# Dreamlet analysis of single cell RNA-seq

# Introduction

As the scale of single cell/nucleus RNA-seq has increased, so has the complexity of study designs. Analysis of datasets with simple study designs can be performed using linear model as in the muscat package. Yet analysis of datsets with complex study designs such as repeated measures or many technical batches can benefit from linear mixed model analysis to model to correlation structure between samples. We previously developed dream to apply linear mixed models to bulk RNA-seq data using a limma-style workflow. Dreamlet extends the previous work of dream and muscat to apply linear mixed models to pseudobulk data. Dreamlet also supports linear models and facilitates application of 1) variancePartition to quantify the contribution of multiple variables to expression variation, and 2) zenith to perform gene set analysis on the differential expression signatures.

# Installation

To install this package, start R (version “4.3”) and enter:

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

    # Select release #1 or #2

    # 1) Bioconductor release
    BiocManager::install("dreamlet")

    # 2) Latest stable release
    devtools::install_github("DiseaseNeurogenomics/dreamlet")

# Process single cell count data

Here we perform analysis of PBMCs from 8 individuals stimulated with interferon-β (Kang, et al, 2018, Nature Biotech). This is a small dataset that does not have repeated measures or high dimensional batch effects, so the sophisticated features of dreamlet are not strictly necessary. But this gives us an opportunity to walk through a standard dreamlet workflow.

## Preprocess data

Here, single cell RNA-seq data is downloaded from ExperimentHub.

    library(dreamlet)
    library(muscat)
    library(ExperimentHub)
    library(zenith)
    library(scater)

    # Download data, specifying EH2259 for the Kang, et al study
    eh <- ExperimentHub()
    sce <- eh[["EH2259"]]

    sce$ind = as.character(sce$ind)

    # only keep singlet cells with sufficient reads
    sce <- sce[rowSums(counts(sce) > 0) > 0, ]
    sce <- sce[, colData(sce)$multiplets == "singlet"]

    # compute QC metrics
    qc <- perCellQCMetrics(sce)

    # remove cells with few or many detected genes
    ol <- isOutlier(metric = qc$detected, nmads = 2, log = TRUE)
    sce <- sce[, !ol]

    # set variable indicating stimulated (stim) or control (ctrl)
    sce$StimStatus <- sce$stim

## Aggregate to pseudobulk

Dreamlet, like muscat, performs analysis at the pseudobulk-level by summing raw counts across cells for a given sample and cell type. `aggregateToPseudoBulk` is substantially faster for large on-disk datasets than `muscat::aggregateData`.

    # Since 'ind' is the individual and 'StimStatus' is the stimulus status,
    # create unique identifier for each sample
    sce$id <- paste0(sce$StimStatus, sce$ind)

    # Create pseudobulk data by specifying cluster_id and sample_id
    # Count data for each cell type is then stored in the `assay` field
    # assay: entry in assayNames(sce) storing raw counts
    # cluster_id: variable in colData(sce) indicating cell clusters
    # sample_id: variable in colData(sce) indicating sample id for aggregating cells
    pb <- aggregateToPseudoBulk(sce,
      assay = "counts",
      cluster_id = "cell",
      sample_id = "id",
      verbose = FALSE
    )

    # one 'assay' per cell type
    assayNames(pb)

    ## [1] "B cells"           "CD14+ Monocytes"   "CD4 T cells"
    ## [4] "CD8 T cells"       "Dendritic cells"   "FCGR3A+ Monocytes"
    ## [7] "Megakaryocytes"    "NK cells"

# Voom for pseudobulk

Apply voom-style normalization for pseudobulk counts within each cell cluster using voomWithDreamWeights to handle random effects (if specified).

