Missingness

Oftentimes when collecting data, there are missing values. Let’s use the plot_missing function to determine where our missing values are:

# Plot the missingness summary
plot_missing(
    exposomicset = expom,
    plot_type = "summary",
    threshold = 0
)

Count of features with missing data above a 0% missingness threshold by data layer. Exposure data have variables with missingness.

Here we see that there are 4 variables in the exposure data that are missing data. Let’s take a look at them:

# Plot missing variables withing exposure group
plot_missing(
    exposomicset = expom,
    plot_type = "lollipop",
    threshold = 0,
    layers = "Exposure"
)

Percent missingness per exposure variable. Parity, h_parity_None, shows the highest missingness.

Here we see that one variable, h_parity_None, has about 4% missing values. We can apply a missingness filter using the filter_missing function. However, given that this level of missingness is quite low, we will not be applying a missingness filter and instead impute the missing data.

Imputation

The run_impute_missing function is used to impute missing values. Here we can specify the imputation method for exposure and omics data separately.

The exposure_impute_method argument is used to set the imputation method for exposure data, and the omics_impute_method argument is used to set the imputation method for omics data. The omics_to_impute argument is used to specify which omics data to impute. Here we will impute the exposure data given using the missforest method, but other options for imputation methods include:

• median: Imputes missing values with the median of the variable.

• mean: Imputes missing values with the mean of the variable.

• knn: Uses k-nearest neighbors to impute missing values.

• mice: Uses the Multivariate Imputation by Chained Equations (MICE) method to impute missing values.

• missforest: Uses the MissForest method to impute missing values.

• lod_sqrt2: Imputes missing values using the square root of the lower limit of detection (LOD) for each variable. This is useful for variables that have a lower limit of detection, such as chemical exposures.

# Impute missing values
expom <- run_impute_missing(
    exposomicset = expom,
    exposure_impute_method = "missforest",
    exposure_cols = exp_vars
)

## Imputing exposure data using method: missforest

Filtering Omics Features

We can filter omics features based on variance or expression levels. The filter_omics function is used to filter omics features. The method argument is used to set the method for filtering. Here we can use either:

• Variance: Filters features based on variance. We recommend this for omics based on continuous measurements, such as log-transformed counts, M-values, protein intensities, or metabolite concentrations.

• Expression: Filters features based on expression levels. We recommend this for omics where many values may be near-zero or zero, such as RNA-seq data.

The assays argument is used to specify which omics data to filter. The assay_name argument is used to specify which assay to filter. The min_var, min_value, and min_prop arguments are used to set the minimum variance, minimum expression value, and minimum proportion of samples exceeding the minimum value, respectively.

# filter omics layers by variance and expression
# Methylation filtering
expom <- filter_omics(
    exposomicset = expom,
    method = "variance",
    assays = "Methylation",
    assay_name = 1,
    min_var = 0.05
)

## Filtering assay: Methylation

## Filtered 223 of 500 features from 'Methylation' using method 'variance'

# Gene expression filtering
expom <- filter_omics(
    exposomicset = expom,
    method = "expression",
    assays = "Gene Expression",
    assay_name = 1,
    min_value = 1,
    min_prop = 0.3
)

## Filtering assay: Gene Expression

## Filtered 29 of 500 features from 'Gene Expression' using method 'expression'

Normality Check

When determining variable associations, it is important to check the normality of the data. The run_normality_check function is used to check the normality of the data.

# Check variable normality
expom <- run_normality_check(
    exposomicset = expom,
    action = "add"
)

## Checking Normality Using Shapiro-Wilk Test

## 9 Exposure Variables are Normally Distributed

## 6 Exposure Variables are NOT Normally Distributed

The transform_exposure function is used to transform the data to make it more normal. Here the transform_method is set to boxcox_best as it will automatically select the best transformation method based on the data. The transform_method can be manually set to log2, sqrt, or x_1_3 as well. We specify the exposure_cols argument to set the columns to transform.

