RNAseqCovarImpute 1.0.2
The RNAseqCovarImpute package makes linear model analysis for RNA-seq read counts compatible with multiple imputation of missing covariates. Relying on the Bioconductor limma package, RNAseqCovarImpute is included in Bioconductor as an extension of the variance modeling at the observational level (voom) method which can be applied in circumstances with missing covariate data.
Missing data is a common problem in observational studies, as modeling techniques such as linear regression cannot be fit to data with missing points. Missing data is frequently handled using complete case analyses in which any individuals with missing data are dropped from the study. Dropping participants can reduce statistical power and, in some cases, result in biased model estimates. A common technique to address these problems is to replace or ‘impute’ missing data points with substituted values. Typically, for a given covariate, missing data points are imputed using a prediction model including other relevant covariates as independent variables. In single imputation, a missing value is replaced with the most likely value based on the predictive model. However, by ignoring the uncertainty inherent with predicting missing data, single imputation methods can result in biased coefficients and over-confident standard errors. Multiple imputation addresses this problem by generating several predictions, thereby allowing for uncertainty about the missing data. In a typical multiple imputation procedure: 1) M imputed data sets are created, 2) each data set is analyzed separately (e.g., using linear regression), and 3) estimates and standard errors across the M analyses are pooled using Rubin’s rules.
The RNAseqCovarImpute package implements multiple imputation of missing covariates and differential gene expression analysis by 1) randomly binning genes into smaller groups, 2) creating M imputed datasets separately within each bin, where the imputation predictor matrix includes all covariates and the log counts per million (CPM) for the genes within each bin, 3) estimating gene expression changes using limma::voom followed by limma::lmFit functions, separately on each M imputed dataset within each gene bin, 4) un-binning the gene sets and stacking the M sets of model results before applying the limma::squeezeVar function to apply a variance shrinking Bayesian procedure to each M set of model results, 5) pooling the results with Rubins’ rules to produce combined coefficients, standard errors, and P-values, and 6) adjusting P-values for multiplicity to account for false discovery rate (FDR).
# Install from github
library(devtools)
install_github("brennanhilton/RNAseqCovarImpute")
# Install from Bioconductor (not yet on Bioconductor)
if (!require("BiocManager", quietly = TRUE)) {
install.packages("BiocManager")
}
BiocManager::install("RNAseqCovarImpute")Normally you would have your own covariate and RNA-sequencing data. We generated random data for the purpose of this demonstration. The exact code used to generate these data are found in the Example Data for RNAseqCovarImpute vignette. In short, example_data contains 500 rows with data for variables x, y, and z, which are continuous normally distributed, and a and b, which are binary variables. Missigness was simulated for all variables other than x such that a complete case analysis would drop 24.2% of participants. example_DGE contains random count data from the Poisson distribution for 500 made up genes, ENS1-ENS500
library(RNAseqCovarImpute)
library(dplyr)
library(BiocParallel)
data(example_data)
data(example_DGE)The default is approximately 1 gene per 10 individuals in the study, but the user can specify a different ratio. For example, in a study with 500 participants and 10,000 genes, 200 bins of 50 genes would be created using the default ratio. When the total number of genes is not divisible by the bin size, the method flexibly creates bins of two different sizes. For example, if the same hypothetical study included 10,001 genes, 199 bins of 50 and 1 bin of 51 genes would be created. The order of the features (e.g., ENSEMBL gene identifiers) should be randomized before binning.
intervals <- get_gene_bin_intervals(example_DGE, example_data, n = 10)| start | end | number |
|---|---|---|
| 1 | 50 | 50 |
| 51 | 100 | 50 |
| 101 | 150 | 50 |
| 151 | 200 | 50 |
| 201 | 250 | 50 |
| 251 | 300 | 50 |
| 301 | 350 | 50 |
| 351 | 400 | 50 |
| 401 | 450 | 50 |
| 451 | 500 | 50 |
Our goal is to bin genes randomly, so we must randomize the order of the genes in our DGE list. Without this step, genes would be binned together based on their sequential order within the chosen gene annotation (e.g., ENSEMBL or ENTREZ).
# Randomize the order of gene identifiers
annot <- example_DGE$genes
annot <- annot[sample(seq_len(nrow(annot))), ]
# Match order of the genes in the DGE to the randomized order of genes in the annotation
example_DGE <- example_DGE[annot, ]Data are imputed using the mice R package with its default predictive modeling methods, which are predictive mean matching, logistic regression, polytomous regression, and proportional odds modeling for continuous, binary, categorical, and unordered variables, respectively. The user may specify “m”, the number of imputed datasets, and “maxit”, the number of iterations for each imputation (default = 10). M imputed datasets are created separately for each gene bin, where the imputation predictor matrix includes all covariates along with the log-CPM for all the genes in a particular bin. Thus, each gene bin contains M sets of imputed data.
