Contents

1 Introduction

BERT (Batch-Effect Removal with Trees) offers flexible and efficient batch effect correction of omics data, while providing maximum tolerance to missing values. Tested on multiple datasets from proteomic analyses, BERT offered a typical 5-10x runtime improvement over existing methods, while retaining more numeric values and preserving batch effect reduction quality.

As such, BERT is a valuable preprocessing tool for data analysis workflows, in particular for proteomic data. By providing BERT via Bioconductor, we make this tool available to a wider research community. An accompanying research paper is currently under preparation and will be made public soon.

BERT addresses the same fundamental data integration challenges than the [HarmonizR][https://github.com/HSU-HPC/HarmonizR] package, which is released on Bioconductor in November 2023. However, various algorithmic modications and optimizations of BERT provide better execution time and better data coverage than HarmonizR. Moreover, BERT offers a more user-friendly design and a less error-prone input format.

Please note that our package BERT is neither affiliated with nor related to Bidirectional Encoder Representations from Transformers as published by Google.

Please report any questions and issues in the GitHub forum, the BioConductor forum or directly contact the authors,

2 Installation

Please download and install a current version of R (Windows binaries). You might want to consider installing a development environment as well, e.g. RStudio. Finally, BERT can be installed via Bioconductor using

if (!require("BiocManager", quietly = TRUE)){
    install.packages("BiocManager")
}
BiocManager::install("BERT")

which will install all required dependencies. To install the development version of BERT, you can use devtools as follows

devtools::install_github("HSU-HPC/BERT")

which may require the manual installation of the dependencies sva and limma.

if (!require("BiocManager", quietly = TRUE)){
    install.packages("BiocManager")
}
BiocManager::install("sva")
BiocManager::install("limma")

3 Data Preparation

As input, BERT requires a dataframe1 Matrices and SummarizedExperiments work as well, but will automatically be converted to dataframes. with samples in rows and features in columns. For each sample, the respective batch should be indicated by an integer or string in a corresponding column labelled Batch. Missing values should be labelled as NA. A valid example dataframe could look like this:

example = data.frame(feature_1 = stats::rnorm(5), feature_2 = stats::rnorm(5), Batch=c(1,1,2,2,2))
example
#>    feature_1  feature_2 Batch
#> 1 -0.2096920  0.8316255     1
#> 2  0.6273626 -0.8657119     1
#> 3 -1.5485734 -1.3864449     2
#> 4 -0.9148711 -0.2138413     2
#> 5  1.0956188  0.3426784     2

Note that each batch should contain at least two samples. Optional columns that can be passed are

Note that BERT tries to find all metadata information for a SummarizedExperiment, including the mandatory batch information, using colData. For instance, a valid SummarizedExperiment might be defined as

nrows <- 200
ncols <- 8
expr_values <- matrix(runif(nrows * ncols, 1, 1e4), nrows)
# colData also takes all other metadata information, such as Label, Sample,
# Covariables etc.
colData <- data.frame(Batch=c(1,1,1,1,2,2,2,2), Reference=c(1,1,0,0,1,1,0,0))
dataset_raw = SummarizedExperiment::SummarizedExperiment(assays=list(expr=expr_values), colData=colData)

4 Basic Usage

BERT can be invoked by importing the BERT library and calling the BERT function. The batch effect corrected data is returned as a dataframe that mirrors the input dataframe2 In particular, the row and column names are in the same order and the optional columns are preserved..