# Transform variables
expom <- transform_exposure(
    exposomicset = expom,
    transform_method = "boxcox_best",
    exposure_cols = exp_vars
)

## Applying the boxcox_best transformation.

To check the normality of the exposure data, we can use the plot_normality_summary function. This function plots the normality of the data before and after transformation. The transformed argument is set to TRUE to plot the normality status of the transformed data.

# Examine normality summary
plot_normality_summary(
    exposomicset = expom,
    transformed = TRUE
)

Normality status of numeric exposure variables after Box-Cox transformation.

Principal Component Analysis

To identify the variability of the data, we can perform a principal component analysis (PCA). The run_pca performs a joint PCA across all numeric exposures and omic assays after standardization, identifying shared axes of variation across layers. The resulting PCs in colData() reflect integrated sample-level variance across all data types, and outliers are defined in that joint multi-omics PC space.

Here we specify that we would like to log-transform the exposure and omics data before performing PCA using the log_trans_exp and the log_trans_omics arguments, respectively. We automatically identify sample outliers based on the Mahalanobis distance, a measure of the distance between a point and a distribution.

# Perform principal component analysis
expom <- run_pca(
    exposomicset = expom,
    log_trans_exp = TRUE,
    log_trans_omics = TRUE,
    action = "add"
)

## Identifying common samples.

## Subsetting exposure data.

## Subsetting omics data.

## Performing PCA on Feature Space.

## Performing PCA on Sample Space.

## Outliers detected: s1231

# Plot the PCA plot of sample and feature space
plot_pca(exposomicset = expom)

PCA of sample and feature space with sample outlier detection.

Here we see one sample outlier, and that most variation is captured in the first two principal components for both features and samples. We can filter out the outlier using the filter_sample_outliers function.

# Filter out sample outliers
expom <- filter_sample_outliers(
    exposomicset = expom,
    outliers = c("s1231")
)

## Removing outliers: s1231

To understand the relationship between the principal components and exposures we can correlate them using the run_correlation function. Here we specify that the feature_type is pcs for principal components, specify a set of exposure variables, exp_vars, and the number of principal components, n_pcs. We set correlation_cutoff to 0 and pval_cutoff to 1 to initially include all correlations.

# Run the correlation analysis
expom <- run_correlation(
    exposomicset = expom,
    feature_type = "pcs",
    exposure_cols = exp_vars,
    n_pcs = 20,
    action = "add",
    correlation_cutoff = 0,
    pval_cutoff = 1
)

We can visualize these correlations with the plot_correlation_tile function. We specify we are plotting the feature_type of pcs to grab the principal component correlation results. We then set the significance threshold to 0.05 with the pval_cutoff argument.

# Plot the correlation tile plot
plot_correlation_tile(
    exposomicset = expom,
    feature_type = "pcs",
    pval_cutoff = 0.05
)

Correlation heatmap of exposures versus principal components. Child lead levels (hs_pb_c_Log2) and maternal BPA levels (hs_bpa_madj_Log2) are associated with the most principal components.

Exposure Summary

We can summarize the exposure data using the run_summarize_exposures function. This function calculates summary statistics for each exposure variable, including the number of values, number of missing values, minimum, maximum, range, sum, median, mean, standard error, and confidence intervals. The exposure_cols argument determines which variables to include in the summary.

