Exploring and updating FDR benchmarking results
29 October 2020
Abstract
Instructions on how to re-create results from Korthauer and Kimes et al. (2019) on benchmarking methods that control the false discovery rate (FDR).
Package
benchmarkfdrData2019 1.4.0
1 Introduction
This package provides a R / Bioconductor resource to re-create plots and extend the analyses of Korthauer and Kimes et al. (2019). In this paper, methods controlling the False Discovery Rate (FDR) were applied to a collection of simulated and biological data sets to generate the benchmarking summaries provided with this package. Here, we give an example of how to load summary objects, plot results, and apply a new method to the dataset.
The package can be installed from R (version >= 3.6) using the
BiocManager package,
available on CRAN.
if (!requireNamespace("BiocManager", quietly = TRUE))
install.packages("BiocManager")
BiocManager::install("benchmarkfdrData2019")2 Load Packages
suppressPackageStartupMessages({
library(ExperimentHub)
library(benchmarkfdrData2019)
library(SummarizedBenchmark)
library(dplyr)
library(ggplot2)
library(rlang)
})In addition to the ExperimentHub and benchmarkfdrData2019
packages, we also load the SummarizedBenchmark package. Benchmarking
results made available with this package for all case studies and simulations described
in Korthauer and Kimes et al. (2019) were created using the SummarizedBenchmark
package and are stored as SummarizedBenchmark objects.
However, note that the objects were generated using the fdrbenchmark
branch of the corresponding SummarizedBenchmark GitHub repository, and do not include
all of the features described in newer versions of the package (e.g. available on Bioconductor).
In this vignette, we use the release version of the SummarizedBenchmark package
available on Bioconductor.
However, the fdrbenchmark version of the SummarizedBenchmark package can be
installed from GitHub, again, using the BiocManager package.
BiocManager::install("areyesq89/SummarizedBenchmark", ref = "fdrbenchmark")3 Load Data
The data are available for downloaded from the Bioconductor
ExperimentHub
web resource. The complete list of resources availble with the
benchmarkfdrData2019 package can be queried using the following
command.
hub <- ExperimentHub()
bfdrData <- query(hub, "benchmarkfdrData2019")
bfdrData## ExperimentHub with 171 records
## # snapshotDate(): 2020-10-02
## # $dataprovider: NA, Geoffrey J. Barton lab, University of Dundee, Dundee, U...
## # $species: Saccharomyces cerevisiae, Homo sapiens, human gut metagenome, Mu...
## # $rdataclass: SummarizedBenchmark
## # additional mcols(): taxonomyid, genome, description,
## # coordinate_1_based, maintainer, rdatadateadded, preparerclass, tags,
## # rdatapath, sourceurl, sourcetype
## # retrieve records with, e.g., 'object[["EH2267"]]'
##
## title
## EH2267 | h3k4me3-promoters-benchmark
## EH2268 | h3k4me3-csaw-benchmark
## EH2269 | h3k4me3-csaw-uninf-benchmark
## EH2270 | h3k4me3-csaw-cov-benchmark
## EH2271 | cbp-csaw-benchmark
## ... ...
## EH2433 | varyingpi0-benchmark-nullprop70
## EH2434 | varyingpi0-benchmark-nullprop80
## EH2435 | varyingpi0-benchmark-nullprop90
## EH2436 | varyingpi0-benchmark-nullprop95
## EH2437 | varyingpi0-benchmark-nullprop99The above command only returns the metadata associated with each data object available on ExperimentHub. Individual resources must be retrieved from ExperimentHub before they can be loaded in R. Here, we retrieve and load two resource objects to illustrate the analyses that can be performed using the data available with this package.
First, we load the benchmark results for a ChIP-seq case study where differential
binding was tested using the csaw package with region width used
as the independent covariate. The resource is stored with the title "cbp-csaw-benchmark".
