Author: Elisabetta Sciacca, Myles Lewis

# Differential Network Analysis with multiDEGGs

#### Elisabetta Sciacca, Myles Lewis

## Introduction

The multiDEGGs package performs multi-omic differential network analysis by identifying differential interactions between molecular entities (genes, proteins, miRNAs, or other biomolecules) across the omic datasets provided.

For each omic dataset, a differential network is constructed, where links represent statistically significant differential interactions between entities. These networks are then integrated into a comprehensive visualization using distinct colors to distinguish interactions from different omic layers. This unified visualization allows interactive exploration of cross-omic patterns (e.g., differential interactions present at both transcript and protein level). For each link, users can access differential statistical significance metrics (p-values or adjusted p-values, calculated via robust or traditional linear regression with interaction term), and differential regression plots.

Beyond network visualization and exploration, multiDEGGs extends its utility into predictive modeling applications. The identified differential interactions can be leveraged as engineered features in machine learning pipelines, providing biologically meaningful predictors that capture relational information between molecular entities. The package includes specialized functions for nested cross-validation that ensure proper feature selection and engineering without data leakage, enabling the construction of robust and interpretable predictive models (see `vignette("2. Feature Selection", package = "multiDEGGs")` for details).

## Installation

Install from CRAN:
`install.packages("multiDEGGs")`

Install from Github:
`devtools::install_github("elisabettasciacca/multiDEGGs")`

## Quick start - Generate Differential Networks

If you are working with human data, you can start differential analysis by using the internal multiDEGGs’ default reference network.
Users working with other species or requiring custom interaction sets can provide their own biological reference netowork as detailed in the last paragraph of this vignette.

Let’s start by loading the package and sample data:

    library(multiDEGGs)
    data("synthetic_metadata")
    data("synthetic_rnaseqData")
    data("synthetic_proteomicData")
    data("synthetic_OlinkData")

Generate Differential Networks:

    assayData_list <- list("RNAseq" = synthetic_rnaseqData,
                           "Proteomics" = synthetic_proteomicData,
                           "Olink" = synthetic_OlinkData)

    deggs_object <- get_diffNetworks(assayData = assayData_list,
                                     metadata = synthetic_metadata,
                                     category_variable = "response",
                                     regression_method = "lm",
                                     padj_method = "bonferroni",
                                     verbose = FALSE,
                                     show_progressBar = FALSE,
                                     cores = 2)

### Key Parameters of `get_diffNetworks`

It’s worth explaining some of the important parameters of `get_diffNetworks`:

- `assayData`: accepts either a single normalized matrix/data frame (for single omic differential analysis), or a list of matrices/data frames (for multi-omic scenarios). For multi-omic analysis, it’s highly recommended to use a named list of data. If unnamed, sequential names (assayData1, assayData2, etc.) will be assigned to identify each matrix or data frame.

- `metadata`: can also be a named factor vector, with names matching the patient IDs in column names of the assay data matrices/data frames. In that case, the category_variable can remain unset (NULL by default).

- `category_subset`: this parameter can restrict the analysis to a certain subset of categories available in the metadata/category vector.

- `regression_method`: set to `"lm"` by default because it is faster and highly recommended in machine learning scenarios, where the function might be repeatedly called many times. For basic differential analyses, `"rlm"` can also be used and may perform better in some cases.

- `percentile_vector`: by default, molecular targets (genes, proteins, etc.) whose expression level is below the 35th percentile of the entire data matrix are excluded from the analysis. This threshold can be modified by specifying the percentile vector that is internally used for the percolation analysis. For example, to remove only targets below the 25th percentile, set `percentile_vector = seq(0.25, 0.98, by = 0.05)`.

- `padj_method`: the default method is Bonferroni. Storey’s q values often give more generous results but the `qvalue` package needs to be installed first.

NOTE: Not all patient IDs need to be present across datasets. Different numbers of samples per omic are acceptable. Only IDs whose data is available in the colnames of the assayData will be included in the analysis. Missing IDs will be listed in a message similar to:

`The following samples IDs are missing in Proteomics: PT001, PT005, PT0030`

## Visualization

The `deggs_object` now contains the differential networks for each omic data in `assayData_list`. These networks can be integrated into a comprehensive visualization where different colors distinguish links from different omic layers.