library(BERT)
# generate test data with 10% missing values as provided by the BERT library
dataset_raw <- generate_dataset(features=60, batches=10, samplesperbatch=10, mvstmt=0.1, classes=2)
# apply BERT
dataset_adjusted <- BERT(dataset_raw)
#> 2024-04-30 22:40:41.093596 INFO::Formatting Data.
#> 2024-04-30 22:40:41.109441 INFO::Replacing NaNs with NAs.
#> 2024-04-30 22:40:41.121829 INFO::Removing potential empty rows and columns
#> 2024-04-30 22:40:41.418587 INFO::Found  600  missing values.
#> 2024-04-30 22:40:41.432039 INFO::Introduced 0 missing values due to singular proteins at batch/covariate level.
#> 2024-04-30 22:40:41.432982 INFO::Done
#> 2024-04-30 22:40:41.433751 INFO::Acquiring quality metrics before batch effect correction.
#> 2024-04-30 22:40:41.44976 INFO::Starting hierarchical adjustment
#> 2024-04-30 22:40:41.450853 INFO::Found  10  batches.
#> 2024-04-30 22:40:41.451554 INFO::Cores argument is not defined or BPPARAM has been specified. Argument corereduction will not be used.
#> 2024-04-30 22:40:43.526564 INFO::Using default BPPARAM
#> 2024-04-30 22:40:43.52714 INFO::Processing subtree level 1
#> 2024-04-30 22:40:46.128428 INFO::Processing subtree level 2
#> 2024-04-30 22:40:48.812049 INFO::Adjusting the last 1 batches sequentially
#> 2024-04-30 22:40:48.816822 INFO::Done
#> 2024-04-30 22:40:48.818068 INFO::Acquiring quality metrics after batch effect correction.
#> 2024-04-30 22:40:48.825087 INFO::ASW Batch was 0.431876094060176 prior to batch effect correction and is now -0.0566329415457089 .
#> 2024-04-30 22:40:48.825896 INFO::ASW Label was 0.389059894091273 prior to batch effect correction and is now 0.781214433175144 .
#> 2024-04-30 22:40:48.828753 INFO::Total function execution time is  7.76767897605896  s and adjustment time is  7.36634707450867 s ( 94.83 )

BERT uses the logging library to convey live information to the user during the adjustment procedure. The algorithm first verifies the shape and suitability of the input dataframe (lines 1-6) before continuing with the actual batch effect correction (lines 8-14). BERT measure batch effects before and after the correction step by means of the average silhouette score (ASW) with respect to batch and labels (lines 7 and 15). The ASW Label should increase in a successful batch effect correction, whereas low values (\(\leq 0\)) are desireable for the ASW Batch3 The optimum of ASW Label is 1, which is typically however not achieved on real-world datasets. Also, the optimum of ASW Batch can vary, depending on the class distributions of the batches.. Finally, BERT prints the total function execution time (including the computation time for the quality metrics).

5 Advanced Options

5.1 Parameters

BERT offers a large number of parameters to customize the batch effect adjustment. The full function call, including all defaults is

BERT(data, cores = NULL, combatmode = 1, corereduction=2, stopParBatches=2, backend="default", method="ComBat", qualitycontrol=TRUE, verify=TRUE, labelname="Label", batchname="Batch", referencename="Reference", samplename="Sample", covariatename=NULL, BPPARAM=NULL, assayname=NULL)

In the following, we list the respective meaning of each parameter: - data: The input dataframe/matrix/SummarizedExperiment to adjust. See Data Preparation for detailed formatting instructions. - data The data for batch-effect correction. Must contain at least two samples per batch and 2 features.

  • cores: BERT uses BiocParallel for parallelization. If the user specifies a value cores, BERT internally creates and uses a new instance of BiocParallelParam, which is however not exhibited to the user. Setting this parameter can speed up the batch effect adjustment considerably, in particular for large datasets and on unix-based operating systems. A value between \(2\) and \(4\) is a reasonable choice for typical commodity hardware. Multi-node computations are not supported as of now. If, however, cores is not specified, BERT will default to BiocParallel::bpparam(), which may have been set by the user or the system. Additionally, the user can directly specify a specific instance of BiocParallelParam to be used via the BPPARAM argument.
  • combatmode An integer that encodes the parameters to use for ComBat.
Value par.prior mean.only
1 TRUE FALSE
2 TRUE TRUE
3 FALSE FALSE
4 FALSE TRUE

The value of this parameter will be ignored, if method!="ComBat".

  • corereduction Positive integer indicating the factor by which the number of processes should be reduced, once no further adjustment is possible for the current number of batches.4 E.g. consider a BERT call with 8 batches and 8 processes. Further adjustment is not possible with this number of processes, since batches are always processed in pairs. With corereduction=2, the number of processes for the following adjustment steps would be set to \(8/2=4\), which is the maximum number of usable processes for this example. This parameter is used only, if the user specified a custom value for parameter cores.

