findmarkers volcano plot

The other six methods involved DS testing with cells as the units of analysis. For example, a simple definition of sjc is the number of unique molecular identifiers (UMIs) collected from cell c of subject j. These analyses provide guidance on strengths and weaknesses of different methods in practice. As we observed in Figure 2, the subject method had a larger area under the curve than the other six methods in all simulation settings, with larger differences for higher signal-to-noise ratios. ## locale: Crowell et al. For each setting, 100 datasets were simulated, and we compared seven different DS methods. The marker genes list can be a list or a dictionary. (a) AUPR, (b) PPV with adjusted P-value cutoff 0.05 and (c) NPV with adjusted P-value cutoff 0.05 for 7 DS analysis methods. ## [1] patchwork_1.1.2 ggplot2_3.4.1 In another study, mixed models were found to be superior alternatives to both pseudobulk and marker detection methods (Zimmerman et al., 2021). First, a random proportion of genes, pDE, were flagged as differentially expressed. ## [85] mime_0.12 formatR_1.14 compiler_4.2.0 Analysis of AT2 cells and AMs from healthy and IPF lungs. In the bulk RNA-seq, genes with adjusted P-values less than 0.05 and at least a 2-fold difference in gene expression between CD66+ and CD66-basal cells are considered true positives and all others are considered true negatives. ## [76] goftest_1.2-3 knitr_1.42 fs_1.6.1 Yes, you can use the second one for volcano plots, but it might help to understand what it's implying. baseplot <- DimPlot (pbmc3k.final, reduction = "umap") # Add custom labels and titles baseplot + labs (title = "Clustering of 2,700 PBMCs") Oxford University Press is a department of the University of Oxford. I prefer to apply a threshold when showing Volcano plots, displaying any points with extreme / impossible p-values (e.g. Until computationally efficient methods exist to fit hierarchical models incorporating all sources of biological variation inherent to scRNA-seq, we believe that pseudobulk methods are useful tools for obtaining time-efficient DS results with well-controlled FDR. ## [61] labeling_0.4.2 rlang_1.1.0 reshape2_1.4.4 ## [46] xtable_1.8-4 reticulate_1.28 ggmin_0.0.0.9000 ## [97] Matrix_1.5-3 vctrs_0.6.1 pillar_1.9.0 ## [88] plotly_4.10.1 png_0.1-8 spatstat.utils_3.0-2 For a sequence of cutoff values between 0 and 1, precision, also known as positive predictive value (PPV), is the fraction of genes with adjusted P-values less than a cutoff (detected genes) that are differentially expressed. The scRNA-seq data for the analysis of human lung tissue were obtained from GEO accession GSE122960, and the bulk RNA-seq of purified AT2 and AM fractions were shared by the authors immediately upon request. DGE methods to address this additional complexity, which have been referred to as differential state (DS) analysis are just being explored in the scRNA-seq field (Crowell et al., 2020; Lun et al., 2016; McCarthy et al., 2017; Van den Berge et al., 2019; Zimmerman et al., 2021). Among the other five methods, when the number of differentially expressed genes was small (pDE = 0.01), the mixed method had the highest PPV values, whereas for higher numbers of differentially expressed genes (pDE > 0.01), the DESeq2 method had the highest PPV values. If a gene was differentially expressed, i2 was simulated from a normal distribution with mean 0 and standard deviation (SD) . Infinite p-values are set defined value of the highest -log(p) + 100. I keep receiving an error that says: "data must be a , or an object coercible by fortify(), not an S4 object with class . Tried. All of the other methods compute P-values that are much smaller than those computed by the permutation tests. This is done by passing the Seurat object used to make the plot into CellSelector(), as well as an identity class. In addition to simulated data, we analysed an animal model dataset containing large and small airway epithelia from CF and non-CF pigs (Rogers et al., 2008). We are deprecating this functionality in favor of the patchwork system. The top 50 genes for each method were defined to be the 50 genes with smallest adjusted P-values. Theorem 1 provides a straightforward approach to estimating regression coefficients i1,,iR, testing hypotheses and constructing confidence intervals that properly account for variation in gene expression between subjects. The number of UMIs for cell c was