    # Normalize and apply voom/voomWithDreamWeights
    res.proc <- processAssays(pb, ~StimStatus, min.count = 5)

    # the resulting object of class dreamletProcessedData stores
    # normalized data and other information
    res.proc

    ## class: dreamletProcessedData
    ## assays(8): B cells CD14+ Monocytes ... Megakaryocytes NK cells
    ## colData(4): ind stim multiplets StimStatus
    ## metadata(3): cell id cluster
    ## Samples:
    ##  min: 13
    ##  max: 16
    ## Genes:
    ##  min: 164
    ##  max: 5262
    ## details(7): assay n_retain ... n_errors error_initial

`processAssays()` retains samples with at least `min.cells` in a given cell type. While dropping a few samples usually is not a problem, in some cases dropping sames can mean that a variable included in the regression formula no longer has any variation. For example, dropping all stimulated samples from analysis of a given cell type would be mean the variable `StimStatus` has no variation and is perfectly colinear with the intercept term. This colinearity issue is detected internally and variables with these problem are dropped from the regression formula for that particular cell type. The number of samples retained and the resulting formula used in each cell type can be accessed as follows. In this analysis, samples are dropped from 3 cell types but the original formula remains valid in each case.

    # view details of dropping samples
    details(res.proc)

    ##               assay n_retain     formula formDropsTerms n_genes n_errors
    ## 1           B cells       16 ~StimStatus          FALSE    1961        0
    ## 2   CD14+ Monocytes       16 ~StimStatus          FALSE    3087        0
    ## 3       CD4 T cells       16 ~StimStatus          FALSE    5262        0
    ## 4       CD8 T cells       16 ~StimStatus          FALSE    1030        0
    ## 5   Dendritic cells       13 ~StimStatus          FALSE     164        0
    ## 6 FCGR3A+ Monocytes       16 ~StimStatus          FALSE    1160        0
    ## 7    Megakaryocytes       13 ~StimStatus          FALSE     172        0
    ## 8          NK cells       16 ~StimStatus          FALSE    1656        0
    ##   error_initial
    ## 1         FALSE
    ## 2         FALSE
    ## 3         FALSE
    ## 4         FALSE
    ## 5         FALSE
    ## 6         FALSE
    ## 7         FALSE
    ## 8         FALSE

Here the mean-variance trend from voom is shown for each cell type. Cell types with sufficient number of cells and reads show a clear mean-variance trend. While in rare cell types like megakaryocytes, fewer genes have sufficient reads and the trend is less apparent.

    # show voom plot for each cell clusters
    plotVoom(res.proc)

    # Show plots for subset of cell clusters
    # plotVoom( res.proc[1:3] )

    # Show plots for one cell cluster
    # plotVoom( res.proc[["B cells"]])

# Variance partitioning

The variancePartition package uses linear and linear mixed models to quanify the contribution of multiple sources of expression variation at the gene-level. For each gene it fits a linear (mixed) model and evalutes the fraction of expression variation explained by each variable.

Variance fractions can be visualized at the gene-level for each cell type using a bar plot, or genome-wide using a violin plot.

    # run variance partitioning analysis
    vp.lst <- fitVarPart(res.proc, ~StimStatus)

    # Show variance fractions at the gene-level for each cell type
    genes <- vp.lst$gene[2:4]
    plotPercentBars(vp.lst[vp.lst$gene %in% genes, ])

    # Summarize variance fractions genome-wide for each cell type
    plotVarPart(vp.lst, label.angle = 60)

# Differential expression

Since the normalized expression data and metadata are stored within `res.proc`, only the regression formula remains to be specified. Here we only included the stimulus status, but analyses of larger datasets can include covariates and random effects. With formula `~ StimStatus`, an intercept is fit and coefficient `StimStatusstim` log fold change between simulated and controls.

    # Differential expression analysis within each assay,
    # evaluated on the voom normalized data
    res.dl <- dreamlet(res.proc, ~StimStatus)

    # names of estimated coefficients
    coefNames(res.dl)

    ## [1] "(Intercept)"    "StimStatusstim"

    # the resulting object of class dreamletResult
    # stores results and other information
    res.dl

    ## class: dreamletResult
    ## assays(8): B cells CD14+ Monocytes ... Megakaryocytes NK cells
    ## Genes:
    ##  min: 164
    ##  max: 5262
    ## details(7): assay n_retain ... n_errors error_initial
    ## coefNames(2): (Intercept) StimStatusstim

## Volcano plots

The volcano plot can indicate the strength of the differential expression signal with each cell type. Red points indicate FDR < 0.05.

    plotVolcano(res.dl, coef = "StimStatusstim")

## Gene-level heatmap

For each cell type and specified gene, show z-statistic from `dreamlet` analysis. Grey indicates that insufficient reads were observed to include the gene in the analysis.

    genes <- c("ISG20", "ISG15")
    plotGeneHeatmap(res.dl, coef = "StimStatusstim", genes = genes)

## Extract results

Each entry in `res.dl` stores a model fit by `dream()`, and results can be extracted using `topTable()` as in `limma` by specifying the coefficient of interest. The results shows the gene name, log fold change, average expression, t-statistic, p-value, FDR (i.e. adj.P.Val).