    View_diffNetworks(deggs_object)

This visualization interface allows to:

1. Navigate the networks associated with each patient category
2. Filter by link significance
3. Search for specific genes inside the network

Thicker links correspond to higher significant p-values.
The direction of the arrows shows the relationship direction reported in literature, not derived from the data.

The user can visualize differential regression plots by clicking on a link:

This visual inspection of individual links is essential before drawing any biological conclusions. These regression plots allow assessment of:

- Effect size: the magnitude of the difference in interaction strength between groups
- Model fit quality: how well the regression lines represent the data
- Noise levels: the scatter and confidence intervals around the regression lines
- Outliers: presence of influential data points that might drive the observed difference

Single node differential expressions can also be visualized by clicking on the nodes:

NOTE: For multi-omic scenarios, the data from the first matrix in the list passed to `assayData` will be used for this boxplot.

## List All Differential Interactions

Outside of the interactive environment, the `get_multiOmics_diffNetworks()` function can be used to get a table of all differential interactions, ordered by p-value or adjusted p-value:

    get_multiOmics_diffNetworks(deggs_object, sig_threshold = 0.05)
    #> $Non_responder
    #>                  from       to      p.value        p.adj      layer
    #> TNF-TNFRSF1A      TNF TNFRSF1A 3.325023e-04 1.330009e-03     RNAseq
    #> IL1B-IL1R2       IL1B    IL1R2 5.389195e-04 2.155678e-03     RNAseq
    #> TGFB3-TGFBR1    TGFB3   TGFBR1 5.329071e-15 2.131628e-14     RNAseq
    #> AKT2-MTOR        AKT2     MTOR 4.347083e-04 1.738833e-03     RNAseq
    #> FANCD2-FAN1    FANCD2     FAN1 4.440892e-16 3.552714e-15 Proteomics
    #> GNG12-RASA2     GNG12    RASA2 0.000000e+00 0.000000e+00 Proteomics
    #> RASGRP3-RRAS  RASGRP3     RRAS 2.202344e-04 1.761875e-03 Proteomics
    #> TNF-TNFRSF1A1     TNF TNFRSF1A 0.000000e+00 0.000000e+00 Proteomics
    #> RASGRP1-RAP1A RASGRP1    RAP1A 2.840564e-03 2.272452e-02 Proteomics
    #>
    #> $Responder
    #>                from    to      p.value        p.adj  layer
    #> FANCD2-FAN1  FANCD2  FAN1 0.000000e+00 0.000000e+00 RNAseq
    #> FASLG-FAS     FASLG   FAS 6.947839e-07 2.084352e-06 RNAseq
    #> MAP2K2-MAPK3 MAP2K2 MAPK3 1.153300e-12 3.459899e-12 RNAseq

For single omic scenarios, use the `get_sig_deggs()` function:

    deggs_object_oneOmic <- get_diffNetworks(assayData = synthetic_rnaseqData,
                                     metadata = synthetic_metadata,
                                     category_variable = "response",
                                     regression_method = "lm",
                                     padj_method = "bonferroni",
                                     verbose = FALSE,
                                     show_progressBar = FALSE,
                                     cores = 2)

    get_sig_deggs(deggs_object_oneOmic, sig_threshold = 0.05)
    #>                              from       to      p.value        p.adj
    #> Non_responder.TNF-TNFRSF1A    TNF TNFRSF1A 3.325023e-04 1.330009e-03
    #> Non_responder.IL1B-IL1R2     IL1B    IL1R2 5.389195e-04 2.155678e-03
    #> Non_responder.TGFB3-TGFBR1  TGFB3   TGFBR1 5.329071e-15 2.131628e-14
    #> Non_responder.AKT2-MTOR      AKT2     MTOR 4.347083e-04 1.738833e-03
    #> Responder.FANCD2-FAN1      FANCD2     FAN1 0.000000e+00 0.000000e+00
    #> Responder.FASLG-FAS         FASLG      FAS 6.947839e-07 2.084352e-06
    #> Responder.MAP2K2-MAPK3     MAP2K2    MAPK3 1.153300e-12 3.459899e-12

## Differential Regression Plots

To plot the differential regression fits outside of the interactive environment, use `plot_regressions()` specifying the omic data to be used and the two targets:

    plot_regressions(deggs_object,
                     assayDataName = "RNAseq",
                     gene_A = "MTOR",
                     gene_B = "AKT2",
                     legend_position = "bottomright")

In single omic analyses, the `assayDataName` parameter can remain unset.

