scHiCcompare Vignette

Introduction

scHiCcompare is designed for the imputation, joint normalization, and detection of differential chromatin interactions between two groups of chromosome-specific single-cell Hi-C datasets (scHi-C). The groups can be pre-defined based on biological conditions or created by clustering cells according to their chromatin interaction patterns. Clustering can be performed using methods like Higashi, scHiCcluster methods, etc.

scHiCcompare works with processed Hi-C data, specifically chromosome-specific chromatin interaction matrices, and accepts five-column tab-separated text files in a sparse matrix format.

The package provides two key functionalities:

  • Imputation of single-cell Hi-C data by random forest model with pooling technique
  • Differential analysis to identify differences in chromatin interactions between groups.

Installation

if (!requireNamespace("BiocManager", quietly = TRUE)) {
  install.packages("BiocManager")
}

BiocManager::install("scHiCcompare")

# For the latest version install from GitHub
# devtools::install_github("dozmorovlab/scHiCcompare")
library(scHiCcompare)
library(HiCcompare)
library(tidyr)
library(ggplot2)
library(gridExtra)
library(lattice)
library(data.table)
library(mclust)

scHiCcompare function

Overview

scHiCcompare() function conducts a differential analysis workflow, including imputation and normalization, using chromosome-specific chromatin interaction matrices split into two conditions (or two cell type groups).

  • Imputation - First, scHiC data in each group can optionally undergo imputation to address data sparsity. As resolution increases, the percentage of ‘0’ values or missing data also rises drastically. To address this, scHiCompare applies the random forest (RF) imputation method on each genomic distance (no pooling) or pooled bands with the option of a pooling technique. There are two pooling strategies:

    1. Progressive pooling, where each subsequent band combines interaction frequencies (IFs) within a linearly increasing range of distances.

    2. Fibonacci pooling, where each subsequent band combines IFs within increasing distance ranges, and this increase follows the Fibonacci sequence.

An example of how different pooling styles assign genomic distance into each band

An example of how different pooling styles assign genomic distance into each band

Due to extreme sparsity at higher genomic distances and randomness of long-range interactions, scHiCcompare, by default, workflow focuses on a distance range of 1 to 10MB (main.Distance). If any pool band falls outside this range and has a percentage of missing values exceeding the specified threshold (default missPerc.threshold is 95%), the missing interaction frequencies (IFs) values are imputed using the mean IF values from the available data within that pool band.

  • Pseudo-bulk scHi-C - Second, imputed single-cell Hi-C data in each group are transformed into group-specific pseudo-bulk scHi-C matrices by summing all group-specific single-cell Hi-C matrices.

  • Normalization - After obtaining two group-specific pseudo-bulk matrices, normalization removes global and local biases between two pseudo-bulk matrices. The scHiCcompare workflow applies a LOESS regression model from HiCcompare to jointly normalize two imputed pseudo-bulk matrices. Briefly,

    • The data is visualized using a mean difference (MD) plot, where \(M\), Mean difference (calculated as \(M = \log_2(IF_2 / IF_1)\), Y-axis) is plotted against \(D\), the Distance between interacting regions (X-axis). In this plot, a LOESS regression curve is fitted to adjust the interaction frequencies of the two condition groups, centering the \(M\) differences around a baseline of \(M = 0\).

  • Differential analysis - differential analysis is performed on the processed pseudo-bulk matrices to identify differential chromatin interactions between the two cell types or conditions. This involves separating the normalized log fold changes of interaction frequencies (the M-values) into difference and non-difference groups. This analysis is performed on a per-distance basis.

    • The non-difference group is assumed to follow a normal distribution centered around 0, identified using a Gaussian Mixture Model (GMM). The difference group consists of log fold changes from other distributions that deviate from the non-difference group’s normal distribution. To improve precision, a log fold change threshold fprControl.logfc is applied to values in the difference group, excluding low log fold changes.
    • When the differences are not large enough to form distinct distributions, the default differential analysis of HiCcompare is used.

