bio-metabolomics-statistical-analysis

Version Compatibility

Reference examples tested with: R stats (base), ggplot2 3.5+

Before using code patterns, verify installed versions match. If versions differ:

• R: packageVersion('<pkg>') then ?function_name to verify parameters

If code throws ImportError, AttributeError, or TypeError, introspect the installed

package and adapt the example to match the actual API rather than retrying.

Metabolomics Statistical Analysis

Univariate Analysis

Goal: Identify differentially abundant metabolites between experimental groups using feature-wise statistical tests.

Approach: Apply t-tests to each feature independently, then correct for multiple testing with Benjamini-Hochberg FDR.

"Find the differentially abundant metabolites between my groups" → Apply univariate and multivariate statistical methods to identify metabolites with significant abundance differences.

library(tidyverse)

# Load normalized data
data <- read.csv('normalized_data.csv', row.names = 1)
groups <- factor(read.csv('sample_info.csv')$group)

# T-test for each feature
ttest_results <- apply(data, 2, function(x) {
    test <- t.test(x ~ groups)
    c(pvalue = test$p.value,
      fc = mean(x[groups == levels(groups)[2]]) - mean(x[groups == levels(groups)[1]]))
})
ttest_results <- as.data.frame(t(ttest_results))
ttest_results$fdr <- p.adjust(ttest_results$pvalue, method = 'BH')

# Significant features
sig_features <- ttest_results[ttest_results$fdr < 0.05, ]
cat('Significant features (FDR<0.05):', nrow(sig_features), '\n')

Fold Change Calculation

Goal: Quantify the magnitude and direction of abundance changes between groups.

Approach: Compute group means for each feature and calculate log2 fold change as the ratio of group means.

# Calculate fold change between groups
calculate_fc <- function(data, groups) {
    group_means <- aggregate(data, by = list(groups), FUN = mean, na.rm = TRUE)
    rownames(group_means) <- group_means$Group.1
    group_means <- group_means[, -1]

    fc <- as.numeric(group_means[2, ]) / as.numeric(group_means[1, ])
    log2fc <- log2(fc)

    return(data.frame(feature = colnames(data), fold_change = fc, log2fc = log2fc))
}

fc_results <- calculate_fc(data, groups)

Volcano Plot

Goal: Visualize both statistical significance and effect size for all features in a single plot.

Approach: Plot log2 fold change (x-axis) vs -log10 p-value (y-axis), highlighting features passing both thresholds.

library(ggplot2)

# Combine statistics
results <- merge(ttest_results, fc_results, by.x = 'row.names', by.y = 'feature')
results$significant <- results$fdr < 0.05 & abs(results$log2fc) > 1

# Plot
ggplot(results, aes(x = log2fc, y = -log10(pvalue), color = significant)) +
    geom_point(alpha = 0.6) +
    scale_color_manual(values = c('gray', 'red')) +
    geom_hline(yintercept = -log10(0.05), linetype = 'dashed') +
    geom_vline(xintercept = c(-1, 1), linetype = 'dashed') +
    labs(x = 'Log2 Fold Change', y = '-log10(p-value)', title = 'Metabolomics Volcano Plot') +
    theme_bw()

ggsave('volcano_plot.png', width = 8, height = 6)

PCA

Goal: Explore overall sample variation and detect outliers or batch effects in an unsupervised manner.

Approach: Perform PCA on the feature matrix and plot the first two principal components colored by experimental group.

library(pcaMethods)

# PCA
pca_result <- pca(data, nPcs = 5, method = 'ppca')

# Scores plot
scores <- as.data.frame(scores(pca_result))
scores$group <- groups

ggplot(scores, aes(x = PC1, y = PC2, color = group)) +
    geom_point(size = 3) +
    stat_ellipse(level = 0.95) +
    labs(x = paste0('PC1 (', round(pca_result@R2[1] * 100, 1), '%)'),
         y = paste0('PC2 (', round(pca_result@R2[2] * 100, 1), '%)')) +
    theme_bw()

ggsave('pca_plot.png', width = 8, height = 6)

# Loadings
loadings <- as.data.frame(loadings(pca_result))
top_pc1 <- loadings[order(abs(loadings$PC1), decreasing = TRUE)[1:20], ]

PLS-DA

Goal: Build a supervised classification model that maximizes separation between experimental groups.