First, we determine the corresponding ExperimentHub ID for the resource.
cbp_id <- bfdrData$ah_id[bfdrData$title == "cbp-csaw-benchmark"]
cbp_id## [1] "EH2271"Using the ID, we can now access the metadata associated with the resource by
subsetting bfdrData using single brackets ([). Using double brackets ([[)
will retrieve the resource from the ExperimentHub server.
bfdrData[cbp_id]## ExperimentHub with 1 record
## # snapshotDate(): 2020-10-02
## # names(): EH2271
## # package(): benchmarkfdrData2019
## # $dataprovider: Biochemistry, St Jude Children's Research Hospital
## # $species: Mus musculus
## # $rdataclass: SummarizedBenchmark
## # $rdatadateadded: 2019-04-23
## # $title: cbp-csaw-benchmark
## # $description: Differential peak calling in CREB-binding protein (CBP) knoc...
## # $taxonomyid: 10090
## # $genome: mm10
## # $sourcetype: FASTQ
## # $sourceurl: https://www.ebi.ac.uk/ena/data/view/PRJNA236594
## # $sourcesize: NA
## # $tags: c("SingleCellData", "ExperimentData", "RNASeqData",
## # "ExpressionData", "ExperimentHub")
## # retrieve record with 'object[["EH2271"]]'chipres <- bfdrData[[cbp_id]]
chipres## class: SummarizedBenchmark
## dim: 59596 21
## metadata(0):
## assays(1): bench
## rownames: NULL
## rowData names(2): bench ind_covariate
## colnames(21): unadjusted bonf ... lfdr adapt-glm
## colData names(24): bfunc bpost ... param.alphas blabelNext, we load the benchmark results from a yeast in silico RNA-seq experiment where differential expression was tested using DESeq2 with a strong (simulated) independent and informative covariate. Unlike the ChIP-seq analysis above, with the in silico experiment, we know ground truth, and therefore can evaluate FDR control as well as the true positive rate (TPR) at nominal FDR significance thresholds.
Since the in silico experiments were repeated 100 times, the data object is
a list of 100 SummarizedBenchmark objects for each replication. The resource
is stored with the title "yeast-results-de5". Here, we demonstrate an alternative approach
to retrieving the resource from the ExperimentHub server. Rather than subset bfdrData
using double brackets ([[), we retrieve the resource by calling the
resource name as a function (yeast-results-de5()). This functionality is available
for all resources available with this package (including the ChIP-seq resource
loaded above).
yeast_id <- bfdrData$ah_id[bfdrData$title == "yeast-results-de5"]
bfdrData[yeast_id]## ExperimentHub with 1 record
## # snapshotDate(): 2020-10-02
## # names(): EH2320
## # package(): benchmarkfdrData2019
## # $dataprovider: Geoffrey J. Barton lab, University of Dundee, Dundee, UK
## # $species: Saccharomyces cerevisiae
## # $rdataclass: SummarizedBenchmark
## # $rdatadateadded: 2019-04-23
## # $title: yeast-results-de5
## # $description: Yeast RNA-seq 48 sample simulation study: Unimodal alternati...
## # $taxonomyid: 4932
## # $genome: Ensembl release 68
## # $sourcetype: tar.gz
## # $sourceurl: https://github.com/bartongroup/profDGE48
## # $sourcesize: NA
## # $tags: c("SingleCellData", "ExperimentData", "RNASeqData",
## # "ExpressionData", "ExperimentHub")
## # retrieve record with 'object[["EH2320"]]'yeastres <- `yeast-results-de5`()
length(yeastres)## [1] 100yeastres[[1]]## class: SummarizedBenchmark
## dim: 6544 23
## metadata(0):
## assays(1): qvalue
## rownames: NULL
## rowData names(3): qvalue ind_covariate log2FC
## colnames(23): unadjusted bonf ... fdrreg-t fdrreg-e
## colData names(28): bfunc bpost ... param.control blabelTo be able to work with the latest release of the SummarizedBenchmark package,
we must fill in a missing slot of the SummarizedBenchmark objects.
chipres@BenchDesign <- BenchDesign()
yeastres <- lapply(yeastres, function(x) { x@BenchDesign <- BenchDesign(); x })3.1 SummarizedBenchmark Objects
The SummarizedBenchmark objects include the original p-values, informative covariate, and corrected significance values for the various methods compared in Korthauer and Kimes et al. (2019).