Input

To use scHiCcompare, you’ll need to define two groups of cells to compare and save cell-specific scHi-C data (individual files in .txt format) in two folders.

Each cell-specific scHi-C .txt file should be formatted as modified sparse upper triangular matrices in R, which consist of five columns (chr1, start1, chr2, start2, IF). Since the full matrix of chromatin interactions is symmetric, only the upper triangular portion, including the diagonal and excluding any 0, is stored in a sparse matrix format. The required sparse matrix format of each single-cell Hi-C is:

  • “chr1” - Chromosome of the first region.
  • “start1” - a start coordinate (in bp) of the first region.
  • “chr2” - Chromosome of the second region.
  • “start2” - a start coordinate (in bp) of the second region.
  • “IF” - the interaction frequency between 2 two regions (IFs).

The ‘.txt’ files need to be saved in tab-separated columns and no row names, column names, or quotes around character strings with the example format below.

##        chr1  start1  chr2  start2  IF
## 17669 chr20       0 chr20       0 128
## 17670 chr20       0 chr20 1000000   1
## 17671 chr20 1000000 chr20 1000000 179
## 17672 chr20       0 chr20 2000000   1
## 17673 chr20 1000000 chr20 2000000   1
## 17674 chr20 2000000 chr20 2000000 174

To run scHiCcompare(), you need two folders with condition-specific scHiC ‘.txt’ files. The condition-specific groups of cells should be pre-defined based on criteria such as experimental conditions, clustering results, or biological characteristics.

In section Others, we shows examples of steps to download and import scHi-C data into R. User can refer to it for more information.

Prepare input folders

Here is an example workflow using scHiC human brain datasets (Lee et al., 2019) with ODC and MG cell types at chromosome 20 with a 1MB resolution.

For the following example sections, we will load samples of 10 single-cell Hi-C data (in ‘.txt’) for each cell type group in two example folders (ODCs_example and MGs_axample). The files follow the same format as those downloaded via download_schic() of Bandnorm. You can extract the folder path by the code below, which could be used as input for scHiCcompare() function.

## Load folder of ODC file path
ODCs_example_path <- system.file("extdata/ODCs_example",
  package = "scHiCcompare"
)

## Load folder of MG file path
MGs_example_path <- system.file("extdata/MGs_example",
  package = "scHiCcompare"
)

Since the data downloaded by Bandnorm has the required input format (5 columns of [chr1, start1, chr2, start2, IF]), we don’t need an extra step for data modification. If, after importing your data into R, its format does not follow the sparse upper triangular input format requirement, you need to modify the data.

scHiCcompare function

scHiCcompare(
  file.path.1, file.path.2,
  select.chromosome = "chr1",
  imputation = "RF",
  normalization = "LOESS",
  differential.detect = "MD.cluster",
  save.output.path = "results/",
  ...
)

Core Parameter :

The core workflow consists of the following steps:

  • Input Preparation: Load two sets of scHi-C data, one for each condition.
    • file.path.1, file.path.2 - Character strings specifying paths to folders containing scHi-C data for the first and second cell type or condition groups.
    • select.chromosome - Integer or character indicating the chromosome to be analyzed (e.g., ‘chr1’ or ‘chr10’.)
  • Imputation (optional) - imputation: Handle missing values in sparse single-cell matrices. 'RF' enables Random Forest-based imputation.
  • Normalization (optional) - normalization: Apply 'LOESS' normalization to correct for systematic biases.
  • Differential Testing - differential.detect: Identify significant changes in chromatin interactions. "MD.cluster" indicates scHiCcompare’s differential detection test on MD plot.

Optional Parameter :

In addition to core functionalities, scHiCcompare provides multiple optional parameters to customize imputation, normalization, differential analysis, and output handling.