# Summarize exposure data
run_summarize_exposures(
    exposomicset = expom,
    action = "get",
    exposure_cols = exp_vars
) |>
    head()

## # A tibble: 6 × 27
##   variable   n_values  n_na   min   max range    sum median  mean    se ci_lower
##   <chr>         <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl> <dbl> <dbl>    <dbl>
## 1 h_pm10_ra…       47     0 16.6  25.8   9.25 989.    21.2  21.0   0.32    20.4 
## 2 h_pm25_ra…       47     0 10.6  18.2   7.55 697.    14.6  14.8   0.25    14.3 
## 3 hs_bpa_ma…       47     0  0     2.31  2.31  71.3    1.58  1.52  0.06     1.41
## 4 hs_mibp_c…       47     0  0.1   0.22  0.11   7.65   0.17  0.16  0        0.16
## 5 hs_pb_c_L…       47     0  1.44  5     3.56 156.     3.31  3.31  0.11     3.1 
## 6 hs_pfhxs_…       47     0  0     2.14  2.13  65.7    1.48  1.4   0.07     1.25
## # ℹ 16 more variables: ci_upper <dbl>, variance <dbl>, sd <dbl>,
## #   coef_var <dbl>, period <chr>, location <chr>, description <chr>,
## #   var_type <chr>, transformation <chr>, selected_ontology_label <chr>,
## #   selected_ontology_id <chr>, root_id <chr>, root_label <chr>,
## #   category <chr>, category_source <chr>, transformation_applied <chr>

Exposure Visualization

To visualize our exposure data, we can use the plot_exposures function. This function allows us to plot the exposure data in a variety of ways. Here we will plot the exposure data using a boxplot. The exposure_cat argument is used to set the exposure category to plot. Additionally, we could specify exposure_cols to only plot certain exposures. The plot_type argument is used to set the type of plot to create. Here we use a boxplot, but we could also use a ridge plot.

# Plot aerosol exposure distributions by sex
plot_exposures(
    exposomicset = expom,
    group_by = "e3_sex_None",
    exposure_cat = "aerosol",
    plot_type = "boxplot",
    ylab = "Values",
    title = "Aerosol Exposure by Sex"
)

Distribution of aerosol exposures by sex.

Here we do not see any significant differences in aerosol exposure between males and females.

Sample Clustering

The run_cluster_samples function is used to cluster samples based on the exposure data, clustering approaches are available by setting the clustering_approach argument. Here we use the dynamic approach, which uses a dynamic tree cut method to identify clusters. Other options are:

• gap: Gap statistic method (default); estimates optimal k by comparing within-cluster dispersion to that of reference data.

• diana: Divisive hierarchical clustering (DIANA); chooses k based on the largest drop in dendrogram height.

• elbow: Elbow method; detects the point of maximum curvature in within-cluster sum of squares (WSS) to determine k.

• dynamic: Dynamic tree cut; adaptively detects clusters from a dendrogram structure without needing to predefine k.

• density: Density-based clustering (via densityClust); identifies clusters based on local density peaks in distance space.

# Sample clustering
expom <- run_cluster_samples(
    exposomicset = expom,
    exposure_cols = exp_vars,
    clustering_approach = "dynamic",
    action = "add"
)

## Starting clustering analysis...

##  ..cutHeight not given, setting it to 40.7  ===>  99% of the (truncated) height range in dendro.
##  ..done.

## Optimal number of clusters for samples: 2

We plot the sample clusters using the plot_sample_clusters function. This function plots z-scored values of the exposure data for each sample, colored by the cluster assignment. The exposure_cols argument is used to set the columns to plot.

# Plot the sample clusters
plot_sample_clusters(
    exposomicset = expom,
    exposure_cols = exp_vars
)

## Registered S3 method overwritten by 'dendextend':
##   method     from 
##   rev.hclust vegan

## tidyHeatmap says: If you use tidyHeatmap for scientific research, please cite: Mangiola, S. and Papenfuss, A.T., 2020. 'tidyHeatmap: an R package for modular heatmap production based on tidy principles.' Journal of Open Source Software. doi:10.21105/joss.02472.
## This message is displayed once per session.

## Warning: `when()` was deprecated in purrr 1.0.0.
## ℹ Please use `if` instead.
## ℹ The deprecated feature was likely used in the tidyHeatmap package.
##   Please report the issue at
##   <https://github.com/stemangiola/tidyHeatmap/issues>.
## This warning is displayed once per session.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

Sample clustering heatmap using exposure profiles (z-scored). Clusters appear mostly driven by aerosol exposure during pregnancy.