taken to be the size factor sjc in stage 3 of the proposed model. ## [64] later_1.3.0 munsell_0.5.0 tools_4.2.0 Figure 3(b and c) show the PPV and negative predictive value (NPV) for each method and simulation setting under an adjusted P-value cutoff of 0.05. With Seurat, all plotting functions return ggplot2-based plots by default, allowing one to easily capture and manipulate plots just like any other ggplot2-based plot. Supplementary Figure S14 shows the results of marker detection for T cells and macrophages. Figure 4a shows volcano plots summarizing the DS results for the seven methods. CellSelector() will return a vector with the names of the points selected, so that you can then set them to a new identity class and perform differential expression. data("pbmc_small") # Find markers for cluster 2 markers <- FindMarkers(object = pbmc_small, ident.1 = 2) head(x = markers) # Take all cells in cluster 2, and find markers that separate cells in the 'g1' group (metadata # variable 'group') markers <- FindMarkers(pbmc_small, ident.1 = "g1", group.by = 'groups', subset.ident = "2") head(x = markers) # Pass 'clustertree' or an object of class . EnhancedVolcano (Blighe, Rana, and Lewis 2018) will attempt to fit as many labels in the plot window as possible, thus avoiding 'clogging' up the . This research was supported in part through computational resources provided by The University of Iowa, Iowa City, Iowa. We considered three values for pDE{0.01,0.3,0.6}, giving 1%, 30% and 60% of genes as differentially expressed, respectively, and we considered three values for {0.5,1.0,1.5}, representing low, medium and high signal-to-noise ratios, respectively. Volcano plots represent a useful way to visualise the results of differential expression analyses. As a gold standard, results from bulk RNA-seq comparing CD66+ and CD66- basal cells (bulk). The vertical axis gives the precision (PPV) and the horizontal axis gives recall (TPR). We then compare multiple differential expression testing methods on scRNA-seq datasets from human samples and from animal models. To characterize these sources of variation, we consider the following three-stage model: In stage i, variation in expression between subjects is due to differences in covariates via the regression function qij and residual subject-to-subject variation via the dispersion parameter i. . The cluster contains hundreds of computation nodes with varying numbers of processor cores and memory, but all jobs were submitted to the same job queue, ensuring that the relative computation times for these jobs were comparable. Data for the analysis of human skin biopsies were obtained from GEO accession GSE130973. Cons: Seurat utilizes Rs plotly graphing library to create interactive plots. # search for positive markers monocyte.de.markers <- FindMarkers (pbmc, ident.1 = "CD14+ Mono", ident.2 = NULL, only.pos = TRUE) head (monocyte.de.markers) First, we present a statistical model linking differences in gene counts at the cellular level to four sources: (i) subject-specific factors (e.g. Along with new functions add interactive functionality to plots, Seurat provides new accessory functions for manipulating and combining plots. For the AM cells (Fig. In addition, it will plot either 'umap', 'tsne', or, # DoHeatmap now shows a grouping bar, splitting the heatmap into groups or clusters. Specifically, if Kijc is the count of gene i in cell c from pig j, we defined Eijc=Kijc/i'Ki'jc to be the normalized expression for cell c from subject j and Eij=cKijc/i'cKi'jc to be the normalized expression for subject j. These methods appear to form two clusters: the cell-level methods (wilcox, NB, MAST, DESeq2 and Monocle) and the subject-level method (subject), with mixed sharing modest concordance with both clusters. The FindAllMarkers () function has three important arguments which provide thresholds for determining whether a gene is a marker: logfc.threshold: minimum log2 foldchange for average expression of gene in cluster relative to the average expression in all other clusters combined. a, Volcano plot of RNA-seq data from bulk hippocampal tissue from 8- to 9-month-old P301S transgenic and non-transgenic mice (Wald test). The study by Zimmerman et al. Supplementary Figure S11 shows cumulative distribution functions (CDFs) of permutation P-values and method P-values. Further, the cell-level variance and subject-level variance parameters were matched to the pig data. Aggregation