  • stopParBatches Positive integer indicating the minimum number of batches required at a hierarchy level to proceed with parallelized adjustment. If the number of batches is smaller, adjustment will be performed sequentially to avoid communication overheads.

  • backend: The backend to use for inter-process communication. Possible choices are default and file, where the former refers to the default communication backend of the requested parallelization mode and the latter will create temporary .rds files for data communication. ‘default’ is usually faster for small to medium sized datasets.

  • method: The method to use for the underlying batch effect correction steps. Should be either ComBat, limma for limma::removeBatchEffects or ref for adjustment using specified references (cf. Data Preparation). The underlying batch effect adjustment method for ref is a modified version of the limma method.

  • qualitycontrol: A boolean to (de)activate the ASW computation. Deactivating the ASW computations accelerates the computations.

  • verify: A boolean to (de)activate the initial format check of the input data. Deactivating this verification step accelerates the computations.

  • labelname: A string containing the name of the column to use as class labels. The default is “Label”.

  • batchname: A string containing the name of the column to use as batch labels. The default is “Batch”.

  • referencename: A string containing the name of the column to use as reference labels. The default is “Reference”.

  • covariatename: A vector containing the names of columns with categorical covariables.The default is NULL, in which case all column names are matched agains the pattern “Cov”.

  • BPPARAM: An instance of BiocParallelParam that will be used for parallelization. The default is null, in which case the value of cores determines the behaviour of BERT.

  • assayname: If the user chooses to pass a SummarizedExperiment object, they need to specify the name of the assay that they want to apply BERT to here. BERT then returns the input SummarizedExperiment with an additional assay labeled assayname_BERTcorrected.

5.2 Verbosity

BERT utilizes the logging package for output. The user can easily specify the verbosity of BERT by setting the global logging level in the script. For instance

logging::setLevel("WARN") # set level to warn and upwards
result <- BERT(data,cores = 1) # BERT executes silently

5.3 Choosing the Optimal Number of Cores

BERT exhibits a large number of parameters for parallelisation as to provide users with maximum flexibility. For typical scenarios, however, the default parameters are well suited. For very large experiments (\(>15\) batches), we recommend to increase the number of cores (a reasonable value is \(4\) but larger values may be possible on your hardware). Most users should leave all parameters to their respective default.

6 Examples

In the following, we present simple cookbook examples for BERT usage. Note that ASWs (and runtime) will most likely differ on your machine, since the data generating process involves multiple random choices.

6.1 Sequential Adjustment with limma

Here, BERT uses limma as underlying batch effect correction algorithm (method='limma') and performs all computations on a single process (cores parameter is left on default).

# import BERT
library(BERT)
# generate data with 30 batches, 60 features, 15 samples per batch, 15% missing values and 2 classes
dataset_raw <- generate_dataset(features=60, batches=20, samplesperbatch=15, mvstmt=0.15, classes=2)
# BERT
dataset_adjusted <- BERT(dataset_raw, method="limma")
#> 2024-04-30 22:40:49.162495 INFO::Formatting Data.
#> 2024-04-30 22:40:49.163768 INFO::Replacing NaNs with NAs.
#> 2024-04-30 22:40:49.166541 INFO::Removing potential empty rows and columns
#> 2024-04-30 22:40:49.171025 INFO::Found  2700  missing values.
#> 2024-04-30 22:40:49.207393 INFO::Introduced 0 missing values due to singular proteins at batch/covariate level.
#> 2024-04-30 22:40:49.208554 INFO::Done
#> 2024-04-30 22:40:49.209144 INFO::Acquiring quality metrics before batch effect correction.
#> 2024-04-30 22:40:49.222707 INFO::Starting hierarchical adjustment
#> 2024-04-30 22:40:49.223948 INFO::Found  20  batches.
#> 2024-04-30 22:40:49.224775 INFO::Cores argument is not defined or BPPARAM has been specified. Argument corereduction will not be used.
#> 2024-04-30 22:40:49.226287 INFO::Using default BPPARAM
#> 2024-04-30 22:40:49.226904 INFO::Processing subtree level 1
#> 2024-04-30 22:40:49.910745 INFO::Processing subtree level 2
#> 2024-04-30 22:40:50.560245 INFO::Processing subtree level 3
#> 2024-04-30 22:40:51.254636 INFO::Adjusting the last 1 batches sequentially
#> 2024-04-30 22:40:51.271383 INFO::Done
#> 2024-04-30 22:40:51.273328 INFO::Acquiring quality metrics after batch effect correction.
#> 2024-04-30 22:40:51.30491 INFO::ASW Batch was 0.49667382471506 prior to batch effect correction and is now -0.145687273068095 .
#> 2024-04-30 22:40:51.307012 INFO::ASW Label was 0.265781628513168 prior to batch effect correction and is now 0.866399036190108 .
#> 2024-04-30 22:40:51.313217 INFO::Total function execution time is  2.1491711139679  s and adjustment time is  2.04762983322144 s ( 95.28 )