Here we see two clusters, largely driven by particulate matter/aerosol exposure during pregnancy (h_pm25_ratio_preg_None and h_pm10_ratio_preg_None).

Exposure Correlations

The run_correlation function identifies correlations between exposure variables. We set feature_type to exposures to focus on exposure variables and use a correlation cutoff of 0.3 to filter for meaningful associations. This cutoff can be adjusted based on your data and analysis needs.

# Run correlation analysis
expom <- run_correlation(
    exposomicset = expom,
    feature_type = "exposures",
    action = "add",
    exposure_cols = exp_vars,
    correlation_cutoff = 0.3
)

To visualize the exposure correlations, we can use the plot_circos_correlation function. Here we will plot the circos plot. This function creates a circular plot of the exposure correlations. The correlation_cutoff argument is used to set the minimum correlation score for the association. Here we use a cutoff of 0.3.

# Plot exposure correlation circos plot
plot_circos_correlation(
    exposomicset = expom,
    feature_type = "exposures",
    corr_threshold = 0.3,
    exposure_cols = exp_vars
)

Circos view of exposure-exposure correlations (threshold 0.3).

Exposure-wide association (ExWAS)

The run_association function performs an ExWAS analysis to identify associations between exposures and outcomes. We specify the data source, outcome variable, feature set, and covariates for the analysis. Since we have a binary outcome, we set the model family to binomial.

# Perform ExWAS
expom <- run_association(
    exposomicset = expom,
    source = "exposures",
    outcome = "hs_asthma",
    feature_set = exp_vars,
    action = "add",
    family = "binomial"
)

## Running GLMs.

To visualize the results of the ExWAS analysis, we can use the plot_association function, which will plot results for the the specified features. The terms argument is used to set the features to plot. The filter_thresh argument is used to set the threshold for filtering the results. The filter_col argument is used to set the column to filter on. Here we use p.value to filter on the p-value of the association. We can also include the R^2 or adjusted R^2 (if covariates are included) using the r2_col argument.

# Plot the association forest plot
plot_association(
    exposomicset = expom,
    source = "exposures",
    terms = exp_vars,
    filter_thresh = 0.05,
    filter_col = "p.value",
    r2_col = "r2"
)

ExWAS associations of exposures with asthma status. No exposures are significantly associated (P < 0.05) with asthma status.

Here we see that no exposure variables are significantly associated with our asthma status. Although we do see that confidence interval for child Mono-iso-butyl phthalate (MiBP) levels (hs_mibp_cadj_Log2) does not cross 0, indicating a negative, albeit not significant (P < 0.05) association.

We can also associate our omics features with an outcome of interest using the run_association function. Here we specify an additional argument, top_n, which is used to set the top number of high variance omics features to include per omics layer.

# Perform ExWAS
expom <- run_association(
    exposomicset = expom,
    outcome = "hs_asthma",
    source = "omics",
    top_n = 500,
    action = "add",
    family = "binomial"
)

## Log2-Transforming each assay in MultiAssayExperiment.

## Scaling each assay in MultiAssayExperiment.

## Running GLMs.

Now we can visualize these results with a manhattan plot.

# Plot the manhattan plot
plot_manhattan(
    exposomicset = expom,
    min_per_cat = 0,
    feature_col = "feature_clean",
    vars_to_label = c(
        "TC19001180.hg.1",
        "TC01000565.hg.1",
        "cg01937701",
        "hs_mibp_cadj_Log2"
    ),
    panel_sizes = c(1, 3, 1, 3, 1, 1, 1),
    facet_angle = 0
)

Manhattan plot of omics-wide associations with asthma status.

