimensionality of metabolomics datasets, revealing broader metabolic shifts and network interactions that might be overlooked by univariate methods. This holistic approach enhances the discriminatory power to distinguish between different biological states or experimental groups, making it vital for identifying subtle metabolic differences and potential biomarkers. Multivariate analysis not only identifies patterns within the data but also quantifies the importance of each metabolite in distinguishing conditions, thereby accelerating biomarker discovery and deepening the understanding of their biological relevance. Together, these complementary analyses enable a comprehensive interpretation of metabolic profiles, advancing biomarker discovery, disease understanding, and personalized medicine.

Univariate Analysis Methods

Univariate analysis methods are fundamental in untargeted metabolomics, offering a means to evaluate the statistical significance of individual metabolites across different experimental conditions. These methods are essential for identifying metabolites that exhibit significant changes in response to diseases, treatments, or environmental factors. Key univariate analysis methods include T-tests, Wilcoxon tests, and Analysis of Variance (ANOVA), each serving specific purposes based on data characteristics.

T-Tests

T-tests are widely used when comparing the means of two groups to determine if they are statistically different from each other. There are two main types of T-tests used in metabolomics:

• Independent Samples T-Test: This test compares the means of two independent groups, such as a control group and a treatment group. It assumes that the data follows a normal distribution and that the variances of the two groups are equal. For example, comparing the metabolite levels in a group of patients before and after a specific treatment can reveal which metabolites are significantly affected by the treatment.
• Paired Samples T-Test: This test is used when the data consists of paired samples, such as measurements taken from the same subjects at two different time points. It accounts for the fact that the samples are not independent but related. For instance, it can be used to compare metabolite levels in patients before and after a surgical procedure, providing insights into metabolic changes induced by the surgery.

Wilcoxon Tests

Wilcoxon tests are non-parametric alternatives to T-tests, used when the data does not meet the assumptions of normality. These tests are particularly useful for metabolomics data, which often do not follow a normal distribution. There are two main types of Wilcoxon tests:

• Wilcoxon Rank-Sum Test (Mann-Whitney U Test): This test is used for comparing two independent groups, similar to the independent samples T-test, but without assuming normal distribution. It ranks all the values from both groups together and then compares the sum of ranks between the groups. This method is robust against outliers and skewed data distributions, making it suitable for metabolomics studies where data variability is high.
• Wilcoxon Signed-Rank Test: This test is used for paired or matched samples, similar to the paired samples T-test. It assesses whether the differences between pairs of observations are symmetrically distributed around zero. This is useful for analyzing metabolite levels in paired samples, such as measurements taken from the same subjects at different times or under different conditions.

Analysis of Variance (ANOVA)

ANOVA is used to compare the means of three or more groups to determine if at least one group mean is significantly different from the others. It is a powerful method for handling complex experimental designs and is particularly useful in metabolomics studies involving multiple experimental conditions or treatment groups.

• One-Way ANOVA: This test compares the means of three or more independent groups based on one factor. For example, it can be used to compare metabolite levels across different treatment durations or doses.
• Two-Way ANOVA: This test assesses the effects of two independent factors simultaneously and can evaluate the interaction between them. This is useful in studies where two different variables, such as treatment type and time, are considered together to understand their combined effect on metabolite levels.

Volcano Plots

Volcano plots are a visual representation of univariate analysis results, plotting the magnitude of change (log2 fold change) against statistical significance (-log10 p-value) for each metabolite. Metabolites with large changes and high significance appear as points far from the origin, making it easy to identify potential biomarkers. These plots provide an intuitive way to visualize and interpret univariate analysis results, highlighting metabolites that warrant further investigation.

Correction for Multiple Testing

In untargeted metabolomics, thousands of metabolites are tested simultaneously, increasing the risk of false positives. Therefore, multiple testing correction methods, such as the Bonferroni correction and Benjamini-Hochberg procedure, are applied to adjust p-values and control the false discovery rate (FDR). This ensures that the identified significant metabolites are truly associated with the experimental conditions rather than being false positives due to multiple comparisons.

• Bonferroni Correction: This method is highly stringent and adjusts the significance threshold by dividing the desired alpha level (e.g., 0.05) by the number of tests performed. While it reduces the likelihood of false positives, it can be overly conservative and increase the risk of false negatives.
• Benjamini-Hochberg Procedure: This method controls the FDR, balancing the discovery of significant results with the rate of false positives. It ranks the p-values and applies a less stringent correction compared to Bonferroni, making it more suitable for large-scale metabolomics studies.