The impute_by_gene_bin function loops through a DGE list using the gene bin intervals from the get_gene_bin_intervals function. It returns a list of sets of m imputed datasets, one per gene bin. For instance, if m = 100 and intervals contains 200 gene bin intervals, output will be a list of 200 sets of 100 imputed datasets. Each of the 200 sets are imputed using only the genes in one gene bin.
gene_bin_impute <- impute_by_gene_bin(example_data,
intervals,
example_DGE,
m = 3
)##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a bThis procedure is run in parallel using the BiocParallel package with the default back-end. Users can change the back-end using the BPPARAM argument. This argument is passed to BiocParallel::bplapply. For instance, to run gene_bin_impute in serial:
gene_bin_impute <- impute_by_gene_bin(example_data,
intervals,
example_DGE,
m = 3,
BPPARAM = SerialParam()
)##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a b
##
## iter imp variable
## 1 1 y z a b
## 1 2 y z a b
## 1 3 y z a b
## 2 1 y z a b
## 2 2 y z a b
## 2 3 y z a b
## 3 1 y z a b
## 3 2 y z a b
## 3 3 y z a b
## 4 1 y z a b
## 4 2 y z a b
## 4 3 y z a b
## 5 1 y z a b
## 5 2 y z a b
## 5 3 y z a b
## 6 1 y z a b
## 6 2 y z a b
## 6 3 y z a b
## 7 1 y z a b
## 7 2 y z a b
## 7 3 y z a b
## 8 1 y z a b
## 8 2 y z a b
## 8 3 y z a b
## 9 1 y z a b
## 9 2 y z a b
## 9 3 y z a b
## 10 1 y z a b
## 10 2 y z a b
## 10 3 y z a bThe limmavoom_imputed_data_list function loops through the imputed data list (output from impute_by_gene_bin function) and runs RNA-seq analysis with the limma-voom pipeline. Users specify the formula for the RNA-seq design matrix for which log fold-changes will be estimated. This procedure can also be run with a different parallel back-end or in serial using the BPPARAM argument as above.
coef_se <- limmavoom_imputed_data_list(
gene_intervals = intervals,
DGE = example_DGE,
imputed_data_list = gene_bin_impute,
m = 3,
voom_formula = "~x + y + z + a + b"
)The final step is to combine the results from each imputed dataset using Rubin’s rules. The argument “model_results” is the output from the limmavoom_imputed_data_list function above. The combine_rubins function applies the squeezeVar function before pooling results. The result is a table with one row per gene. The table includes coefficients (e.g., logFC values) standard errors, degrees of freedom, t-statistics, P-Values, and adjusted P-values from the limma-voom pipeline. Both the raw and empirical Bayes moderated statistics are reported. The user selects the predictor of interest in the form of a linear model contrast for which model results will be extracted. For a continuous variable this is just the predictor name. For a categorical variable like b in example_data we could specify predictor = b1 to get the effect of being in the b = 1 versus the b = 0 group.
final_res <- combine_rubins(
DGE = example_DGE,
model_results = coef_se,
predictor = "x"
)| probe | coef_combined | combined_p_bayes | combined_p_adj_bayes |
|---|---|---|---|
| ENS432 | -0.021 | 0.000 | 0.094 |
| ENS65 | -0.023 | 0.001 | 0.318 |
| ENS327 | -0.010 | 0.006 | 0.946 |
| ENS239 | 0.014 | 0.008 | 0.946 |
| ENS411 | 0.022 | 0.010 | 0.980 |
| ENS260 | 0.011 | 0.015 | 0.980 |
| ENS458 | 0.015 | 0.021 | 0.980 |
| ENS219 | 0.013 | 0.023 | 0.980 |
| ENS291 | 0.017 | 0.023 | 0.980 |
| ENS13 | -0.022 | 0.023 | 0.980 |
## R version 4.3.1 (2023-06-16)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 22.04.3 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.18-bioc/R/lib/libRblas.so
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB LC_COLLATE=C
## [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: America/New_York
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] BiocParallel_1.36.0 RNAseqCovarImpute_1.0.2 mice_3.16.0
## [4] edgeR_4.0.0 limma_3.58.0 tidyr_1.3.0
## [7] stringr_1.5.0 dplyr_1.1.3 BiocStyle_2.30.0
##
## loaded via a namespace (and not attached):
## [1] sass_0.4.7 utf8_1.2.4 generics_0.1.3
## [4] shape_1.4.6 stringi_1.7.12 lattice_0.22-5
## [7] lme4_1.1-34 mitml_0.4-5 digest_0.6.33
## [10] magrittr_2.0.3 evaluate_0.22 grid_4.3.1
## [13] bookdown_0.36 iterators_1.0.14 fastmap_1.1.1
## [16] jomo_2.7-6 foreach_1.5.2 jsonlite_1.8.7
## [19] glmnet_4.1-8 Matrix_1.6-1.1 nnet_7.3-19
## [22] backports_1.4.1 survival_3.5-7 BiocManager_1.30.22
## [25] purrr_1.0.2 fansi_1.0.5 codetools_0.2-19
## [28] jquerylib_0.1.4 cli_3.6.1 rlang_1.1.1
## [31] splines_4.3.1 withr_2.5.1 cachem_1.0.8
## [34] yaml_2.3.7 pan_1.9 parallel_4.3.1
## [37] tools_4.3.1 nloptr_2.0.3 minqa_1.2.6
## [40] locfit_1.5-9.8 boot_1.3-28.1 broom_1.0.5
## [43] rpart_4.1.21 vctrs_0.6.4 R6_2.5.1
## [46] lifecycle_1.0.3 MASS_7.3-60 pkgconfig_2.0.3
## [49] pillar_1.9.0 bslib_0.5.1 glue_1.6.2
## [52] Rcpp_1.0.11 statmod_1.5.0 xfun_0.40
## [55] tibble_3.2.1 tidyselect_1.2.0 knitr_1.44
## [58] nlme_3.1-163 htmltools_0.5.6.1 rmarkdown_2.25
## [61] compiler_4.3.1