    # results from full analysis
    topTable(res.dl, coef = "StimStatusstim")

    ## DataFrame with 10 rows and 9 columns
    ##              assay          ID     logFC   AveExpr         t     P.Value
    ##        <character> <character> <numeric> <numeric> <numeric>   <numeric>
    ## 1      CD4 T cells       ISG20   3.05455  10.40388   34.4774 3.14046e-22
    ## 2      CD4 T cells        IFI6   5.66980   8.52892   33.5813 5.89835e-22
    ## 3      CD4 T cells        MT2A   4.32697   7.80640   29.8959 9.44958e-21
    ## 4  CD14+ Monocytes       IL1RN   7.07251   7.79103   35.1828 9.58042e-21
    ## 5          B cells       ISG15   5.53079  10.20272   26.2270 1.16025e-20
    ## 6      CD4 T cells       HERC5   4.23629   6.74189   29.2009 1.65334e-20
    ## 7      CD4 T cells       ISG15   5.18872  10.06906   28.4163 3.15713e-20
    ## 8          B cells       ISG20   3.33103  11.38360   24.1402 9.83897e-20
    ## 9         NK cells       ISG15   4.76379  11.01479   24.7131 1.81450e-19
    ## 10     CD4 T cells     TNFSF10   4.41588   7.49081   25.8759 2.89593e-19
    ##      adj.P.Val         B     z.std
    ##      <numeric> <numeric> <numeric>
    ## 1  4.27395e-18   40.9592   34.4774
    ## 2  4.27395e-18   40.1636   33.5813
    ## 3  3.36287e-17   37.4905   29.8959
    ## 4  3.36287e-17   36.7737   35.1828
    ## 5  3.36287e-17   37.1705   26.2270
    ## 6  3.99337e-17   36.7596   29.2009
    ## 7  6.53617e-17   36.3919   28.4163
    ## 8  1.78233e-16   35.1770   24.1402
    ## 9  2.92175e-16   34.4633   24.7131
    ## 10 4.19679e-16   34.1274   25.8759

    # only B cells
    topTable(res.dl[["B cells"]], coef = "StimStatusstim")

    ##           logFC   AveExpr        t      P.Value    adj.P.Val        B
    ## ISG15  5.530786 10.202722 26.22702 1.160249e-20 2.275249e-17 37.17046
    ## ISG20  3.331031 11.383603 24.14017 9.838971e-20 9.647111e-17 35.17704
    ## LY6E   4.331290  8.706648 19.16241 3.474679e-17 2.271282e-14 29.27957
    ## IRF7   3.730427  8.678591 18.84058 5.310505e-17 2.603475e-14 28.88289
    ## UBE2L6 2.741292  9.241028 18.50765 8.290835e-17 3.251666e-14 28.47212
    ## EPSTI1 3.716921  8.107930 18.18089 1.292430e-16 3.651223e-14 27.96522
    ## PLSCR1 4.113193  8.271191 18.17475 1.303343e-16 3.651223e-14 27.96187
    ## IFITM2 2.999742  8.731566 17.76966 2.282011e-16 5.593779e-14 27.46272
    ## SAT1   2.206045  9.657178 17.41720 3.748297e-16 8.167123e-14 26.94871
    ## SOCS1  2.432287  8.588454 16.28257 1.965142e-15 3.853644e-13 25.32548

## Forest plot

A forest plot shows the log fold change and standard error of a given gene across all cell types. The color indicates the FDR.

    plotForest(res.dl, coef = "StimStatusstim", gene = "ISG20")

## Box plot

Examine the expression of ISG20 between stimulation conditions within CD14+ Monocytes. Use `extractData()` to create a `tibble` with gene expression data and metadata from `colData()` from one cell type.

