Single-cell RNA sequencing (scRNA-seq) has been widely used to deepen our understanding of various biological processes, including cell differentiation, tumor development and disease occurrence. However, it remains challenging to effectively detect differential compositions of cell types when comparing samples coming from different conditions or along with continuous covariates, partly due to the small number of replicates and high uncertainty of cell clustering.
This vignette provides an introduction to the DCATS package, which contains
methods to detect the differential composition abundances between multiple
conditions in singel-cell experiments. It can be easily incooperated with
existing single cell data analysis pipeline and contribute to the whole
analysis process.
To install DCATS, first make sure that you have the devtools package installed:
if (!requireNamespace("devtools", quietly = TRUE))
install.packages("BiocManager")Then, install DCATS using the following command:
BiocManager::install("DCTAS")To use DCATS, start by loading the package:
library(DCATS)Here, we used a built-in simulator in DCATS to simulate the data for following analysis. We simulate count data for four samples coming from the first condition with total cell counts 100, 800, 1300, and 600. We simulate another three samples coming from the second condition with total cell counts 250, 700, 1100.
In this simulator function, a proportion of different cell types is simulate following a dirichlet distribution decided by \(\{p_i\} \times c\) where \(\{p_i\}\) is the true proportion vector and \(c\) is a concentration parameter indicating how far way the simulated proportion can be. The larger the \(c\), the higher probability to simulate a proportion vector close to the true proportion. Then the cell counts are generated from the multinomial distribution with self-defined total cell counts and simulated proportions.
set.seed(6171)
K <- 3
totals1 = c(100, 800, 1300, 600)
totals2 = c(250, 700, 1100)
diri_s1 = rep(1, K) * 20
diri_s2 = rep(1, K) * 20
simil_mat = create_simMat(K, confuse_rate=0.2)
sim_dat <- DCATS::simulator_base(totals1, totals2, diri_s1, diri_s2, simil_mat)The output of simulator_base is the cell counts matrices of two conditions.
print(sim_dat$numb_cond1)
#> [,1] [,2] [,3]
#> [1,] 36 35 29
#> [2,] 271 279 250
#> [3,] 518 379 403
#> [4,] 152 220 228
print(sim_dat$numb_cond2)
#> [,1] [,2] [,3]
#> [1,] 84 87 79
#> [2,] 259 203 238
#> [3,] 345 376 379DCATS provides three methods to get the similarity matrix which indicates the misclassification rate between different cell types. Currently, DCATS provides three ways to estimate the similarity matrix.
The first one describes an unbiased misclassification across all the cell types. It means that one cell from a cell type have equal chance to be assigned to rest other cell types. When the numbers of biological replicates are the same in two conditions and are relatively large, other unbiased random error will contribute more to the difference between the observed proportions and the true proportions. In this case, using this uniform confusion matrix is a better choice.
We use the function create_simMat to create a similarity matrix describe above. We need to specify the number of cell types \(K\) and the confuse rate which indicates the proportion of cells from one cell type being assigned to other cell types.
simil_mat = create_simMat(K = 3, confuse_rate = 0.2)
print(simil_mat)
#> [,1] [,2] [,3]
#> [1,] 0.8 0.1 0.1
#> [2,] 0.1 0.8 0.1
#> [3,] 0.1 0.1 0.8The second kind of confusion matrix is estimated from the knn matrix provided by Seurat. It calculates the proportion of neighborhoods that are regarded as other cell types. In this case, DCATS corrects cell proportions mainly based on the information of similarity between different cell types and variety within each cell types.
The input of this function should be a ‘Graph’ class from SeuratObject and a factor vector containing the cell type information of each cell. We can estimate the knn similarity matrix for the simulation dataset included in the DCATS package.
data(simulation)
print(simulation$knnGraphs[1:10, 1:10])
#> Loading required package: SeuratObject
#> Loading required package: sp
#> 10 x 10 sparse Matrix of class "dgCMatrix"
#> [[ suppressing 10 column names 'Cell7247', 'Cell2462', 'Cell7731' ... ]]
#>
#> Cell7247 1 . . . . . . . . .
#> Cell2462 . 1.0000000 0.1428571 . . 0.1111111 . . . .
#> Cell7731 . 0.1428571 1.0000000 . . . . . . .
#> Cell10644 . . . 1 . . . . . .