Differential Abundance

We provide functionality to test for differentially abundant features associated with an outcome across multiple omics layers. This is done using the run_differential_abundance function, which fits a model defined by the user (using the formula argument) and supports several methods. Here we apply the limma_trend method, a widely used approach for analyzing omics data. Users can also specify how features are scaled (e.g. none, quantile, TMM) before fitting.

# Run differential abundance analysis
expom <- run_differential_abundance(
    exposomicset = expom,
    formula = ~hs_asthma,
    method = "limma_trend",
    scaling_method = "none",
    action = "add"
)

## Running differential abundance testing.

## Processing assay: Gene Expression

## Processing assay: Methylation

## Differential abundance testing completed.

We can summarize the results of the differential abundance analysis with a volcano plot, which highlights features with a high log fold change and that are statistically significant. The plot_volcano function generates this visualization, with options to set thresholds for p-values and log fold changes, and to label a subset of top-ranked features. In this example, we use the feature_clean column to display interpretable feature names.

Note: we set the pval_col to P.Value for the purposes of this example, but we recommend keeping the default of adj.P.Val to use the adjusted p-values.

# Plot the volcano plot
plot_volcano(
    exposomicset = expom,
    top_n_label = 3,
    feature_col = "feature_clean",
    logFC_thresh = log2(1),
    pval_thresh = 0.05,
    pval_col = "P.Value",
    logFC_col = "logFC",
    nrow = 1
)

Volcano plot of differentially abundant features across omics layers.

Exposure-Omics Association

Above we saw that there are not too many omics features associated with asthma. Which may be due to the subsampling in this example or because exposures are driving different biology. Let’s examine what omics features exposures are associated with.

# Run association testing between every exposure and omics feature
expom <- run_exposure_omics_association(
    exposomicset = expom,
    exposures = exp_vars,
    action = "add"
)

## Testing 9 exposures across 2 assays

## Processing assay: Gene Expression

## Processing assay: Methylation

Now let’s see how many omics features each exposure is associated with using the plot_exposure_omics_association function where we can either plot by the individual exposure or exposure category:

# Plot the number of exposure-omics associations
plot_exposure_omics_association(
  exposomicset = expom,
  plot_type = "category",
  pval_col = "p.value",
  pval_thresh = 0.05)

Barplot of the number of omics features associated with exposures.

Here we can see that there are omics features associated with exposures, while there are fewer that are associated with asthma directly.

Enrichment Visualizations

To visualize our enrichment results we provide several options:

• dot`plot: A dot plot showing the top enriched terms. The size of the dots represents the number of features associated with the term, while the color represents the significance of the term.

• cnet: A network plot showing the relationship between features and enriched terms.

• network: A network plot showing the relationship between enriched terms.

• heatmap: A heatmap showing the relationship between features and enriched terms.

• summary: A summary figure of the enrichment results.

Enrichment Summary

To summarize the enrichment results, we can use the plot_enrichment function with the plot_type argument set to summary. This will plot a summary of the enrichment results, showing:

• The number of exposure categories per enrichment term group.

• The number of features driving the enrichment term group.

• A p-value distribution of the enrichment term group.

• The number of terms in the enrichment term group.

• The total number of terms per experiment name.

• The overlap in enrichment terms between experiments (i.e. between gene expression and methylation).

# Plot the summary diagram
plot_enrichment(
    exposomicset = expom,
    feature_type = "omics",
    plot_type = "summary"
)

## Picking joint bandwidth of 0.25

Summary of enriched GO terms grouped by overlap and exposure category.

Here we see that it is just the features associated with “polyatomic entity” exposures that seem to be enriched. Additionally, there appears to be no overlap in terms between methylation and gene expression results.

DotPlot

By setting the plot_type to dotplot we can create a dotplot to show which omics are associated with which terms. By specifying the top_n_genes we can add the most frequent features in that particular enrichment term group.