technique accounting for subject-level variation in DS analysis. In this comparison, many genes were detected by all seven methods. To avoid confounding the results by disease, this analysis is confined to data from six healthy subjects in the dataset. If a gene was not differentially expressed, the value of i2 was set to 0. Because we are comparing different cells from the same subjects, the subject and mixed methods can also account for the matching of cells by subject in the regression models. As an example, were going to select the same set of cells as before, and set their identity class to selected. The vertical axes give the performance measures, and the horizontal axes label each method. Plotting multiple plots was previously achieved with the CombinePlot() function. In (a), vertical axes are negative log10-transformed adjusted P-values, and horizontal axes are log2-transformed fold changes. . The subject method has the strongest type I error rate control and highest PPVs, wilcox has the highest TPRs and mixed has intermediate performance with better TPRs than subject yet lower FPRs than wilcox (Supplementary Table S2). dotplot visualization does not work for scaled or corrected matrices in which cero counts had been replaced by other values. ## #' @return Returns a volcano plot from the output of the FindMarkers function from the Seurat package, which is a ggplot object that can be modified or plotted. ## [94] highr_0.10 desc_1.4.2 lattice_0.20-45 See Supplementary Material for brief example code demonstrating the usage of aggregateBioVar. (a) Volcano plots and (b) heatmaps of top 50 genes for 7 different DS analysis methods. Theorem 1 implies that when the number of cells per subject is large, the aggregated counts follow a distribution with the same mean and variance structure as the negative binomial model used in many software packages for DS analysis of bulk RNA-seq data. Figure 6(e and f) shows ROC and PR curves for the three scRNA-seq methods using the bulk RNA-seq as a gold standard. ## [43] miniUI_0.1.1.1 Rcpp_1.0.10 viridisLite_0.4.1 In our simulation, the analysis focused on transcriptome-wide data simulated from the proposed model for scRNA-seq counts under different numbers of differentially expressed genes and different signal-to-noise ratios. Then, for each method, we defined the permutation test statistic to be the unadjusted P-value generated by the method. To consider characteristics of a real dataset, we matched fixed quantities and parameters of the model to empirical values from a small airway secretory cell subset from the newborn pig data we present again in Section 3.2. Therefore, as experiments that include biological replication become more common, statistical frameworks to account for multiple sources of biological variability will be critical, as recently described by Lhnemann et al. These approaches will likely yield better type I and type II error rate control, but as we saw for the mixed method in our simulation, the computation times can be substantially longer and the computational burden of these methods scale with the number of cells, whereas the pseudobulk method scales with the number of subjects. Improvements in type I and type II error rate control of the DS test could be considered by modeling cell-level gene expression adjusted for potential differences in gene expression between subjects, similar to the mixed method in Section 3. Generally, the NPV values were more similar across methods. 14.1 Basic usage. The volcano plots for the three scRNA-seq methods have similar shapes, but the wilcox and mixed methods have inflated adjusted P-values relative to subject (Fig. (c and d) Volcano plots show results of three methods (subject, wilcox and mixed) used to find differentially expressed genes between IPF and healthy lungs in (c) AT2 cells and (d) AM. ## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C ## [31] progressr_0.13.0 spatstat.data_3.0-1 survival_3.3-1 We compared the performances of subject, wilcox and mixed for DS analysis of the scRNA-seq from healthy and IPF subjects within AT2 and AM cells using bulk RNA-seq of purified AT2 and AM cell type fractions as a gold standard, similar to the method used in Section 3.5. Third, we examine properties of DS testing in practice, comparing cells versus subjects as units of analysis in a simulation study and using available scRNA-seq data from humans and pigs. The observed counts for