#> Cell6352 . . . . 1.00000000 . . . 0.08108108 .
#> Cell202 . 0.1111111 . . . 1.0000000 . . . .
#> Cell3763 . . . . . . 1 . . .
#> Cell11305 . . . . . . . 1 . .
#> Cell1619 . . . . 0.08108108 . . . 1.00000000 .
#> Cell7073 . . . . . . . . . 1
head(simulation$labels, 10)
#> Cell7247 Cell2462 Cell7731 Cell10644 Cell6352 Cell202 Cell3763 Cell11305
#> B B B A B B A B
#> Cell1619 Cell7073
#> B A
#> Levels: A B C D
## estimate the knn matrix
knn_mat = knn_simMat(simulation$knnGraphs, simulation$labels)
print(knn_mat)
#> B A D C
#> B 0.90559742 0.04834084 0.032695520 0.013366219
#> A 0.02978309 0.93819202 0.020730191 0.011294702
#> D 0.04262080 0.04386126 0.905574534 0.007943405
#> C 0.01688846 0.02316331 0.007699363 0.952248861The third way to estimate a confusion matrix is to use a support vector machine classifier. The input for estimating the confusion matrix will be a data frame containing a set of variables that the user believe will influence the result of the clustering process as well as the cell type labels for each cell. We then use 5-fold cross validation and support vector machine as the classifier to predict cell type labels. By comparing given labels and predicted labels, we can get a confusion matrix.
Noted: Two packages tidyverse and tidymodels should be attached.
data(Kang2017)
head(Kang2017$svmDF)
#> PC_1 PC_2 PC_3 PC_4 PC_5 PC_6
#> 25666 3.886605 0.371065498 0.45612412 -2.2158043 0.8367050 -0.5005777
#> 21949 -4.892706 0.005013112 -0.14214031 -2.0263140 -9.1630543 -5.6146838
#> 20993 8.128727 3.413183866 0.77332521 -0.7947297 -0.1259194 1.4354282
#> 12800 -5.291259 1.086436116 0.09297087 -0.3688472 1.2591707 1.1448220
#> 20529 1.348189 -1.540491799 -1.11063041 -0.7533303 -0.1772481 -2.2803474
#> 2260 -4.674048 0.987198436 -0.24743392 -1.1894792 0.7813787 1.7889641
#> PC_7 PC_8 PC_9 PC_10 PC_11 PC_12
#> 25666 0.7803348 0.4800115 3.44807316 -0.74869915 -0.2709463 0.1902547
#> 21949 -1.6259713 1.1843184 -0.34606758 0.06381662 -1.6661260 1.2609511
#> 20993 -0.3926234 -2.9391317 -0.18758445 -1.32352232 -9.5720590 -0.0816473
#> 12800 -0.1894140 -0.3941355 -0.07409775 -0.42776692 0.8500834 -0.1766672
#> 20529 -0.7090460 0.9702130 1.21294621 0.06270241 0.8655038 -1.1263086
#> 2260 -0.2910701 -0.5315665 0.64824174 0.10549453 1.5398666 -0.3199010
#> PC_13 PC_14 PC_15 PC_16 PC_17 PC_18
#> 25666 -0.021474926 -2.0987058 -1.2426865 -1.1569523 -0.03833244 0.09700686
#> 21949 1.216625428 -0.2886003 -0.1862753 1.0963970 1.31225447 -0.89871374
#> 20993 -2.902801030 7.0283078 0.4110564 -2.8937657 -1.43682307 -4.22447218
#> 12800 -0.193047413 -0.1697745 -0.6363052 0.1382581 0.47646661 -0.71018124
#> 20529 0.001359746 0.8215608 1.6677901 -1.1598547 -0.61119430 0.41836462
#> 2260 -1.154064248 -0.6361448 0.4637186 0.4661563 1.40395389 -0.95124980
#> PC_19 PC_20 PC_21 PC_22 PC_23 PC_24
#> 25666 -0.25524675 1.1443263 -0.22962253 -1.1924297 -0.3969562 0.4462946
#> 21949 -0.10255959 -0.2396403 0.08226689 1.3234882 -0.1730629 0.8658607
#> 20993 0.68097214 -4.2858702 5.54567343 3.8301645 0.4483186 -1.9667036