  • Imputation: Users can define pooling strategies (pool.style), set the number of imputations (n.imputation), and control iteration limits (maxit). Additionally, users can include/exclude extreme interaction frequency (IF) values (outlier.rm) and set a missing data threshold (missPerc.threshold), which determines the maximum allowable percentage of missing data in pool bands outside the focal genomic distances.
  • Normalization: The A.min parameter helps filter low interaction frequencies, ensuring robust outlier detection during differential analysis.
  • Differential Testing: Parameters such as fprControl.logfc and alpha regulate the false positive rate for GMM difference clusters and define the significance level for outlier detection.
  • Output : Options like save.output.path allow external storage of results (see output example), while visualization settings (Plot, Plot.normalize) generate MD plots for differential detection and normalization effects.

For further detail, user can refer to ?scHiCcompare()

Example of real analysis

In the following example, we will work with scHi-C data from 10 single cells in both ODC and MG cell types at a 1 MG resolution. We will focus on chromosome 20, applying the full workflow of scHiCcompare, which includes imputation, pseudo-bulk normalization, and differential analysis. Our goal is to detect differences for loci with genomic distances ranging from 1 to 10,000,000 bp. The progressive pooling style will be selected to create pool bands for the random forest imputation. For the differential analysis step, we will set the log fold change - false positive control threshold to 0.8.

The input file path was included in the package and conducted in the Prepare input folders section.

## Imputation with 'progressive' pooling
result <- scHiCcompare(
  file.path.1 = ODCs_example_path,
  file.path.2 = MGs_example_path,
  select.chromosome = "chr20",
  main.Distances = 1:10000000,
  imputation = "RF",
  normalization = "LOESS",
  differential.detect = "MD.cluster",
  pool.style = "progressive",
  fprControl.logfc = 0.8,
  Plot = TRUE
)
Chromatin differential detection between ODC and MG in chromosome 20 in example above

Chromatin differential detection between ODC and MG in chromosome 20 in example above

From the visualizations above, normalization effectively reduces the irregular trend in the M values between the imputed pseudo-bulk matrices of the two cell types. At a 1MB resolution, the differential analysis reveals that most of the detected differences occur at closer genomic distances, particularly below 5MB.

Output

Output objects from the R function

The scHiCcompare() function will return an object that contains plots, differential results, pseudo-bulk matrices, normalized results, and imputation tables. The full differential results are available in $Differential_Analysis. Intermediate results can be accessed with $Intermediate, including the imputation result table ($Intermediate$Imputation), the pseudo-bulk matrix in sparse format ($Intermediate$PseudoBulk), and the normalization table ($Intermediate$Bulk.Normalization). These output table objects have the following structure:

  • $Intermediate$PseudoBulk for each condition group ($condition1 and $condition2) has a standard sparse upper triangular format with 3 columns of [region1, region2, IF].

  • $Intermediate$Imputation for each condition group ($condition1 and $condition2) has modified sparse upper triangular format:

    • Interacting bins coordination [region1, region2, cell (condition 1 or condition2), chr]
    • Imputed interaction frequency of each single-cell [imp.IF_{cell name 1}, imp.IF_{cell name 2}, imp.IF_{cell name 3}, …,etc]

  • $Intermediate$Bulk.Normalization has 15 columns

    • Interacting bins coordination [chr1, start1, end1, chr2, start2, end2, D (scaled genomic distance)]
    • Bulk IF values [bulk.IF1, bulk.IF2, M (their log fold change, \(log(IF_2/IF_1)\))]
    • Normalized bulk IF values [adj.bulk.IF1, adj.bulk.IF2, adj.M (their log fold change, \(log(adj.IF_2/adj.IF_1)\))]
    • LOESS correction factor [mc];
    • Average expression value of bulk IF [A].