# Plot a dotplot of terms
plot_enrichment(
    exposomicset = expom,
    feature_type = "omics",
    plot_type = "dotplot",
    top_n = 15,
    add_top_genes = TRUE,
    top_n_genes = 5
)

Dotplot of top enriched GO terms by omics layer and exposure category.

Term Network Plot

We can set the plot_type to network to understand how our enrichment terms are individually connected.

# Plot the term network plot
# Setting a seed so that the plot layout is consistent
set.seed(42)
plot_enrichment(
    exposomicset = expom,
    feature_type = "omics",
    plot_type = "network",
    label_top_n = 3
)

Network of enriched GO terms connected by shared genes.

At the individual term level, we see that they differ by omics layer, with the gene expression driving terms related to vesicle traficking and the methylation data driving terms related to G protein-coupled receptor signaling.

Heatmap

Setting the plot_type to heatmap can help us understand which genes are driving the enrichment terms. We have the additional benefit of being able to color our tiles by the Log_2_Fold Change from our differential abundance testing. Here we will examine group 2, given it seems to be driven by the most terms and multiple omics layers.

# Plot a heatmap of genes and corresponding GO terms
plot_enrichment(
    exposomicset = expom,
    feature_type = "omics",
    go_groups = "Group 2",
    plot_type = "heatmap",
    heatmap_fill = TRUE,
    feature_col = "feature_clean"
)

Heatmap of genes driving enriched GO terms (Group 2) with log2 fold-change overlay.

Cnet Plot

Another way to visualize this information is with the cnet plot, where the enrichment terms are connected to the genes driving them.

# Plot the gene-term network
# Setting a seed so that the plot layout is consistent
set.seed(42)
plot_enrichment(
    exposomicset = expom,
    feature_type = "omics",
    go_groups = "Group 2",
    plot_type = "cnet",
    feature_col = "feature_clean"
)

Cnet plot linking enriched terms to contributing genes (Group 1).

Saving Results

We can export the results in our MultiAssayExperiment to an Excel spreadsheet using the extract_results_excel function. Here we add all of our results to the Excel file, but we can choose certain results by changing the result_types argument.

# Save results
extract_results_excel(
    exposomicset = expom,
    file = tempfile(),
    result_types = "all"
)

## Writing Correlation Results.

## Writing Association Results.

## Writing Mixture Analysis Results.

## Writing Differential Abundance Results.

## Writing Multiomics Integration Results.

## Writing Network Impact Results.

## Writing Enrichment Results.

## Writing Pipeline Summary.

## Writing Exposure Summary Results.

## Results written to: /tmp/Rtmpjd2w7e/file388e6aefc62f

Session Info

sessionInfo()