## Differential Network Analysis with More Than Two Groups

It’s possible to compare differential interactions among more than two categorical groups. All steps described above stay the same;
the dropdown menu of the interactive environment will show all available categories:

While regressions and boxplots will show all categories:

The statistical significance of the interaction term is calculated via one-way ANOVA in this case.
We highly recommend to have at least 4 or 5 observations per group.

## Custom Reference Network

The multiDEGGs package uses a human-specific reference network by default, consisting of 53,035 molecular interactions obtained both from `Omnipath` (Turei et al., Molecular Systems Biology, 2021) and the `MITHrIL` tool (Alaimo et al., Oncotarget, 2016).

Users working with non-human species or requiring custom interaction sets can provide their own reference network using the `network` parameter of the `get_diffNetworks()` function.

Network Requirements
The custom network must be a `data.frame` with exactly two columns:

- `from`: Origin node (e.g., Transcription Factor, miRNA, or Gene)
- `to`: Target node

Nodes should use the same nomenclature (e.g., Gene Symbols, Entrez IDs) as the expression assay data to ensure proper mapping during the differential network analysis.

Sources for Other Species
If you are working with non-human species, several repositories allow for the extraction of interaction data:

- STRING-db: Ideal for protein-protein interactions (PPI) across thousands of species. You can download the “protein.links” files
- KEGG (via `KEGGgraph` or `TIGER`): Useful for metabolic and signaling pathways
- Omnipath: A comprehensive resource that integrates multiple databases for human and mouse, easily accessible via the `OmnipathR` package
- miRBase or TargetScan: For those needing specific miRNA-target interactions for non-human models

Example: Generating a Custom Network in R
Below is a practical example of how to prepare a custom network, assuming you have a list of interactions:

    # Example: Creating a toy network for a non-human species
    # In a real scenario, you might load a CSV or use a database-specific package
    interaction_data <- data.frame(
      source = c("GeneA", "GeneB", "miRNA1"),
      target = c("GeneC", "GeneA", "GeneB"),
      confidence = c(0.9, 0.8, 0.95)
    )

    # Formatting for get_diffNetworks()
    # We only need the 'from' and 'to' columns
    custom_network <- interaction_data[, c("source", "target")]
    colnames(custom_network) <- c("from", "to")

    # Check class and structure
    print(class(custom_network))
    head(custom_network)

    # Now this can be passed to the function:
    diff_net <- get_diffNetworks(expr_data, network = custom_network, ...)

NOTE
Finally, it is important point to keep in mind that the differential networks obtained will be fundamentally limited by the reference biological network used. multiDEGGs can only identify interactions that are already present in the reference network, so using an incomplete or biased network might cause missing relevant biological relationships or, conversely, finding spurious associations. When choosing a reference network, it is important to assess its source, how comprehensive it is, and the quality of evidence supporting the interactions. These aspects should be documented when reporting multiDEGGs results.

## Citation

    citation("multiDEGGs")
    #> To cite package 'multiDEGGs' in publications use:
    #>
    #>   Sciacca E, Wang S, Pitzalis C, Lewis M (2026). "multiDEGGs: Single or
    #>   Multiomic Differential Network Analysis for Biomarker Discovery and
    #>   Feature Engineering for Predictive Modeling." _Computational and
    #>   Structural Biotechnology Journal_, *35*(1), 0001.
    #>   doi:10.34133/csbj.0001 <https://doi.org/10.34133/csbj.0001>.
    #>
    #> A BibTeX entry for LaTeX users is
    #>
    #>   @Article{,
    #>     title = {multiDEGGs: Single or Multiomic Differential Network Analysis for Biomarker Discovery and Feature Engineering for Predictive Modeling},
    #>     author = {Elisabetta Sciacca and Susan S. Wang and Costantino Pitzalis and Myles J. Lewis},
    #>     journal = {Computational and Structural Biotechnology Journal},
    #>     year = {2026},
    #>     volume = {35},
    #>     number = {1},
    #>     pages = {0001},
    #>     doi = {10.34133/csbj.0001},
    #>   }