  • $Differential_Analysis has same structure as $Intermediate$Bulk.Normalization with addition of 2 differential detection results columns

    • Z score of interaction frequencies’s log fold change [Z]
    • Differential result cluster [Difference.cluster]

Externally saved output files

You also can have the option to save the results into the chosen directory by a parameter in scHiCcompare() function. This will save the normalization result table, differential result table, and imputed cell scHi-C data (each group is a sub-folder). The sample of the saved output folder structure is:

|– Bulk_normalization_table.txt

|– Differential_analysis_table.txt

|– Imputed_{group 1’s name}/

  • |– imp_{cell name}.txt

|– Imputed_{group 2’s name}/

  • |– imp_{cell name}.txt

The normalization result Bulk_normalization_table.txt has the same format as the output object from the scHiCcompare() function, $Intermediate$Bulk.Normalization, which is shown in the structure example below.

The differential result table Differential_analysis_table.txt also has the same format as the output object $Differential_Analysis from the function.

The imputed cell’s scHiC data is saved in a folder for each group, which has a modified sparse upper triangular format of five columns [chr1, start1, chr2, start2, IF].

Example of output

Below is a continuous example from Example of real anlysis above, showing how you can extract different result options from the scHiCcompare() function.

### Summary the analysis
print(result)
## -----------------------------------------------------------------
##    ScHiCcompare - Differential Analysis for single cell Hi-C
## -----------------------------------------------------------------
## ScHiCcompare analyzes 10 cells of condition 1 group and 10 cells of condition 2 group at chromosome chr20.
## 
## The process includes:
## Imputation, Bulk Normalization, Differential Analysis
## 
## Note: See full differential result in $Differential_Analysis. Intermediate results can be accessed with $Intermediate.
### Extract imputed differential result
diff_result <- result$Differential_Analysis

DT::datatable(head(diff_result), options = list(scrollX = TRUE), width = 700)
### Extract imputed pseudo bulk matrices normalization
norm_result <- result$Intermediate$Bulk.Normalization

DT::datatable(head(norm_result), options = list(scrollX = TRUE), width = 700)
### Extract imputed ODC cell type table
imp_ODC_table <- result$Intermediate$Imputation$condition1

DT::datatable(head(imp_ODC_table), options = list(scrollX = TRUE), width = 700)
## Extract Pseudo-bulk matrix from imputed scHi-C data
## Pseudo bulk matrix in standard sparse format
psudobulk_result <- result$Intermediate$PseudoBulk$condition1

DT::datatable(head(psudobulk_result),
  options = list(scrollX = TRUE), width = 700
)

Furthermore, you also have some parameter options in the function to indicate which plots to output and an option to save the results in a given directory.

Helper functions

There are several other functions included in scHiCcompare package.

Heatmap HiC matrix plot

plot_HiCmatrix_heatmap() produces a heatmap visualization for HiC and scHiC matrices. It requires, as input, a modified sparse matrix, the same format from scHiCcompare() Input with five columns of chr1, start1, chr2 start2, IF. More information can be found in its help document and the example below.

data("ODC.bandnorm_chr20_1")

plot_HiCmatrix_heatmap(
  scHiC.sparse = ODC.bandnorm_chr20_1,
  main = "Figure 3. Heatmap of a single cell matrix", zlim = c(0, 5)
)
## Matrix dimensions: 63x63

Imputation Diagnostic plot

plot_imputed_distance_diagnostic() generates a diagnostic visualization of imputation across genomic distances for all single cells. It compares the distribution of all cells’ interaction frequency at a given distance data before and after imputation. It requires, as input, the scHiC table format of the original and imputed scHiC datasets. ScHiC table format includes columns of genomic loci coordinates and interaction frequencies (IF) of each cell (cell, chromosome, start1, end1, IF1, IF2, IF3, etc).

The output of $Intermediate$Imputation of scHiCcompare() function is directly compatible with this format. For more details, see the sections on Output)

# Extract imputed table result
imp_MG_table <- result$Intermediate$Imputation$condition2
imp_ODC_table <- result$Intermediate$Imputation$condition1

We need to create the table input for original IFs values in the same format. Below is a continuous example from Example of real anlysis above, showing how you can construct scHiC table for original IF values and compare them with the output of imputed IF values.