6.2 Parallel Batch Effect Correction with ComBat

Here, BERT uses ComBat as underlying batch effect correction algorithm (method is left on default) and performs all computations on a 2 processes (cores=2).

# import BERT
library(BERT)
# generate data with 30 batches, 60 features, 15 samples per batch, 15% missing values and 2 classes
dataset_raw <- generate_dataset(features=60, batches=20, samplesperbatch=15, mvstmt=0.15, classes=2)
# BERT
dataset_adjusted <- BERT(dataset_raw, cores=2)
#> 2024-04-30 22:40:51.451804 INFO::Formatting Data.
#> 2024-04-30 22:40:51.452507 INFO::Replacing NaNs with NAs.
#> 2024-04-30 22:40:51.453542 INFO::Removing potential empty rows and columns
#> 2024-04-30 22:40:51.455788 INFO::Found  2700  missing values.
#> 2024-04-30 22:40:51.48211 INFO::Introduced 0 missing values due to singular proteins at batch/covariate level.
#> 2024-04-30 22:40:51.482796 INFO::Done
#> 2024-04-30 22:40:51.48327 INFO::Acquiring quality metrics before batch effect correction.
#> 2024-04-30 22:40:51.495288 INFO::Starting hierarchical adjustment
#> 2024-04-30 22:40:51.497265 INFO::Found  20  batches.
#> 2024-04-30 22:40:52.206552 INFO::Set up parallel execution backend with 2 workers
#> 2024-04-30 22:40:52.207409 INFO::Processing subtree level 1 with 20 batches using 2 cores.
#> 2024-04-30 22:40:55.730013 INFO::Adjusting the last 2 batches sequentially
#> 2024-04-30 22:40:55.731187 INFO::Adjusting sequential tree level 1 with 2 batches
#> 2024-04-30 22:40:57.637413 INFO::Done
#> 2024-04-30 22:40:57.638003 INFO::Acquiring quality metrics after batch effect correction.
#> 2024-04-30 22:40:57.647208 INFO::ASW Batch was 0.502489542563288 prior to batch effect correction and is now -0.156552864254054 .
#> 2024-04-30 22:40:57.64785 INFO::ASW Label was 0.263511111099986 prior to batch effect correction and is now 0.86194103982668 .
#> 2024-04-30 22:40:57.648529 INFO::Total function execution time is  6.1968240737915  s and adjustment time is  6.14002394676208 s ( 99.08 )

6.3 Batch Effect Correction Using SummarizedExperiment

Here, BERT takes the input data using a SummarizedExperiment instead. Batch effect correction is then performed using ComBat as underlying algorithm (method is left on default) and all computations are performed on a single process (cores parameter is left on default).