SummarizedBenchmark objects are an extension of the Bioconductor SummarizedExperiment class, with results organized as a rectangular “assay”, with associated row and column metadata. Here, the rows of the objects correspond to individual hypothesis tests and the columns correspond to the approaches used for multiple testing correction.
We can take a look at the names of the methods included in the ChIP-seq results object.
colnames(chipres)## [1] "unadjusted" "bonf" "bh" "qvalue" "ihw-a01"
## [6] "ihw-a02" "ihw-a03" "ihw-a04" "ihw-a05" "ihw-a06"
## [11] "ihw-a07" "ihw-a08" "ihw-a09" "ihw-a10" "ashq"
## [16] "bl-df02" "bl-df03" "bl-df04" "bl-df05" "lfdr"
## [21] "adapt-glm"Notice that the results include the IHW and BL methods multiple times.
These ihw- and bl- columns correspond to separate runs of the
methods with different parameter settings. Briefly, the IHW method requires specifying an
alpha FDR threshold while running the method. Here, the method was run with alpha values of
0.01, 0.02, .., 0.10. The BL method was run with spline degrees of freedom 2, 3, 4, 5.
The corrected significance returned by each method is included in the single assay, "bench"
(corresponding to the benchmarked results).
dim(assay(chipres, "bench"))## [1] 59596 21head(assay(chipres, "bench"))## unadjusted bonf bh qvalue ihw-a01 ihw-a02 ihw-a03
## [1,] 0.09367441 1 0.2750488 0.1587219 0.4153819 1.0000000 1.0000000
## [2,] 0.07635065 1 0.2456775 0.1417726 0.2592850 0.2359257 0.2113001
## [3,] 0.44641540 1 0.6193447 0.3574041 0.6874034 0.6697854 0.4831826
## [4,] 0.54230545 1 0.6976696 0.4026029 0.7825177 1.0000000 1.0000000
## [5,] 0.11280772 1 0.2936016 0.1694281 0.3009025 0.3865540 0.2590641
## [6,] 0.31152661 1 0.5027725 0.2901340 0.5194227 0.4229486 0.3428025
## ihw-a04 ihw-a05 ihw-a06 ihw-a07 ihw-a08 ihw-a09 ihw-a10 ashq
## [1,] 0.2383437 0.2010557 0.1859702 0.1894541 0.1837203 0.2021730 0.1998073 NA
## [2,] 0.2529069 0.1952980 0.2451944 0.1935890 0.1943609 0.1971796 0.1879095 NA
## [3,] 0.6147271 0.4718577 0.4405994 0.4508408 0.4687339 0.4390055 0.4804587 NA
## [4,] 0.8947457 0.9276785 1.0000000 0.9881300 0.6758374 0.8118452 0.7374463 NA
## [5,] 0.2836033 0.2245577 0.2129845 0.2218124 0.2323623 0.2743020 0.2317344 NA
## [6,] 0.3358033 0.2741951 0.3035988 0.3531403 0.3852453 0.3926378 0.4048568 NA
## bl-df02 bl-df03 bl-df04 bl-df05 lfdr adapt-glm
## [1,] 0.09501728 0.1242898 0.1359421 0.1404518 0.05770709 0.1246816
## [2,] 0.09334559 0.1185802 0.1286718 0.1325802 0.05362979 0.1142933
## [3,] 0.17635627 0.2454214 0.2725921 0.2830917 0.24715606 0.2476961
## [4,] 0.35015194 0.4105930 0.4347989 0.4441300 0.38512849 Inf
## [5,] 0.11155442 0.1417115 0.1537717 0.1584425 0.06377030 0.1327596
## [6,] 0.10655455 0.1638255 0.1859225 0.1944646 0.12164067 0.1999106The ASH (ashq) results are NA as the method was not applied to the data.
4 Exploratory Analysis
Given the multiple-testing-corrected results provided in the "bench" assay of the
SummarizedBenchmark objects, we can take a look at several performance metrics
to compare the various methods. For the ChIP-seq case study, we can take a look at the
number of rejections at various significance cutoffs. With the in silico yeast
experiments, since truth is known, we can also look at FDR and TPR, as well as other
related metrics.