# Create scHiC table object for original ODC interaction frequencies (IF)
scHiC.table_ODC <- imp_ODC_table[c("region1", "region2", "cell", "chr")]

# List all files in the specified directory for original ODC data
file.names <- list.files(
  path = ODCs_example_path,
  full.names = TRUE, recursive = TRUE
)

# Loop through each file to read and merge data
for (i in 1:length(file.names)) {
  # Read the current file into a data frame
  data <- read.delim(file.names[[i]])

  names(data) <- c("chr", "region1", "chr2", "region2", paste0("IF_", i))

  data <- data[, names(data) %in%
    c("chr", "region1", "region2", paste0("IF_", i))]

  # Merge the newly read data with the existing scHiC.table_ODC
  scHiC.table_ODC <- merge(scHiC.table_ODC, data,
    by = c("region1", "region2", "chr"), all = TRUE
  )
}

# Create scHiC table object for original MG interaction frequencies (IF)
scHiC.table_MG <- imp_MG_table[c("region1", "region2", "cell", "chr")]

# List all files in the specified directory for original MG data
file.names <- list.files(
  path = MGs_example_path,
  full.names = TRUE, recursive = TRUE
)

# Loop through each file to read and merge data
for (i in 1:length(file.names)) {
  # Read the current file into a data frame
  data <- read.delim(file.names[[i]])

  names(data) <- c("chr", "region1", "chr2", "region2", paste0("IF_", i))

  data <- data[, names(data) %in%
    c("chr", "region1", "region2", paste0("IF_", i))]
  # Merge the newly read data with the existing scHiC.table_MG

  scHiC.table_MG <- merge(scHiC.table_MG, data,
    by = c("region1", "region2", "chr"), all = TRUE
  )
}
# plot imputed Distance Diagnostic of MG
plot1 <- plot_imputed_distance_diagnostic(
  raw_sc_data = scHiC.table_MG,
  imp_sc_data = imp_MG_table, D = 1
)

plot2 <- plot_imputed_distance_diagnostic(
  raw_sc_data = scHiC.table_MG,
  imp_sc_data = imp_MG_table, D = 2
)

plot3 <- plot_imputed_distance_diagnostic(
  raw_sc_data = scHiC.table_MG,
  imp_sc_data = imp_MG_table, D = 3
)

plot4 <- plot_imputed_distance_diagnostic(
  raw_sc_data = scHiC.table_MG,
  imp_sc_data = imp_MG_table, D = 4
)

gridExtra::grid.arrange(plot1, plot2, plot3, plot4, ncol = 2, nrow = 2)
Distribution diagnostic plot of imputed MG cells in some genomic distance

Distribution diagnostic plot of imputed MG cells in some genomic distance

The diagnostic visualizations demonstrate that with a sample of only 10 single cells per group (note: this small sample size is for demonstration purposes only), the imputed values for MG closely match the original distribution only at shorter genomic distances (e.g., D1, D2). Increasing the number of single cells per group enhances imputation accuracy across distances. We recommend using a minimum of 80 single cells per group for optimal imputation performance.

Others

Download scHiC data

To find and download single-cell Hi-C (scHi-C) data, you can use publicly available repositories and databases that host this type of data. Common sources include the Gene Expression Omnibus (GEO), the 4D Nucleome Data Portal (4DN), or data published in research articles, etc. Below are some examples of how to access and download scHi-C data.

  • GEO (Gene Expression Omnibus):

You can search data on GEO using queries such as single-cell Hi-C, scHi-C, or a GEO (GSE) series numbers (e.g., GSE80006), etc. Once you select a dataset, processed data (.txt, .csv, .bed, .hic, etc.)
can be found under the “Supplementary files” section and downloaded via the FTP links at the bottom of the page. Additionally, GEO offers various download formats using different mechanisms. For more details about downloading data in different formats, visit the GEO download guide: https://www.ncbi.nlm.nih.gov/geo/info/download.html.