nrows <- 200
ncols <- 8
# SummarizedExperiments store samples in columns and features in rows (in contrast to BERT).
# BERT will automatically account for this.
expr_values <- matrix(runif(nrows * ncols, 1, 1e4), nrows)
# colData also takes further metadata information, such as Label, Sample,
# Reference or Covariables
colData <- data.frame("Batch"=c(1,1,1,1,2,2,2,2), "Label"=c(1,2,1,2,1,2,1,2), "Sample"=c(1,2,3,4,5,6,7,8))
dataset_raw = SummarizedExperiment::SummarizedExperiment(assays=list(expr=expr_values), colData=colData)
dataset_adjusted = BERT(dataset_raw, assayname = "expr")
#> 2024-04-30 22:40:57.848205 INFO::Formatting Data.
#> 2024-04-30 22:40:57.849198 INFO::Recognized SummarizedExperiment
#> 2024-04-30 22:40:57.849843 INFO::Typecasting input to dataframe.
#> 2024-04-30 22:40:57.895329 INFO::Replacing NaNs with NAs.
#> 2024-04-30 22:40:57.896369 INFO::Removing potential empty rows and columns
#> 2024-04-30 22:40:57.898958 INFO::Found  0  missing values.
#> 2024-04-30 22:40:57.907764 INFO::Introduced 0 missing values due to singular proteins at batch/covariate level.
#> 2024-04-30 22:40:57.908741 INFO::Done
#> 2024-04-30 22:40:57.9098 INFO::Acquiring quality metrics before batch effect correction.
#> 2024-04-30 22:40:57.915078 INFO::Starting hierarchical adjustment
#> 2024-04-30 22:40:57.916105 INFO::Found  2  batches.
#> 2024-04-30 22:40:57.916783 INFO::Cores argument is not defined or BPPARAM has been specified. Argument corereduction will not be used.
#> 2024-04-30 22:40:57.917269 INFO::Using default BPPARAM
#> 2024-04-30 22:40:57.917654 INFO::Adjusting the last 2 batches sequentially
#> 2024-04-30 22:40:57.918492 INFO::Adjusting sequential tree level 1 with 2 batches
#> 2024-04-30 22:40:57.958432 INFO::Done
#> 2024-04-30 22:40:57.959024 INFO::Acquiring quality metrics after batch effect correction.
#> 2024-04-30 22:40:57.962376 INFO::ASW Batch was -0.00257230270324539 prior to batch effect correction and is now -0.0990680181834778 .
#> 2024-04-30 22:40:57.962903 INFO::ASW Label was 0.00831152997666771 prior to batch effect correction and is now 0.0254924622160256 .
#> 2024-04-30 22:40:57.96352 INFO::Total function execution time is  0.115384101867676  s and adjustment time is  0.0425479412078857 s ( 36.88 )

6.4 BERT with Covariables

BERT can utilize categorical covariables that are specified in columns Cov_1, Cov_2, .... These columns are automatically detected and integrated into the batch effect correction process.

# import BERT
library(BERT)
# set seed for reproducibility
set.seed(1)
# generate data with 5 batches, 60 features, 30 samples per batch, 15% missing values and 2 classes
dataset_raw <- generate_dataset(features=60, batches=5, samplesperbatch=30, mvstmt=0.15, classes=2)
# create covariable column with 2 possible values, e.g. male/female condition
dataset_raw["Cov_1"] = sample(c(1,2), size=dim(dataset_raw)[1], replace=TRUE)
# BERT
dataset_adjusted <- BERT(dataset_raw)
#> 2024-04-30 22:40:58.089355 INFO::Formatting Data.
#> 2024-04-30 22:40:58.089974 INFO::Replacing NaNs with NAs.
#> 2024-04-30 22:40:58.090791 INFO::Removing potential empty rows and columns
#> 2024-04-30 22:40:58.092345 INFO::Found  1350  missing values.
#> 2024-04-30 22:40:58.093105 INFO::BERT requires at least 2 numeric values per batch/covariate level. This may reduce the number of adjustable features considerably, depending on the quantification technique.
#> 2024-04-30 22:40:58.112357 INFO::Introduced 0 missing values due to singular proteins at batch/covariate level.
#> 2024-04-30 22:40:58.112926 INFO::Done
#> 2024-04-30 22:40:58.113333 INFO::Acquiring quality metrics before batch effect correction.
#> 2024-04-30 22:40:58.117359 INFO::Starting hierarchical adjustment
#> 2024-04-30 22:40:58.118014 INFO::Found  5  batches.
#> 2024-04-30 22:40:58.118438 INFO::Cores argument is not defined or BPPARAM has been specified. Argument corereduction will not be used.
#> 2024-04-30 22:40:58.118886 INFO::Using default BPPARAM
#> 2024-04-30 22:40:58.119295 INFO::Processing subtree level 1
#> 2024-04-30 22:40:58.414214 INFO::Adjusting the last 2 batches sequentially
#> 2024-04-30 22:40:58.428553 INFO::Adjusting sequential tree level 1 with 2 batches
#> 2024-04-30 22:40:58.509074 INFO::Done
#> 2024-04-30 22:40:58.510262 INFO::Acquiring quality metrics after batch effect correction.
#> 2024-04-30 22:40:58.518102 INFO::ASW Batch was 0.492773245691086 prior to batch effect correction and is now -0.0377157224767566 .
#> 2024-04-30 22:40:58.518954 INFO::ASW Label was 0.40854766060101 prior to batch effect correction and is now 0.895560693013661 .
#> 2024-04-30 22:40:58.520382 INFO::Total function execution time is  0.430937051773071  s and adjustment time is  0.391141176223755 s ( 90.77 )