the PCT study are analogous to the aggregated counts for one cell type in a scRNA-seq study. First, it is assumed that prerequisite steps in the bioinformatic pipeline produced cells that conform to the assumptions of the proposed model. According to this criterion, the subject method had the best performance, and the degree to which subject outperformed the other methods improved with larger values of the signal-to-noise ratio parameter . Performance measures for DS analysis of simulated data. For example, consider a hypothetical gene having heterogeneous expression in CF pigs, where cells were either low expressors or high expressors versus homogeneous expression in non-CF pigs, where cells were moderate expressors. Overall, the subject and mixed methods had the highest concordance between permutation and method P-values. ## [118] sctransform_0.3.5 parallel_4.2.0 grid_4.2.0 In order to determine the reliability of the unadjusted P-values computed by each method, we compared them to the unadjusted P-values obtained from a permutation test. Supplementary Figure S12b shows the top 50 genes for each method, defined as the genes with the 50 smallest adjusted P-values. Below is a brief demonstration but please see the patchwork package website here for more details and examples. Gene counts were simulated from the model in Section 2.1. FindMarkers from Seurat returns p values as 0 for highly significant genes. True positives were identified as those genes in the bulk RNA-seq analysis with FDR<0.05 and |log2(CD66+/CD66)|>1. Second, we make a formal argument for the validity of a DS test with subjects as the units of analysis and discuss our development of a Bioconductor package that can be incorporated into scRNA-seq analysis workflows. ## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8 This creates a data.frame with gene names as rows, and includes avg_log2FC, and adjusted p-values. disease and intervention), (ii) variation between subjects, (iii) variation between cells within subjects and (iv) technical variation introduced by sampling RNA molecules, library preparation and sequencing. This suggests that methods that fail to account for between subject differences in gene expression are more sensitive to biological variation between subjects, leading to more false discoveries. In stage iii, technical variation in counts is generated from a Poisson distribution. The subject and mixed methods are composed of genes that have high inter-group (CF versus non-CF) and low intra-group (between subject) variability, whereas the wilcox, NB, MAST, DESeq2 and Monocle methods tend to be sensitive to a highly variable gene expression pattern from the third CF pig. ## [121] tidyr_1.3.0 rmarkdown_2.21 Rtsne_0.16 These results suggest that only the subject method will exhibit appropriate type I error rate control. In recent years, the reagent and effort costs of scRNA-seq have decreased dramatically as novel techniques have been developed (Aicher et al., 2019; Briggs et al., 2018; Cao et al., 2017; Chen et al., 2019; Gehring et al., 2020; Gierahn et al., 2017; Klein et al., 2015; Macosko et al., 2015; Natarajan et al., 2019; Rosenberg et al., 2018; Vitak et al., 2017; Zhang et al., 2019; Ziegenhain et al., 2017), so that biological replication, meaning data collected from multiple independent biological units such as different research animals or human subjects, is becoming more feasible; biological replication allows generalization of results to the population from which the sample was drawn. Supplementary Figure S14(cd) show that generally the shapes of the volcano plots are more similar between the subject and mixed methods than the wilcox method. On the other hand, subject had the smallest FPR (0.03) compared to wilcox and mixed (0.26 and 0.08, respectively) and had a higher PPV (0.38 compared to 0.10 and 0.23). To illustrate scalability and performance of various methods in real-world conditions, we show results in a porcine model of cystic fibrosis and analyses of skin, trachea and lung tissues in human sample datasets. In each panel, PR curves are plotted for each of seven DS analysis methods: subject (red), wilcox (blue), NB (green), MAST (purple), DESeq2 (orange), Monocle (gold) and mixed (brown). Because these assumptions are difficult to validate in practice, we suggest following the guidelines for library complexity in bulk RNA-seq studies. Default is 0.25. Figure 4b shows the top 50 genes for