You can also download these data by R. The example below shows steps to download the mouse scHi-C dataset (Flyamer et al.2017) on GEO.

if (!requireNamespace("BiocManager", quietly = TRUE)) {
  install.packages("BiocManager")
}

BiocManager::install("GEOquery")
library(GEOquery)
# For example, we want to download (Flyamer et al.2017) data
geo_id <- "GSE80006"
# Download the information, notation, feature data, etc
gse <- getGEO(geo_id, GSEMatrix = TRUE)
# You can read more about this function
?getGEO()

# Download and extract the supplementary files (processed data)
getGEOSuppFiles(geo_id, baseDir = "path/to/save")

Other sources:

Some research papers provide data from external sources, which are usually mentioned in the paper. For example, human brain datasets (Lee et al., 2019) are available through a public box directory located https://salkinstitute.box.com/s/fp63a4j36m5k255dhje3zcj5kfuzkyj1.

Additionally, some tools collect scHi-C data from various studies, like https://noble.gs.washington.edu/proj/schic-topic-model/. Below is an example of an R function from Bandnorm, which also accesses existing single-cell Hi-C data at a 1mbp resolution

To download human brain oligodendrocytes (ODC) and microglia (MG) cell type (Lee et al., 2019), we used the download_schic() function of Bandnorm package to download the scHiC data of ODC and MG cell types groups in 1MB resolution.

install.packages(c("ggplot2", "dplyr", "data.table", "Rtsne", "umap"))

if (!requireNamespace("BiocManager", quietly = TRUE)) {
  install.packages("BiocManager")
}

BiocManager::install("immunogenomics/harmony")

devtools::install_github("sshen82/BandNorm", build_vignettes = FALSE)

library(BandNorm)
### Download scHiC data of ODC and MG
download_schic("Lee2019", cell_type = "ODC", cell_path = "ODCs_example")
download_schic("Lee2019", cell_type = "MG", cell_path = "MGs_example")

Import scHiC data in R

After downloading scHi-C data, the next step is to import the data into R for analysis.

ScHi-C data is available in various formats from different sources. Below are examples of how to extract chromosome-specific data for analysis in R.

  • .bedepe, .csv, or .txt formats :

If your raw scHiC data has been processed to ‘.bedepe’, ‘.csv’, or ‘.txt’ formats, it can be read using read.delim(), read.table(), etc. Once the data is loaded, if you have full Hi-C contact matrices, you can convert them to a sparse upper triangular format using the full2sparse() function of the HiCcompare package, then reformatting the columns to achieve the sparse upper triangular input format.

  • .hic format:

To access and import .hic files into R, you can use tools such as strawr for reading and processing .hic files. You can read other similar example in the HiCcompare package vignette

An example of reading .hic with strawr is shown below. straw() reads the .hic file of each single-cell Hi-C and outputs a data.frame in a sparse upper triangular format. This step must be repeated for single-cell Hi-C of the same cell type (condition) group.

if (!requireNamespace("BiocManager", quietly = TRUE)) {
  install.packages("BiocManager")
}

BiocManager::install("strawr")
library(strawr)

# Example to read the contact matrix from a .hic file of a single-cell
filepath <- "path/to/your/schic.hic"

contact_matrix <- straw(
  norm = "NONE", # Normalization method (KR, VC, or NONE)
  filepath, # Path to .hic file
  chr1loc = "chr1", # Chromosome 1
  chr2loc = "chr1", # Chromosome 2 (intra-chromosomal interactions)
  unit = "BP", # Base pair (BP) resolution or fragment (FRAG) resolution
  binsize = 200000 # Bin size (e.g., 200kb)
)
  • .cool format:

To access and import .cool files into R, you can use cooler2bedpe() function of HiCcompare package or cooler to access the data. You can read example of cooler on HiCcompare vignette

For example, the files can be read directly into R by cooler2bedpe() function, which will return a list object in the format of BEDPE, containing two elements: “cis” - Contains the intra-chromosomal contact matrices, one per chromosome; “trans” - Contains the inter-chromosomal contact matrix. You can read about this in more detail by ?cooler2bedpe().