## R version 4.5.3 (2026-03-11)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.4 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## time zone: Etc/UTC
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] stats4    stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] tidyexposomics_0.99.16      MultiAssayExperiment_1.37.4
##  [3] SummarizedExperiment_1.41.1 Biobase_2.71.0             
##  [5] GenomicRanges_1.63.2        Seqinfo_1.1.0              
##  [7] IRanges_2.45.0              S4Vectors_0.49.2           
##  [9] BiocGenerics_0.57.1         generics_0.1.4             
## [11] MatrixGenerics_1.23.0       matrixStats_1.5.0          
## [13] lubridate_1.9.5             forcats_1.0.1              
## [15] stringr_1.6.0               dplyr_1.2.1                
## [17] purrr_1.2.2                 readr_2.2.0                
## [19] tidyr_1.3.2                 tibble_3.3.1               
## [21] ggplot2_4.0.2               tidyverse_2.0.0            
## [23] BiocStyle_2.39.0           
## 
## loaded via a namespace (and not attached):
##   [1] doParallel_1.0.17     naniar_1.1.0          httr_1.4.8           
##   [4] RColorBrewer_1.1-3    ggsci_5.0.0           dynamicTreeCut_1.63-1
##   [7] tools_4.5.3           doRNG_1.8.6.3         backports_1.5.1      
##  [10] utf8_1.2.6            R6_2.6.1              DT_0.34.0            
##  [13] vegan_2.7-3           mgcv_1.9-4            GetoptLong_1.1.1     
##  [16] permute_0.9-10        withr_3.0.2           gridExtra_2.3        
##  [19] progressr_0.19.0      cli_3.6.6             factoextra_2.0.0     
##  [22] RGCCA_3.0.3           labeling_0.4.3        sass_0.4.10          
##  [25] S7_0.2.1-1            randomForest_4.7-1.2  ggridges_0.5.7       
##  [28] proxy_0.4-29          pbapply_1.7-4         foreign_0.8-91       
##  [31] R.utils_2.13.0        sessioninfo_1.2.3     parallelly_1.47.0    
##  [34] itertools_0.1-3       limma_3.67.2          rstudioapi_0.18.0    
##  [37] RSQLite_2.4.6         FNN_1.1.4.1           shape_1.4.6.1        
##  [40] vroom_1.7.1           zip_2.3.3             dendextend_1.19.1    
##  [43] car_3.1-5             Matrix_1.7-5          clipr_0.8.0          
##  [46] abind_1.4-8           R.methodsS3_1.8.2     lifecycle_1.0.5      
##  [49] edgeR_4.9.8           yaml_2.3.12           carData_3.0-6        
##  [52] Rtsne_0.17            recipes_1.3.2         SparseArray_1.11.13  
##  [55] BiocFileCache_3.1.0   grid_4.5.3            blob_1.3.0           
##  [58] promises_1.5.0        crayon_1.5.3          lattice_0.22-9       
##  [61] sys_3.4.3             maketools_1.3.2       ComplexHeatmap_2.27.1
##  [64] pillar_1.11.1         knitr_1.51            rjson_0.2.23         
##  [67] corpcor_1.6.10        future.apply_1.20.2   mixOmics_6.35.1      
##  [70] codetools_0.2-20      glue_1.8.1            ggvenn_0.1.19        
##  [73] beepr_2.0             data.table_1.18.2.1   png_0.1-9            
##  [76] vctrs_0.7.3           Rdpack_2.6.6          testthat_3.3.2       
##  [79] gtable_0.3.6          assertthat_0.2.1      cachem_1.1.0         
##  [82] openxlsx_4.2.8.1      gower_1.0.2           xfun_0.57            
##  [85] rbibutils_2.4.1       S4Arrays_1.11.1       mime_0.13            
##  [88] prodlim_2026.03.11    tidygraph_1.3.1       survival_3.8-6       
##  [91] timeDate_4052.112     audio_0.1-12          iterators_1.0.14     
##  [94] hardhat_1.4.3         lava_1.9.0            statmod_1.5.1        
##  [97] ipred_0.9-15          nlme_3.1-169          fenr_1.9.2           
## [100] bit64_4.6.0-1         filelock_1.0.3        splines2_0.5.4       
## [103] bslib_0.10.0          Deriv_4.2.0           otel_0.2.0           
## [106] rpart_4.1.27          colorspace_2.1-2      DBI_1.3.0            
## [109] Hmisc_5.2-5           nnet_7.3-20           tidyselect_1.2.1     
## [112] tidyHeatmap_1.13.1    bit_4.6.0             compiler_4.5.3       
## [115] curl_7.0.0            rvest_1.0.5           httr2_1.2.2          
## [118] htmlTable_2.4.3       xml2_1.5.2            DelayedArray_0.37.1  
## [121] stringfish_0.18.0     checkmate_2.3.4       scales_1.4.0         
## [124] rappdirs_0.3.4        digest_0.6.39         mirai_2.6.1          
## [127] rmarkdown_2.31        XVector_0.51.0        htmltools_0.5.9      
## [130] pkgconfig_2.0.3       base64enc_0.1-6       SimDesign_2.25       
## [133] dbplyr_2.5.2          fastmap_1.2.0         GlobalOptions_0.1.4  
## [136] rlang_1.2.0           htmlwidgets_1.6.4     shiny_1.13.0         
## [139] ggh4x_0.3.1           farver_2.1.2          jquerylib_0.1.4      
## [142] jsonlite_2.0.0        BiocParallel_1.45.0   dcurver_0.9.3        
## [145] ModelMetrics_1.2.2.2  R.oo_1.27.1           magrittr_2.0.5       
## [148] Formula_1.2-5         patchwork_1.3.2       Rcpp_1.1.1-1         
## [151] ggnewscale_0.5.2      viridis_0.6.5         visdat_0.6.0         
## [154] stringi_1.8.7         pROC_1.19.0.1         ggraph_2.2.2         
## [157] brio_1.1.5            MASS_7.3-65           plyr_1.8.9           
## [160] parallel_4.5.3        listenv_0.10.1        ggrepel_0.9.8        
## [163] graphlayouts_1.2.3    splines_4.5.3         circlize_0.4.18      
## [166] hms_1.1.4             locfit_1.5-9.12       igraph_2.2.3         
## [169] ggpubr_0.6.3          ranger_0.18.0         ggsignif_0.6.4       
## [172] rngtools_1.5.2        buildtools_1.0.0      reshape2_1.4.5       
## [175] qs2_0.1.7             GPArotation_2025.3-1  tidybulk_2.1.2       
## [178] evaluate_1.0.5        RcppParallel_5.1.11-2 BiocManager_1.30.27  
## [181] tweenr_2.0.3          tzdb_0.5.0            nanonext_1.8.2       
## [184] foreach_1.5.2         missForest_1.6.1      httpuv_1.6.17        
## [187] polyclip_1.10-7       clue_0.3-68           future_1.70.0        
## [190] mirt_1.46.1           ggforce_0.5.0         BiocBaseUtils_1.13.0 
## [193] broom_1.0.12          xtable_1.8-8          e1071_1.7-17         
## [196] RSpectra_0.16-2       rstatix_0.7.3         later_1.4.8          
## [199] viridisLite_0.4.3     class_7.3-23          rARPACK_0.11-0       
## [202] memoise_2.0.1         ellipse_0.5.0         densityClust_0.3.3   
## [205] cluster_2.1.8.2       timechange_0.4.0      globals_0.19.1       
## [208] caret_7.0-1