6.5 BERT with references

In rare cases, class distributions across experiments may be severely skewed. In particular, a batch might contain classes that other batches don’t contain. In these cases, samples of common conditions may serve as references (bridges) between the batches (method="ref"). BERT utilizes those samples as references that have a condition specified in the “Reference” column of the input. All other samples are co-adjusted. Please note, that this strategy implicitly uses limma as underlying batch effect correction algorithm.

# import BERT
library(BERT)
# generate data with 4 batches, 6 features, 15 samples per batch, 15% missing values and 2 classes
dataset_raw <- generate_dataset(features=6, batches=4, samplesperbatch=15, mvstmt=0.15, classes=2)
# create reference column with default value 0.  The 0 indicates, that the respective sample should be co-adjusted only.
dataset_raw[, "Reference"] <- 0
# randomly select 2 references per batch and class - in practice, this choice will be determined by external requirements (e.g. class known for only these samples)
batches <- unique(dataset_raw$Batch) # all the batches
for(b in batches){ # iterate over all batches
    # references from class 1
    ref_idx = sample(which((dataset_raw$Batch==b)&(dataset_raw$Label==1)), size=2, replace=FALSE)
    dataset_raw[ref_idx, "Reference"] <- 1
    # references from class 2
    ref_idx = sample(which((dataset_raw$Batch==b)&(dataset_raw$Label==2)), size=2, replace=FALSE)
    dataset_raw[ref_idx, "Reference"] <- 2
}
# BERT
dataset_adjusted <- BERT(dataset_raw, method="ref")
#> 2024-04-30 22:40:58.674391 INFO::Formatting Data.
#> 2024-04-30 22:40:58.67608 INFO::Replacing NaNs with NAs.
#> 2024-04-30 22:40:58.678034 INFO::Removing potential empty rows and columns
#> 2024-04-30 22:40:58.680169 INFO::Found  60  missing values.
#> 2024-04-30 22:40:58.685146 INFO::Introduced 0 missing values due to singular proteins at batch/covariate level.
#> 2024-04-30 22:40:58.685724 INFO::Done
#> 2024-04-30 22:40:58.686198 INFO::Acquiring quality metrics before batch effect correction.
#> 2024-04-30 22:40:58.688935 INFO::Starting hierarchical adjustment
#> 2024-04-30 22:40:58.690036 INFO::Found  4  batches.
#> 2024-04-30 22:40:58.690567 INFO::Cores argument is not defined or BPPARAM has been specified. Argument corereduction will not be used.
#> 2024-04-30 22:40:58.691115 INFO::Using default BPPARAM
#> 2024-04-30 22:40:58.691816 INFO::Processing subtree level 1
#> 2024-04-30 22:40:58.937601 INFO::Adjusting the last 2 batches sequentially
#> 2024-04-30 22:40:58.941392 INFO::Adjusting sequential tree level 1 with 2 batches
#> 2024-04-30 22:40:59.022524 INFO::Done
#> 2024-04-30 22:40:59.024133 INFO::Acquiring quality metrics after batch effect correction.
#> 2024-04-30 22:40:59.027987 INFO::ASW Batch was 0.440355021914032 prior to batch effect correction and is now -0.087480278736629 .
#> 2024-04-30 22:40:59.028578 INFO::ASW Label was 0.373906827748893 prior to batch effect correction and is now 0.919791677398366 .
#> 2024-04-30 22:40:59.030592 INFO::Total function execution time is  0.356313943862915  s and adjustment time is  0.332491874694824 s ( 93.31 )

7 Issues

Issues can be reported in the GitHub forum, the BioConductor forum or directly to the authors.