SummarizedBenchmark objects include functionality to easily add and evaluate metrics
for data stored as assays. This is performed by first adding performance metrics
with addPerformanceMetric, followed by a call to estimatePerformanceMetrics.
While custom performance metrics can be defined by users, the package fortunately
includes several default metrics that can be added by name.
availableMetrics()## functions description
## 1 rejections Number of rejections
## 2 TPR True Positive Rate
## 3 TNR True Negative Rate
## 4 FDR False Discovery Rate (estimated)
## 5 FNR False Negative Rate
## 6 correlation Pearson correlation
## 7 sdad Standard Deviation of the Absolute Difference
## 8 hamming Hamming distance
## 9 LPnorm L_{p} norm
## 10 adjustedRandIndex Adjusted Rand Index
## requiresTruth
## 1 FALSE
## 2 TRUE
## 3 TRUE
## 4 TRUE
## 5 TRUE
## 6 TRUE
## 7 TRUE
## 8 TRUE
## 9 TRUE
## 10 TRUE4.1 ChIP-seq Case Study
We will add the "rejections" metric to the "bench" assay and compute the number
of rejections for each method at cutoffs between 0.01 and 0.10.
chipres <- addPerformanceMetric(chipres,
evalMetric = "rejections",
assay = "bench")Next, we compute the number of rejections and organize this as a tidy data.frame.
chipdf <- estimatePerformanceMetrics(chipres,
alpha = seq(0.01, 0.10, by = .01),
tidy = TRUE)
dim(chipdf)## [1] 210 29head(chipdf)## bfunc bpost bfunc_anon vers_src
## 1 function(p) {; p;} <NA> TRUE bfunc
## 2 p.adjust <NA> FALSE bfunc
## 3 p.adjust <NA> FALSE bfunc
## 4 qvalue::qvalue function(x) {; x$qvalues;} FALSE bfunc
## 5 IHW::ihw IHW::adj_pvalues FALSE bfunc
## 6 IHW::ihw IHW::adj_pvalues FALSE bfunc
## pkg_name pkg_vers param.p param.method param.pvalues param.covariates
## 1 <NA> <NA> pval <NA> <NA> <NA>
## 2 stats 3.5.0 pval "bonferroni" <NA> <NA>
## 3 stats 3.5.0 pval "BH" <NA> <NA>
## 4 qvalue 2.12.0 pval <NA> <NA> <NA>
## 5 IHW 1.8.0 <NA> <NA> pval ind_covariate
## 6 IHW 1.8.0 <NA> <NA> pval ind_covariate
## param.alpha param.betahat param.sebetahat param.pValues param.X
## 1 <NA> <NA> <NA> <NA> <NA>
## 2 <NA> <NA> <NA> <NA> <NA>
## 3 <NA> <NA> <NA> <NA> <NA>
## 4 <NA> <NA> <NA> <NA> <NA>
## 5 0.01 <NA> <NA> <NA> <NA>
## 6 0.02 <NA> <NA> <NA> <NA>
## param.smooth.df param.unadj_p param.groups param.pvals param.x
## 1 <NA> <NA> <NA> <NA> <NA>
## 2 <NA> <NA> <NA> <NA> <NA>
## 3 <NA> <NA> <NA> <NA> <NA>
## 4 <NA> <NA> <NA> <NA> <NA>
## 5 <NA> <NA> <NA> <NA> <NA>
## 6 <NA> <NA> <NA> <NA> <NA>
## param.pi_formulas param.mu_formulas param.alphas blabel label value
## 1 <NA> <NA> <NA> unadjusted unadjusted 5342
## 2 <NA> <NA> <NA> bonf bonf 0
## 3 <NA> <NA> <NA> bh bh 0
## 4 <NA> <NA> <NA> qvalue qvalue 4
## 5 <NA> <NA> <NA> ihw-a01 ihw-a01 0
## 6 <NA> <NA> <NA> ihw-a02 ihw-a02 0
## assay performanceMetric alpha
## 1 bench rejections 0.01
## 2 bench rejections 0.01
## 3 bench rejections 0.01
## 4 bench rejections 0.01
## 5 bench rejections 0.01
## 6 bench rejections 0.01Each row in the data.frame corresponds to a method + metric + cutoff combination
(e.g. "unadjusted" + "rejections" + "alpha = 0.01"). This information is stored in
the "label", "performanceMetric", and "alpha" columns, with the corresponding
metric value in the "value" column. All other columns contain method metadata,
such as the package version, when the method was evaluated.