each method, defined by the smallest 50 adjusted P-values. This will mean, however, that FindMarkers() takes longer to complete. Nine simulation settings were considered. It is helpful to inspect the proposed model under a simplifying assumption. They also thank Paul A. Reyfman and Alexander V. Misharin for sharing bulk RNA-seq data used in this study. Applying the assumptions Cj-1csjck1 and Cj-1csjc2k2 completes the proof. This work was supported by the National Institutes of Health [NHLBI K01HL140261]; the Parker B. Francis Fellowship Program; the Cystic Fibrosis Foundation University of Iowa Research Development Program (Bioinformatics Core); a Pilot Grant from the University of Iowa Center for Gene Therapy [NIH NIDDK DK54759] and a Pilot Grant from the University of Iowa Environmental Health Sciences Research Center [NIH NIEHS ES005605]. The expression parameter for the difference between groups 1 and 2, i2, was varied in order to evaluate the properties of DS analysis under a number of different scenarios. #' @param output_dir The relative directory that will be used to save results. The difference between these formulas is in the mean calculation. < 10e-20) with a different symbol at the top of the graph. The lists of genes detected by the other six methods likely contain many false discoveries. ## [10] digest_0.6.31 htmltools_0.5.5 fansi_1.0.4 Step 1: Set up your script. In order to objectively measure the performance of our tested approaches in scRNA-seq DS analysis, we compared them to a gold standard consistent of bulk RNA-seq analysis of purified/sorted cell types. ## loaded via a namespace (and not attached): ## [1] systemfonts_1.0.4 plyr_1.8.8 igraph_1.4.1, ## [4] lazyeval_0.2.2 sp_1.6-0 splines_4.2.0, ## [7] crosstalk_1.2.0 listenv_0.9.0 scattermore_0.8, ## [10] digest_0.6.31 htmltools_0.5.5 fansi_1.0.4, ## [13] magrittr_2.0.3 memoise_2.0.1 tensor_1.5, ## [16] cluster_2.1.3 ROCR_1.0-11 limma_3.54.1, ## [19] globals_0.16.2 matrixStats_0.63.0 pkgdown_2.0.7, ## [22] spatstat.sparse_3.0-1 colorspace_2.1-0 rappdirs_0.3.3, ## [25] ggrepel_0.9.3 textshaping_0.3.6 xfun_0.38, ## [28] dplyr_1.1.1 crayon_1.5.2 jsonlite_1.8.4, ## [31] progressr_0.13.0 spatstat.data_3.0-1 survival_3.3-1, ## [34] zoo_1.8-11 glue_1.6.2 polyclip_1.10-4, ## [37] gtable_0.3.3 leiden_0.4.3 future.apply_1.10.0, ## [40] abind_1.4-5 scales_1.2.1 spatstat.random_3.1-4, ## [43] miniUI_0.1.1.1 Rcpp_1.0.10 viridisLite_0.4.1, ## [46] xtable_1.8-4 reticulate_1.28 ggmin_0.0.0.9000, ## [49] htmlwidgets_1.6.2 httr_1.4.5 RColorBrewer_1.1-3, ## [52] ellipsis_0.3.2 ica_1.0-3 farver_2.1.1, ## [55] pkgconfig_2.0.3 sass_0.4.5 uwot_0.1.14, ## [58] deldir_1.0-6 utf8_1.2.3 tidyselect_1.2.0, ## [61] labeling_0.4.2 rlang_1.1.0 reshape2_1.4.4, ## [64] later_1.3.0 munsell_0.5.0 tools_4.2.0, ## [67] cachem_1.0.7 cli_3.6.1 generics_0.1.3, ## [70] ggridges_0.5.4 evaluate_0.20 stringr_1.5.0, ## [73] fastmap_1.1.1 yaml_2.3.7 ragg_1.2.5, ## [76] goftest_1.2-3 knitr_1.42 fs_1.6.1, ## [79] fitdistrplus_1.1-8 purrr_1.0.1 RANN_2.6.1, ## [82] pbapply_1.7-0 future_1.32.0 nlme_3.1-157, ## [85] mime_0.12 formatR_1.14 compiler_4.2.0, ## [88] plotly_4.10.1 png_0.1-8 spatstat.utils_3.0-2, ## [91] tibble_3.2.1 bslib_0.4.2 stringi_1.7.12, ## [94] highr_0.10 desc_1.4.2 lattice_0.20-45, ## [97] Matrix_1.5-3 vctrs_0.6.1 pillar_1.9.0, ## [100] lifecycle_1.0.3 spatstat.geom_3.1-0 lmtest_0.9-40, ## [103] jquerylib_0.1.4 RcppAnnoy_0.0.20 data.table_1.14.8, ## [106] cowplot_1.1.1 irlba_2.3.5.1 httpuv_1.6.9, ## [109] R6_2.5.1 promises_1.2.0.1 KernSmooth_2.23-20, ## [112] gridExtra_2.3 parallelly_1.35.0 codetools_0.2-18, ## [115] MASS_7.3-56 rprojroot_2.0.3 withr_2.5.0, ## [118] sctransform_0.3.5 parallel_4.2.0 grid_4.2.0, ## [121] tidyr_1.3.0 rmarkdown_2.21 Rtsne_0.16, ## [124] spatstat.explore_3.1-0 shiny_1.7.4, Fast integration using reciprocal PCA (RPCA), Integrating scRNA-seq and scATAC-seq data, Demultiplexing with hashtag oligos (HTOs), Interoperability between single-cell object formats. In our simulation study, we also found that the pseudobulk method was conservative, but in some settings, mixed models had inflated FDR. This issue is most likely to arise with rare cell types, in which few or no cells are profiled for any subject. Search for other works by this author on: Iowa Institute of Human Genetics, Roy J. and Lucille A. For full access to this pdf, sign in to an existing account, or purchase an annual subscription. We set xj1=1 for all j and define