Multivariate Analysis Methods

Multivariate analysis methods are essential in untargeted metabolomics for examining the intricate relationships between multiple metabolites and understanding the broader patterns within complex datasets. These methods allow researchers to capture the interactions and correlations among metabolites, offering a comprehensive view of the metabolic changes occurring under different biological conditions. Key multivariate analysis techniques include PCA, PLS-DA, and Random Forest, each providing unique insights and advantages.

Untargeted metabolomics and multivariate data analysis (Nan et al., 2022).

Principal Component Analysis (PCA)

PCA is an unsupervised method used to reduce the dimensionality of metabolomics data while preserving as much variance as possible. By transforming the original variables into a new set of orthogonal components, PCA simplifies the dataset and highlights the most significant sources of variation.

• Dimensionality Reduction: PCA projects the high-dimensional data into a lower-dimensional space, typically into two or three principal components (PCs). These PCs capture the maximum variance in the data, allowing researchers to visualize complex datasets in a simpler form.
• Pattern Recognition: By plotting the scores of the first few PCs, PCA enables the identification of patterns and clusters within the data. This can reveal natural groupings of samples, such as different treatment groups or disease states, based on their metabolic profiles.
• Outlier Detection: PCA can also help identify outliers that deviate significantly from the main data clusters. Outliers may indicate experimental errors, sample contamination, or unique biological variations, warranting further investigation.

Partial Least Squares Discriminant Analysis (PLS-DA)

PLS-DA is a supervised method that combines features of PCA with discriminant analysis to maximize the separation between predefined groups. Unlike PCA, which only considers the variance within the data, PLS-DA also incorporates information about the group labels, making it particularly powerful for classification and biomarker discovery.

• Classification: PLS-DA models the relationship between metabolite levels (X matrix) and the group membership (Y matrix), optimizing the separation between groups. This method is highly effective in distinguishing between different biological conditions, such as healthy vs. diseased states.
• Variable Importance in Projection (VIP) Scores: PLS-DA provides VIP scores for each metabolite, indicating their contribution to the model and their importance in distinguishing between groups. Metabolites with high VIP scores are considered potential biomarkers and are prioritized for further validation.
• Interpretability: The loadings plot in PLS-DA helps interpret the relationship between metabolites and the experimental conditions. By examining the metabolites that contribute most to the separation, researchers can gain insights into the underlying biological mechanisms.

Random Forest

Random Forest is an ensemble learning method based on decision trees, widely used for classification and regression tasks. In metabolomics, Random Forest can handle complex datasets with many variables and interactions, making it a robust tool for biomarker discovery and predictive modeling.

• Ensemble Learning: Random Forest constructs multiple decision trees using bootstrap sampling and random feature selection. The final model aggregates the predictions of individual trees, improving accuracy and reducing overfitting.
• Feature Importance: Random Forest calculates the importance of each metabolite based on its contribution to the model's accuracy. Metabolites with high importance scores are key discriminators between groups, guiding the selection of biomarkers.
• Robustness: Random Forest is resilient to noise and can handle non-linear relationships between metabolites. This robustness makes it suitable for metabolomics data, which often exhibits complex and non-linear patterns.

Orthogonal Partial Least Squares Discriminant Analysis (OPLS-DA)

OPLS-DA is an extension of PLS-DA that separates the predictive variation (related to group differences) from the orthogonal variation (unrelated to group differences). This enhances model interpretability and reduces complexity.

• Improved Interpretability: By filtering out the orthogonal variation, OPLS-DA simplifies the model and focuses on the variation that is directly related to the group differences. This makes it easier to identify the key metabolites driving the separation.
• Enhanced Model Performance: OPLS-DA often improves the predictive performance and robustness of the model compared to PLS-DA, providing clearer insights into the metabolic changes associated with different conditions.

Visualization and Interpretation

The results of multivariate analyses are often visualized using score plots, loading plots, and importance plots. These visualizations facilitate the interpretation of complex data and the identification of meaningful patterns.

• Score Plots: These plots display the samples in the space of the principal components or latent variables, revealing group separations and clusters. They are essential for assessing the model's ability to discriminate between groups.
• Loading Plots: Loading plots illustrate the contribution of each metabolite to the principal components or latent variables. They help identify which metabolites are most influential in driving the separation between groups.
• Importance Plots: In Random Forest, importance plots rank the metabolites based on their importance scores, highlighting the key variables that contribute to the classification or regression task.

Reference

1. Nan, Wengang, et al. "Myristoyl lysophosphatidylcholine is a biomarker and potential therapeutic target for community-acquired pneumonia." Redox biology 58 (2022): 102556.