We will now clean up the IHW and BL methods which, as described above, include multiple parameter settings.
## subset IHW
chipdf <- dplyr:::filter(chipdf, !(grepl("ihw", label) & param.alpha != alpha))
chipdf <- dplyr:::mutate(chipdf, label = gsub("(ihw)-a\\d+", "\\1", label))
## subset BL
chipdf <- dplyr:::filter(chipdf, ! label %in% paste0("bl-df0", c(2, 4, 5)))We only keep a subset of the columns and drop NA values.
chipdf <- dplyr::select(chipdf, label, performanceMetric, alpha, value)
chipdf <- dplyr::filter(chipdf, !is.na(value))
head(chipdf)## label performanceMetric alpha value
## 1 unadjusted rejections 0.01 5342
## 2 bonf rejections 0.01 0
## 3 bh rejections 0.01 0
## 4 qvalue rejections 0.01 4
## 5 ihw rejections 0.01 0
## 6 bl-df03 rejections 0.01 78We now plot the number of rejections.
ggplot(chipdf, aes(x = alpha, y = value, color = label)) +
geom_point() +
geom_line() +
scale_color_viridis_d("Method") +
scale_x_continuous(breaks = seq(0, 1, .01), limits = c(0, .11)) +
ylab("Rejections") +
theme_bw() +
ggtitle("Number of rejections across multiple-testing methods",
"ChIP-seq CBP differential analysis with informative covariate")
4.2 Yeast in silico Data
We can similarly add performance metrics to each replication of the yeast in silico experiment and aggregate across replicates. We demonstrate this process using a subset of the 100 replications in the interest of computational cost.
yeastres10 <- yeastres[1:10]As with the ChIP-seq results, we can add and evaluate performance
metrics using addPerformanceMetric and estimatePerformanceMetrics.
However, note that the yeast in silico results already include
several default performance metrics.
names(performanceMetrics(yeastres10[[1]])[["qvalue"]])## [1] "TPR" "FDR" "TNR" "FNR" "rejections"We can skip the process of adding performance metrics and just use these metrics.
yeastdf <- lapply(yeastres10, estimatePerformanceMetrics,
alpha = seq(0.01, 0.10, by = .01), tidy = TRUE)Finally, we merge the 10 replications to a single data.frame.
yeastdf <- dplyr::bind_rows(yeastdf, .id = "rep")As above, we clean IHW and BL results, remove NA values, and only keep
a subset of useful columns.
## subset IHW
yeastdf <- dplyr:::filter(yeastdf,
!(grepl("ihw", label) & param.alpha != alpha))
yeastdf <- dplyr:::mutate(yeastdf, label = gsub("(ihw)-a\\d+", "\\1", label))
## subset BL
yeastdf <- dplyr:::filter(yeastdf, ! label %in% paste0("bl-df0", c(2, 4, 5)))
yeastdf <- dplyr::select(yeastdf, rep, label, performanceMetric, alpha, value)
yeastdf <- dplyr::filter(yeastdf, !is.na(value))
head(yeastdf)## rep label performanceMetric alpha value
## 1 1 unadjusted TPR 0.01 0.4430
## 2 1 bonf TPR 0.01 0.1900
## 3 1 bh TPR 0.01 0.3395
## 4 1 qvalue TPR 0.01 0.3415
## 5 1 ihw TPR 0.01 0.3440
## 6 1 ashq TPR 0.01 0.3365Finally, we summarize across replications for each method, for each metric, at each nominal threshold.
yeastdf <- dplyr::group_by(yeastdf, label, performanceMetric, alpha)
yeastdf <- dplyr::summarize(yeastdf,
meanValue = mean(value),
seValue = sd(value) / sqrt(n()))
yeastdf <- dplyr::ungroup(yeastdf)Now, we can plot the average and standard errors across replicates for each method. Here, we will just plot FDR and TPR.