xj2 as a dummy variable indicating that subject j belongs to the treated group. (d) ROC and PR curves for subject, wilcox and mixed methods using bulk RNA-seq as a gold standard. Was this translation helpful? The second stage represents technical variation introduced by the processes of sampling from a population of RNAs, building a cDNA library and sequencing. For each subject, the number of cells and numbers of UMIs per cell were matched to the pig data. "poisson" : Likelihood ratio test assuming an . ## [15] Seurat_4.2.1.9001 ## loaded via a namespace (and not attached): Generally, tests for marker detection, such as the wilcox method, are sufficient if type I error rate control is less of a concern than type II error rate and in circumstances where type I error rate is most important, methods like subject and mixed can be used. ## [22] spatstat.sparse_3.0-1 colorspace_2.1-0 rappdirs_0.3.3 We also assume that cell types or states have been identified, DS analysis will be performed within each cell type of interest and henceforth, the notation corresponds to one cell type. Next, we used subject, wilcox and mixed to test for differences in expression between healthy and IPF subjects within the AT2 and AM cell populations. Developed by Paul Hoffman, Satija Lab and Collaborators. ## [25] ggrepel_0.9.3 textshaping_0.3.6 xfun_0.38 The following differential expression tests are currently supported: "wilcox" : Wilcoxon rank sum test (default) "bimod" : Likelihood-ratio test for single cell feature expression, (McDavid et al., Bioinformatics, 2013) "roc" : Standard AUC classifier. In scRNA-seq studies, where cells are collected from multiple subjects (e.g. Cons: For the AT2 cells (Fig. A volcano plot is a type of scatterplot that shows statistical significance (P value) versus magnitude of change (fold change). 5c). Then, we consider the top g genes for each method, which are the g genes with the smallest adjusted P-values, and find what percentage of these top genes are known markers. For higher numbers of differentially expressed genes (pDE > 0.01), the subject method had lower NPV values when = 0.5 and similar or higher NPV values when > 0.5. Published by Oxford University Press. We have developed the software package aggregateBioVar (available on Bioconductor) to facilitate broad adoption of pseudobulk-based DE testing; aggregateBioVar includes a detailed vignette, has low code complexity and minimal dependencies and is highly interoperable with existing RNA-seq analysis software using Bioconductor core data structures (Fig. Let Gammaa,b denote the gamma distribution with shape parameter a and scale parameter b, Poissonm denote the Poisson distribution with mean m and XY denote the conditional distribution of random variable X given random variable Y. True positives were identified as those genes in the bulk RNA-seq analysis with FDR<0.05 and |log2(IPF/healthy)|>1. The regression component of the model took the form logqij=i1+xj2i2, where xj2 is an indicator that subject j is in group 2. sessionInfo()## R version 4.2.0 (2022-04-22) For example, lets pretend that DCs had merged with monocytes in the clustering, but we wanted to see what was unique about them based on their position in the tSNE plot. ## [70] ggridges_0.5.4 evaluate_0.20 stringr_1.5.0 Finally, we discuss potential shortcomings and future work. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, https://doi.org/10.1093/bioinformatics/btab337, https://www.bioconductor.org/packages/release/bioc/html/aggregateBioVar.html, https://creativecommons.org/licenses/by/4.0/, Receive exclusive offers and updates from Oxford Academic, Academic Pulmonary Sleep Medicine Physician Opportunity in Scenic Central Pennsylvania, MEDICAL MICROBIOLOGY AND CLINICAL LABORATORY MEDICINE PHYSICIAN, CLINICAL CHEMISTRY LABORATORY MEDICINE PHYSICIAN. The implemented methods are subject (red), wilcox (blue), NB (green), MAST (purple), DESeq2 (orange), monocle (gold) and mixed (brown). For each of these two cell types, the expression profiles are compared to all other cells as in traditional marker detection analysis. This study found that generally pseudobulk methods and mixed models had better statistical characteristics than marker detection methods, in terms of detecting differentially expressed genes with well-controlled false discovery rates (FDRs), and pseudobulk methods had fast computation times.

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