    # get data
    df <- extractData(res.proc, "CD14+ Monocytes", genes = "ISG20")

    # set theme
    thm <- theme_classic() +
      theme(aspect.ratio = 1, plot.title = element_text(hjust = 0.5))

    # make plot
    ggplot(df, aes(StimStatus, ISG20)) +
      geom_boxplot() +
      thm +
      ylab(bquote(Expression ~ (log[2] ~ CPM))) +
      ggtitle("ISG20")

## Advanced used of contrasts

A hypothesis test of the difference between two or more coefficients can be performed using contrasts. The contrast matrix is evaluated for each cell type in the backend, so only the contrast string must be supplied to `dreamlet()`.

    # create a contrasts called 'Diff' that is the difference between expression
    # in the stimulated and controls.
    # More than one can be specified
    contrasts <- c(Diff = "StimStatusstim - StimStatusctrl")

    # Evalaute the regression model without an intercept term.
    # Instead estimate the mean expression in stimulated, controls and then
    # set Diff to the difference between the two
    res.dl2 <- dreamlet(res.proc, ~ 0 + StimStatus, contrasts = contrasts)

    # see estimated coefficients
    coefNames(res.dl2)

    ## [1] "Diff"           "StimStatusctrl" "StimStatusstim"

    # Volcano plot of Diff
    plotVolcano(res.dl2[1:2], coef = "Diff")

This new `Diff` variable can then be used downstream for analysis asking for a coefficient. But note that since there is no intercept term in this model, the meaning of `StimStatusstim` changes here. When the formula is `0 + StimStatus` then `StimStatusstim` is the mean expression in stimulated samples.

For further information about using contrasts see makeContrastsDream() and vignette.

# Gene set analysis

While standard enrichment methods like Fishers exact test, requires specifying a FDR cutoff to identify differentially expressed genes. However, dichotomizing differential expression results is often too simple and ignores the quantitative variation captured by the differential expression test statistics. Here we use `zenith`, a wrapper for `limma::camera`, to perform gene set analysis using the full spectrum of differential expression test statistics. `zenith/camera` is a competetive test that compares the mean test statistic for genes in a given gene set, to genes not in that set while accounting for correlation between genes.

Here, `zenith_gsa` takes a `dreamletResult` object, the coefficient of interest, and gene sets as a `GeneSetCollection` object from GSEABase.

    # Load Gene Ontology database
    # use gene 'SYMBOL', or 'ENSEMBL' id
    # use get_MSigDB() to load MSigDB
    # Use Cellular Component (i.e. CC) to reduce run time here
    go.gs <- get_GeneOntology("CC", to = "SYMBOL")

    # Run zenith gene set analysis on result of dreamlet
    res_zenith <- zenith_gsa(res.dl, coef = "StimStatusstim", go.gs)

    # examine results for each ell type and gene set
    head(res_zenith)

    ##     assay           coef
    ## 1 B cells StimStatusstim
    ## 2 B cells StimStatusstim
    ## 3 B cells StimStatusstim
    ## 4 B cells StimStatusstim
    ## 5 B cells StimStatusstim
    ## 6 B cells StimStatusstim
    ##                                                        Geneset NGenes
    ## 1                                GO0022626: cytosolic ribosome     77
    ## 2                 GO0022625: cytosolic large ribosomal subunit     45
    ## 3 GO0090575: RNA polymerase II transcription regulator complex     38
    ## 4                                   GO0032587: ruffle membrane     13
    ## 5                                    GO0005925: focal adhesion    111
    ## 6                           GO0030055: cell-substrate junction    111
    ##   Correlation      delta        se      p.less  p.greater      PValue Direction
    ## 1        0.01 -1.1189600 0.3494488 0.003197077 0.99680292 0.006394153      Down
    ## 2        0.01 -1.0609674 0.4129425 0.011134062 0.98886594 0.022268124      Down
    ## 3        0.01  1.0388011 0.4381026 0.983689509 0.01631049 0.032620982        Up
    ## 4        0.01 -1.5672380 0.6746900 0.017880611 0.98211939 0.035761223      Down
    ## 5        0.01 -0.7188655 0.3193516 0.020487674 0.97951233 0.040975349      Down
    ## 6        0.01 -0.7188655 0.3193516 0.020487674 0.97951233 0.040975349      Down
    ##         FDR
    ## 1 0.2661423
    ## 2 0.4992161
    ## 3 0.5028482
    ## 4 0.5277951
    ## 5 0.5573183
    ## 6 0.5573183