yeastdf %>%
dplyr::filter(performanceMetric %in% c("FDR", "TPR")) %>%
ggplot(aes(x = alpha, y = meanValue,
color = label,
ymin = meanValue - seValue,
ymax = meanValue + seValue)) +
geom_point() +
geom_errorbar(width = .01 / 4, alpha = 1/4) +
geom_line(alpha = 1/2) +
scale_color_viridis_d("Method") +
scale_x_continuous(breaks = seq(0, 1, .01), limits = c(0, .11)) +
facet_wrap(~ performanceMetric, scales = 'free_y', nrow = 1) +
ylab("average across replicates") +
theme_bw() +
geom_abline(aes(intercept = i_, slope = s_), color = 'red', linetype = 2,
data = tibble(performanceMetric = 'FDR', i_ = 0, s_ = 1)) +
ggtitle("FDR and TPR across multiple-testing methods",
"yeast in silico experiment with informative covariate")
We have also included a red line to the FDR plot to assess whether methods are appropriately controlling the FDR at the nominal thresholds.
5 Adding Methods
The summary objects made available with this packages were constructed using an older version
of the SummarizedBenchmark package. Since then, functions have been added to the package
for updating benchmark comparisons and adding new methods to an existing SummarizedBenchmark
object. Unfortuntately, these functions cannot be used with the current objects made
available with this package.
However, the summary objects include both unadjusted p-values (as the unadjusted column) and
corresponding independent covariate values (as the ind_covariate rowData column). These values
can be used to apply new methods which only depend on these inputs.
dat <- tibble(pval = assay(chipres)[, "unadjusted"],
covariate = rowData(chipres)$ind_covariate)
dat## # A tibble: 59,596 x 2
## pval covariate
## <dbl> <int>
## 1 0.0937 360
## 2 0.0764 310
## 3 0.446 460
## 4 0.542 160
## 5 0.113 310
## 6 0.312 610
## 7 0.708 60
## 8 0.347 910
## 9 0.484 210
## 10 0.761 160
## # … with 59,586 more rowsTo analyze this data using the SummarizedBenchmark package, we can
construct a new BenchDesign object with any collection of new methods
to benchmark, and the above data as input. More details on the
SummarizedBenchmark package and the BenchDesign class can be found in
the package vignettes.
As an illustration of how a new method could be applied to this data, we will re-apply the Benjamini-Hochberg correction and show that the results that we obtain in this re-analysis match the results reported in the loaded SummarizedBenchmark object.
We construct a BenchDesign with a single method, newBH, and the data given above.
bh_method <- BDMethod(x = p.adjust,
params = rlang::quos(p = pval,
method = "BH"))
new_design <- BenchDesign(newBH = bh_method, data = dat)
new_design## BenchDesign ------------------------------------------------
## benchmark data:
## type: data
## names: pval, covariate
## benchmark methods:
## method: newBH; func: p.adjustTo evaluate the benchmark experiment stored in the BenchDesign object, we call
buildBench.
new_res <- buildBench(new_design)
new_res## class: SummarizedBenchmark
## dim: 59596 1
## metadata(1): sessions
## assays(1): default
## rownames: NULL
## rowData names(1): default
## colnames(1): newBH
## colData names(6): func.pkg func.pkg.vers ... param.method session.idxNow that we have a SummarizedBenchmark object, we can evaluate performance metrics as before.
new_res <- addPerformanceMetric(new_res,
evalMetric = "rejections",
assay = "default")
new_df <- estimatePerformanceMetrics(new_res,
alpha = seq(0.01, 0.10, by = 0.01),
tidy = TRUE)Finally, we subset on columns of interest and examine how many tests would be rejected using BH in our re-analysis.