8 License

This code is published under the GPLv3.0 License and is available for non-commercial academic purposes.

9 Reference

Please cite our manuscript, if you use BERT for your research: Yannis Schumann, Simon Schlumbohm et al., BERT - Batch Effect Reduction Trees with Missing Value Tolerance, 2023

10 Session Info

sessionInfo()
#> R version 4.4.0 beta (2024-04-14 r86421)
#> Platform: x86_64-apple-darwin20
#> Running under: macOS Monterey 12.7.1
#> 
#> Matrix products: default
#> BLAS:   /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRblas.0.dylib 
#> LAPACK: /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0
#> 
#> locale:
#> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#> 
#> time zone: America/New_York
#> tzcode source: internal
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] BERT_1.0.0       BiocStyle_2.32.0
#> 
#> loaded via a namespace (and not attached):
#>  [1] tidyselect_1.2.1            blob_1.2.4                 
#>  [3] Biostrings_2.72.0           fastmap_1.1.1              
#>  [5] janitor_2.2.0               XML_3.99-0.16.1            
#>  [7] digest_0.6.35               timechange_0.3.0           
#>  [9] lifecycle_1.0.4             cluster_2.1.6              
#> [11] statmod_1.5.0               survival_3.6-4             
#> [13] KEGGREST_1.44.0             invgamma_1.1               
#> [15] RSQLite_2.3.6               magrittr_2.0.3             
#> [17] genefilter_1.86.0           compiler_4.4.0             
#> [19] rlang_1.1.3                 sass_0.4.9                 
#> [21] tools_4.4.0                 yaml_2.3.8                 
#> [23] knitr_1.46                  S4Arrays_1.4.0             
#> [25] bit_4.0.5                   DelayedArray_0.30.0        
#> [27] abind_1.4-5                 BiocParallel_1.38.0        
#> [29] BiocGenerics_0.50.0         grid_4.4.0                 
#> [31] stats4_4.4.0                xtable_1.8-4               
#> [33] edgeR_4.2.0                 iterators_1.0.14           
#> [35] logging_0.10-108            SummarizedExperiment_1.34.0
#> [37] cli_3.6.2                   rmarkdown_2.26             
#> [39] crayon_1.5.2                generics_0.1.3             
#> [41] httr_1.4.7                  DBI_1.2.2                  
#> [43] cachem_1.0.8                stringr_1.5.1              
#> [45] zlibbioc_1.50.0             splines_4.4.0              
#> [47] parallel_4.4.0              AnnotationDbi_1.66.0       
#> [49] BiocManager_1.30.22         XVector_0.44.0             
#> [51] matrixStats_1.3.0           vctrs_0.6.5                
#> [53] Matrix_1.7-0                jsonlite_1.8.8             
#> [55] sva_3.52.0                  bookdown_0.39              
#> [57] comprehenr_0.6.10           IRanges_2.38.0             
#> [59] S4Vectors_0.42.0            bit64_4.0.5                
#> [61] locfit_1.5-9.9              foreach_1.5.2              
#> [63] limma_3.60.0                jquerylib_0.1.4            
#> [65] annotate_1.82.0             glue_1.7.0                 
#> [67] codetools_0.2-20            lubridate_1.9.3            
#> [69] stringi_1.8.3               GenomeInfoDb_1.40.0        
#> [71] GenomicRanges_1.56.0        UCSC.utils_1.0.0           
#> [73] htmltools_0.5.8.1           GenomeInfoDbData_1.2.12    
#> [75] R6_2.5.1                    evaluate_0.23              
#> [77] lattice_0.22-6              Biobase_2.64.0             
#> [79] png_0.1-8                   memoise_2.0.1              
#> [81] snakecase_0.11.1            bslib_0.7.0                
#> [83] Rcpp_1.0.12                 SparseArray_1.4.0          
#> [85] nlme_3.1-164                mgcv_1.9-1                 
#> [87] xfun_0.43                   MatrixGenerics_1.16.0