## Heatmap of top genesets

    # for each cell type select 5 genesets with largest t-statistic
    # and 1 geneset with the lowest
    # Grey boxes indicate the gene set could not be evaluted because
    #    to few genes were represented
    plotZenithResults(res_zenith, 5, 1)

### All gene sets with FDR < 30%

Here, show all genes with FDR < 5% in any cell type

    # get genesets with FDR < 30%
    # Few significant genesets because uses Cellular Component (i.e. CC)
    gs <- unique(res_zenith$Geneset[res_zenith$FDR < 0.3])

    # keep only results of these genesets
    df <- res_zenith[res_zenith$Geneset %in% gs, ]

    # plot results, but with no limit based on the highest/lowest t-statistic
    plotZenithResults(df, Inf, Inf)

# Comparing expression in clusters

Identifying genes that are differentially expressed between cell clusters incorporates a paired analysis design, since each individual is observed for each cell cluster.

    # test differential expression between B cells and the rest of the cell clusters
    ct.pairs <- c("CD4 T cells", "rest")

    fit <- dreamletCompareClusters(pb, ct.pairs, method = "fixed")

    # The coefficient 'compare' is the value logFC between test and baseline:
    # compare = cellClustertest - cellClusterbaseline
    df_Bcell <- topTable(fit, coef = "compare")

    head(df_Bcell)

    ##                             logFC   AveExpr         t      P.Value    adj.P.Val
    ## TYROBP                  -7.414914  7.917618 -90.80445 6.842120e-32 3.215797e-28
    ## FTL                     -4.940092 13.169468 -66.22295 1.268317e-28 2.980544e-25
    ## CD63                    -5.078535  8.760309 -59.02003 1.962995e-27 3.075358e-24
    ## C15orf48                -7.280995  8.398874 -54.88795 1.101340e-26 1.294075e-23
    ## HLA-DRA_ENSG00000204287 -6.420347  8.865795 -52.50758 3.155315e-26 2.965996e-23
    ## CCL2                    -7.288475  8.725990 -52.05456 3.875641e-26 3.035919e-23
    ##                                B
    ## TYROBP                  61.56044
    ## FTL                     55.69682
    ## CD63                    52.81595
    ## C15orf48                51.05221
    ## HLA-DRA_ENSG00000204287 50.11427
    ## CCL2                    49.86496

# Gene-cluster specificity

Evaluate the specificity of each gene for each cluster, retaining only highly expressed genes:

    df_cts <- cellTypeSpecificity(pb)

    # retain only genes with total CPM summed across cell type > 100
    df_cts <- df_cts[df_cts$totalCPM > 100, ]

    # Violin plot of specificity score for each cell type
    plotViolin(df_cts)

Highlight expression fraction for most specific gene from each cell type:

    genes <- rownames(df_cts)[apply(df_cts, 2, which.max)]
    plotPercentBars(df_cts, genes = genes)

    dreamlet::plotHeatmap(df_cts, genes = genes)