new_df <- dplyr::select(new_df, label, value, performanceMetric, alpha)
new_df## label value performanceMetric alpha
## 1 newBH 0 rejections 0.01
## 2 newBH 5 rejections 0.02
## 3 newBH 12 rejections 0.03
## 4 newBH 30 rejections 0.04
## 5 newBH 660 rejections 0.05
## 6 newBH 1287 rejections 0.06
## 7 newBH 1768 rejections 0.07
## 8 newBH 2589 rejections 0.08
## 9 newBH 3435 rejections 0.09
## 10 newBH 4311 rejections 0.10We verify that this matches the number of rejections reported in the results from above.
dplyr::filter(chipdf, label == "bh")## label performanceMetric alpha value
## 1 bh rejections 0.01 0
## 2 bh rejections 0.02 5
## 3 bh rejections 0.03 12
## 4 bh rejections 0.04 30
## 5 bh rejections 0.05 660
## 6 bh rejections 0.06 1287
## 7 bh rejections 0.07 1768
## 8 bh rejections 0.08 2589
## 9 bh rejections 0.09 3435
## 10 bh rejections 0.10 4311Since the results are now just data.frame objects with similar columns, they can be combined to compare new results with previous results.
6 Session Information
sessionInfo()## R version 4.0.3 (2020-10-10)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.5 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.12-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.12-bioc/R/lib/libRlapack.so
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_US.UTF-8 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
##
## attached base packages:
## [1] stats4 parallel stats graphics grDevices utils datasets
## [8] methods base
##
## other attached packages:
## [1] SummarizedBenchmark_2.8.0 tibble_3.0.4
## [3] crayon_1.3.4 sessioninfo_1.1.1
## [5] digest_0.6.27 dplyr_1.0.2
## [7] mclust_5.4.6 ggplot2_3.3.2
## [9] BiocParallel_1.24.0 stringr_1.4.0
## [11] rlang_0.4.8 UpSetR_1.4.0
## [13] tidyr_1.1.2 benchmarkfdrData2019_1.4.0
## [15] SummarizedExperiment_1.20.0 Biobase_2.50.0
## [17] GenomicRanges_1.42.0 GenomeInfoDb_1.26.0
## [19] IRanges_2.24.0 S4Vectors_0.28.0
## [21] MatrixGenerics_1.2.0 matrixStats_0.57.0
## [23] ExperimentHub_1.16.0 AnnotationHub_2.22.0
## [25] BiocFileCache_1.14.0 dbplyr_1.4.4
## [27] BiocGenerics_0.36.0 knitr_1.30
## [29] BiocStyle_2.18.0
##
## loaded via a namespace (and not attached):
## [1] httr_1.4.2 viridisLite_0.3.0
## [3] bit64_4.0.5 shiny_1.5.0
## [5] assertthat_0.2.1 interactiveDisplayBase_1.28.0
## [7] BiocManager_1.30.10 blob_1.2.1
## [9] GenomeInfoDbData_1.2.4 yaml_2.2.1
## [11] BiocVersion_3.12.0 pillar_1.4.6
## [13] RSQLite_2.2.1 lattice_0.20-41
## [15] glue_1.4.2 promises_1.1.1
## [17] XVector_0.30.0 colorspace_1.4-1
## [19] htmltools_0.5.0 httpuv_1.5.4
## [21] Matrix_1.2-18 plyr_1.8.6
## [23] pkgconfig_2.0.3 magick_2.5.0
## [25] bookdown_0.21 zlibbioc_1.36.0
## [27] purrr_0.3.4 xtable_1.8-4
## [29] scales_1.1.1 later_1.1.0.1
## [31] farver_2.0.3 generics_0.0.2
## [33] ellipsis_0.3.1 withr_2.3.0
## [35] cli_2.1.0 magrittr_1.5
## [37] mime_0.9 memoise_1.1.0
## [39] evaluate_0.14 fansi_0.4.1
## [41] tools_4.0.3 lifecycle_0.2.0
## [43] munsell_0.5.0 DelayedArray_0.16.0
## [45] AnnotationDbi_1.52.0 compiler_4.0.3
## [47] grid_4.0.3 RCurl_1.98-1.2
## [49] rappdirs_0.3.1 labeling_0.4.2
## [51] bitops_1.0-6 rmarkdown_2.5
## [53] gtable_0.3.0 DBI_1.1.0
## [55] curl_4.3 R6_2.5.0
## [57] gridExtra_2.3 utf8_1.1.4
## [59] fastmap_1.0.1 bit_4.0.4
## [61] stringi_1.5.3 Rcpp_1.0.5
## [63] vctrs_0.3.4 tidyselect_1.1.0
## [65] xfun_0.18