Approach: Fit a PLS-DA model with cross-validation to determine optimal components, then extract VIP scores to rank discriminatory features.

library(mixOmics)

# PLS-DA
plsda_result <- plsda(as.matrix(data), groups, ncomp = 3)

# Cross-validation
perf_plsda <- perf(plsda_result, validation = 'Mfold', folds = 5, nrepeat = 50)
plot(perf_plsda, col = color.mixo(5:7))

# Optimal components
ncomp_opt <- perf_plsda$choice.ncomp['BER', 'centroids.dist']
cat('Optimal components:', ncomp_opt, '\n')

# Final model
final_plsda <- plsda(as.matrix(data), groups, ncomp = ncomp_opt)

# Plot
plotIndiv(final_plsda, group = groups, ellipse = TRUE, legend = TRUE)

# VIP scores
vip <- vip(final_plsda)
top_vip <- sort(vip[, ncomp_opt], decreasing = TRUE)[1:20]
print(top_vip)

sPLS-DA (Sparse)

Goal: Perform feature selection simultaneously with classification to identify a minimal discriminatory feature set.

Approach: Tune the number of features to retain per component via cross-validation, then fit a sparse PLS-DA model.

# Tune number of features to select
tune_splsda <- tune.splsda(as.matrix(data), groups, ncomp = 3,
                            validation = 'Mfold', folds = 5, nrepeat = 50,
                            test.keepX = c(5, 10, 20, 50, 100))

optimal_keepX <- tune_splsda$choice.keepX

# Final sparse model
splsda_result <- splsda(as.matrix(data), groups, ncomp = ncomp_opt, keepX = optimal_keepX)

# Selected features
selected_features <- selectVar(splsda_result, comp = 1)$name
cat('Selected features (comp 1):', length(selected_features), '\n')

OPLS-DA (Orthogonal PLS-DA)

Goal: Separate group-predictive variation from orthogonal (within-group) variation for cleaner class separation.

Approach: Fit an OPLS-DA model using ropls, then use the S-plot to identify features with high predictive weight and correlation.

library(ropls)

# OPLS-DA
oplsda <- opls(data, groups, predI = 1, orthoI = NA)

# Summary
print(oplsda)

# Scores plot
plot(oplsda, typeVc = 'x-score')

# S-plot (loadings vs correlation)
plot(oplsda, typeVc = 'x-loading')

# VIP
vip_scores <- getVipVn(oplsda)
top_vip <- sort(vip_scores, decreasing = TRUE)[1:20]

Random Forest

Goal: Rank features by importance using a non-linear ensemble classifier.

Approach: Train a Random Forest on the feature matrix, then extract MeanDecreaseAccuracy to identify the most discriminatory features.

library(randomForest)

# Random Forest classification
rf_model <- randomForest(x = data, y = groups, importance = TRUE, ntree = 500)

# Importance
importance <- importance(rf_model)
top_features <- rownames(importance)[order(importance[, 'MeanDecreaseAccuracy'], decreasing = TRUE)[1:20]]

# Plot importance
varImpPlot(rf_model, n.var = 20)

ROC Analysis

Goal: Evaluate the diagnostic performance of candidate biomarker metabolites.

Approach: Generate ROC curves and compute AUC for individual features using pROC.

library(pROC)

# ROC for top biomarker
top_feature <- 'feature_123'  # Replace with actual feature name
roc_result <- roc(groups, data[, top_feature])

# Plot
plot(roc_result, main = paste('AUC =', round(auc(roc_result), 3)))

# Multiple features
biomarkers <- c('feature_1', 'feature_2', 'feature_3')
for (feat in biomarkers) {
    roc_i <- roc(groups, data[, feat])
    cat(feat, ': AUC =', round(auc(roc_i), 3), '\n')
}

Heatmap

Goal: Visualize abundance patterns of top differential features across all samples.

Approach: Select top significant features, create an annotated heatmap with hierarchical clustering using pheatmap.

library(pheatmap)

# Top differential features
top_features <- rownames(sig_features)[1:50]
data_top <- data[, top_features]

# Annotation
annotation_row <- data.frame(Group = groups)
rownames(annotation_row) <- rownames(data)

pheatmap(t(data_top), annotation_col = annotation_row,
         scale = 'row', clustering_method = 'ward.D2',
         filename = 'heatmap.png', width = 10, height = 12)

Related Skills

• normalization-qc - Data preparation
• pathway-mapping - Functional interpretation
• multi-omics-integration/mixomics-analysis - Advanced multivariate methods