# Session Info

    ## R version 4.5.2 (2025-10-31)
    ## Platform: x86_64-pc-linux-gnu
    ## Running under: Ubuntu 24.04.4 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
    ##  [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
    ##
    ## time zone: Etc/UTC
    ## tzcode source: system (glibc)
    ##
    ## attached base packages:
    ## [1] stats4    stats     graphics  grDevices utils     datasets  methods
    ## [8] base
    ##
    ## other attached packages:
    ##  [1] GO.db_3.22.0                org.Hs.eg.db_3.22.0
    ##  [3] AnnotationDbi_1.73.0        zenith_1.13.0
    ##  [5] muscData_1.25.0             scater_1.39.2
    ##  [7] scuttle_1.21.0              ExperimentHub_3.1.0
    ##  [9] AnnotationHub_4.1.0         BiocFileCache_3.1.0
    ## [11] dbplyr_2.5.2                muscat_1.25.2
    ## [13] dreamlet_1.9.1              SingleCellExperiment_1.33.0
    ## [15] SummarizedExperiment_1.41.1 Biobase_2.71.0
    ## [17] GenomicRanges_1.63.1        Seqinfo_1.1.0
    ## [19] IRanges_2.45.0              S4Vectors_0.49.0
    ## [21] BiocGenerics_0.57.0         generics_0.1.4
    ## [23] MatrixGenerics_1.23.0       matrixStats_1.5.0
    ## [25] variancePartition_1.41.3    BiocParallel_1.45.0
    ## [27] limma_3.67.0                ggplot2_4.0.2
    ## [29] BiocStyle_2.39.0
    ##
    ## loaded via a namespace (and not attached):
    ##   [1] bitops_1.0-9              httr_1.4.8
    ##   [3] RColorBrewer_1.1-3        doParallel_1.0.17
    ##   [5] Rgraphviz_2.55.0          numDeriv_2016.8-1.1
    ##   [7] tools_4.5.2               sctransform_0.4.3
    ##   [9] backports_1.5.0           utf8_1.2.6
    ##  [11] R6_2.6.1                  metafor_4.8-0
    ##  [13] mgcv_1.9-4                GetoptLong_1.1.0
    ##  [15] withr_3.0.2               prettyunits_1.2.0
    ##  [17] gridExtra_2.3             fdrtool_1.2.18
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    ##  [95] tidyselect_1.2.1          bit_4.6.0
    ##  [97] compiler_4.5.2            curl_7.0.0
    ##  [99] httr2_1.2.2               graph_1.89.1
    ## [101] BiocNeighbors_2.5.4       DelayedArray_0.37.0
    ## [103] scales_1.4.0              caTools_1.18.3
    ## [105] remaCor_0.0.20            rappdirs_0.3.4
    ## [107] stringr_1.6.0             digest_0.6.39
    ## [109] minqa_1.2.8               rmarkdown_2.30
    ## [111] aod_1.3.3                 XVector_0.51.0
    ## [113] RhpcBLASctl_0.23-42       htmltools_0.5.9
    ## [115] pkgconfig_2.0.3           lme4_1.1-38
    ## [117] sparseMatrixStats_1.23.0  lpsymphony_1.39.0
    ## [119] mashr_0.2.79              fastmap_1.2.0
    ## [121] rlang_1.1.7               GlobalOptions_0.1.3
    ## [123] DelayedMatrixStats_1.33.0 farver_2.1.2
    ## [125] jquerylib_0.1.4           IHW_1.39.0
    ## [127] zoo_1.8-15                jsonlite_2.0.0
    ## [129] BiocSingular_1.27.1       RCurl_1.98-1.17
    ## [131] magrittr_2.0.4            Rcpp_1.1.1
    ## [133] babelgene_22.9            viridis_0.6.5
    ## [135] EnrichmentBrowser_2.41.0  stringi_1.8.7
    ## [137] MASS_7.3-65               plyr_1.8.9
    ## [139] listenv_0.10.0            parallel_4.5.2
    ## [141] ggrepel_0.9.6             Biostrings_2.79.4
    ## [143] splines_4.5.2             hms_1.1.4
    ## [145] circlize_0.4.17           locfit_1.5-9.12
    ## [147] buildtools_1.0.0          reshape2_1.4.5
    ## [149] ScaledMatrix_1.19.0       BiocVersion_3.23.1
    ## [151] XML_3.99-0.22             evaluate_1.0.5
    ## [153] RcppParallel_5.1.11-1     BiocManager_1.30.27
    ## [155] nloptr_2.2.1              foreach_1.5.2
    ## [157] tidyr_1.3.2               purrr_1.2.1
    ## [159] future_1.69.0             clue_0.3-67
    ## [161] scattermore_1.2           ashr_2.2-63
    ## [163] rsvd_1.0.5                broom_1.0.12
    ## [165] xtable_1.8-8              fANCOVA_0.6-1
    ## [167] viridisLite_0.4.3         truncnorm_1.0-9
    ## [169] tibble_3.3.1              lmerTest_3.2-0
    ## [171] glmmTMB_1.1.14            memoise_2.0.1
    ## [173] beeswarm_0.4.0            cluster_2.1.8.2
    ## [175] globals_0.19.0            GSEABase_1.73.0