References

fenr. (n.d.). Bioconductor. Retrieved August 18, 2025, from https://www.bioconductor.org/packages/release/bioc/html/fenr.html

Maitre, L., Guimbaud, J.-B., Warembourg, C., Güil-Oumrait, N., Petrone, P. M., Chadeau-Hyam, M., Vrijheid, M., Basagaña, X., Gonzalez, J. R., & Exposome Data Challenge Participant Consortium. (2022). State-of-the-art methods for exposure-health studies: Results from the exposome data challenge event. Environment International, 168(107422), 107422. https://doi.org/10.1016/j.envint.2022.107422

mixOmics. (n.d.). Bioconductor. Retrieved August 18, 2025, from https://www.bioconductor.org/packages/devel/bioc/html/mixOmics.html

MOFA2. (n.d.). Bioconductor. Retrieved August 18, 2025, from https://www.bioconductor.org/packages/release/bioc/html/MOFA2.html

MultiAssay Special Interest Group. (2025, April 15). MultiAssayExperiment: The Integrative Bioconductor Container. https://www.bioconductor.org/packages/release/bioc/vignettes/MultiAssayExperiment/inst/doc/MultiAssayExperiment.html

nipalsMCIA. (n.d.). Bioconductor. Retrieved August 18, 2025, from https://www.bioconductor.org/packages/release/bioc/html/nipalsMCIA.html

Regularized and Sparse Generalized Canonical Correlation Analysis for Multiblock Data. (n.d.). Retrieved August 18, 2025, from https://rgcca-factory.github.io/RGCCA/