# Install BiocManager if not already installed
if (!requireNamespace("BiocManager", quietly = TRUE)) {
  install.packages("BiocManager")
}

# Install HiCcompare package from Bioconductor
BiocManager::install("HiCcompare")

# Load the HiCcompare package
library(HiCcompare)
cool.file <- read_files("path/to/schic.cool")

Session Info

## R version 4.5.1 (2025-06-13)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.3 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               LC_TIME=en_US.UTF-8        LC_COLLATE=C               LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8    LC_PAPER=en_US.UTF-8       LC_NAME=C                  LC_ADDRESS=C               LC_TELEPHONE=C             LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## time zone: Etc/UTC
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] mclust_6.1.1       data.table_1.17.8  lattice_0.22-7     gridExtra_2.3      ggplot2_4.0.0      tidyr_1.3.1        HiCcompare_1.31.0  dplyr_1.1.4        scHiCcompare_1.3.0 BiocStyle_2.37.1  
## 
## loaded via a namespace (and not attached):
##   [1] Rdpack_2.6.4                DBI_1.2.3                   rlang_1.1.6                 magrittr_2.0.4              miceadds_3.18-36            matrixStats_1.5.0           compiler_4.5.1              mgcv_1.9-3                  vctrs_0.6.5                 pkgconfig_2.0.3             shape_1.4.6.1               fastmap_1.2.0               backports_1.5.0             XVector_0.49.3              labeling_0.4.3              rmarkdown_2.30              nloptr_2.2.1                purrr_1.1.0                 xfun_0.53                   glmnet_4.1-10               jomo_2.7-6                  cachem_1.1.0                jsonlite_2.0.0              rhdf5filters_1.23.0         DelayedArray_0.37.0         pan_1.9                     Rhdf5lib_1.33.0             BiocParallel_1.43.4         broom_1.0.10                parallel_4.5.1              R6_2.6.1                    bslib_0.9.0                 RColorBrewer_1.1-3          ranger_0.17.0               car_3.1-3                  
##  [36] boot_1.3-32                 rpart_4.1.24                GenomicRanges_1.63.0        jquerylib_0.1.4             Rcpp_1.1.0                  Seqinfo_0.99.4              SummarizedExperiment_1.39.2 iterators_1.0.14            knitr_1.50                  IRanges_2.45.0              Matrix_1.7-4                splines_4.5.1               nnet_7.3-20                 tidyselect_1.2.1            abind_1.4-8                 yaml_2.3.10                 codetools_0.2-20            tibble_3.3.0                withr_3.0.2                 InteractionSet_1.37.1       Biobase_2.69.1              S7_0.2.0                    evaluate_1.0.5              survival_3.8-3              pillar_1.11.1               BiocManager_1.30.26         MatrixGenerics_1.21.0       carData_3.0-5               mice_3.18.0                 KernSmooth_2.23-26          DT_0.34.0                   foreach_1.5.2               stats4_4.5.1                reformulas_0.4.2            generics_0.1.4             
##  [71] S4Vectors_0.47.6            scales_1.4.0                minqa_1.2.8                 gtools_3.9.5                glue_1.8.0                  pheatmap_1.0.13             maketools_1.3.2             tools_4.5.1                 sys_3.4.3                   lme4_1.1-37                 buildtools_1.0.0            rhdf5_2.55.0                grid_4.5.1                  mitools_2.4                 crosstalk_1.2.2             rbibutils_2.3               nlme_3.1-168                Formula_1.2-5               cli_3.6.5                   S4Arrays_1.9.3              gtable_0.3.6                rstatix_0.7.3               sass_0.4.10                 digest_0.6.37               BiocGenerics_0.55.4         SparseArray_1.9.2           htmlwidgets_1.6.4           farver_2.1.2                htmltools_0.5.8.1           lifecycle_1.0.4             mitml_0.4-5                 MASS_7.3-65