#> 12800 0.07136216 0.1128140 0.37217345 0.2601427 0.4763722 0.2402885
#> 20529 1.13865990 0.6297999 -1.47643207 0.6574216 -1.2929223 -0.8044571
#> 2260 -0.52253534 -0.5443369 0.96723500 -0.4688763 1.0660959 0.4273633
#> PC_25 PC_26 PC_27 PC_28 PC_29 PC_30
#> 25666 -0.3862561 -1.2606189 -0.8322474 1.553621371 0.1971527 -1.55214561
#> 21949 -1.6100130 0.8802375 -2.5770211 -1.332021381 -0.6425592 -0.64571058
#> 20993 -2.3599685 0.4662246 0.9815318 0.190612316 1.0932119 1.32292269
#> 12800 0.2302071 -0.1369112 -0.1914076 -0.006736424 -0.5333921 0.74430509
#> 20529 0.1209402 0.3862782 0.7380538 -1.592696959 1.2786249 -0.95457380
#> 2260 0.6038350 -0.1864475 -0.1897286 0.282929965 1.3877823 -0.04619324
#> condition clusterRes
#> 25666 ctrl CD14+ Monocytes
#> 21949 stim NK cells
#> 20993 stim FCGR3A+ Monocytes
#> 12800 ctrl CD4 T cells
#> 20529 ctrl CD14+ Monocytes
#> 2260 stim CD4 T cellslibrary(tidyverse)
library(tidymodels)
## estimate the svm matrix
svm_mat = svm_simMat(Kang2017$svmDF)
print(svm_mat)#>
#> B cells CD14+ Monocytes CD4 T cells CD8 T cells
#> B cells 0.9214804566 0.0096650338 0.0092441099 0.0015343306
#> CD14+ Monocytes 0.0076098236 0.8290745399 0.0054810209 0.0038358266
#> CD4 T cells 0.0349360083 0.0140341586 0.9460078534 0.0698120445
#> CD8 T cells 0.0065721204 0.0039719317 0.0274869110 0.7974683544
#> Dendritic cells 0.0134901418 0.0274063286 0.0011452880 0.0003835827
#> FCGR3A+ Monocytes 0.0093393290 0.1028730306 0.0028632199 0.0015343306
#> Megakaryocytes 0.0048426150 0.0074142725 0.0048265707 0.0003835827
#> NK cells 0.0017295054 0.0055607044 0.0029450262 0.1250479478
#>
#> Dendritic cells FCGR3A+ Monocytes Megakaryocytes
#> B cells 0.0376569038 0.0009124088 0.0237388724
#> CD14+ Monocytes 0.0418410042 0.0310218978 0.1364985163
#> CD4 T cells 0.0000000000 0.0045620438 0.1364985163
#> CD8 T cells 0.0000000000 0.0027372263 0.0207715134
#> Dendritic cells 0.8744769874 0.0018248175 0.0059347181
#> FCGR3A+ Monocytes 0.0418410042 0.9562043796 0.0267062315
#> Megakaryocytes 0.0041841004 0.0018248175 0.6142433234
#> NK cells 0.0000000000 0.0009124088 0.0356083086
#>
#> NK cells
#> B cells 0.0014224751
#> CD14+ Monocytes 0.0033191086
#> CD4 T cells 0.0109056425
#> CD8 T cells 0.0796586060
#> Dendritic cells 0.0000000000
#> FCGR3A+ Monocytes 0.0014224751
#> Megakaryocytes 0.0018966335
#> NK cells 0.9013750593Here we used the simulated result to demonstrate the usage of dcats_GLM. We combine two cell counts matrices to create the count matrix, and create a corresponding data frame indicating the condition of those samples. dcats_GLM can give results based on the count matrix and design matrix.
Noted Even though we call it design matrix, we allow it to be both matrix and data.frame.
sim_count = rbind(sim_dat$numb_cond1, sim_dat$numb_cond2)
print(sim_count)
#> [,1] [,2] [,3]
#> [1,] 36 35 29
#> [2,] 271 279 250
#> [3,] 518 379 403
#> [4,] 152 220 228
#> [5,] 84 87 79
#> [6,] 259 203 238
#> [7,] 345 376 379
sim_design = data.frame(condition = c("g1", "g1", "g1", "g1", "g2", "g2", "g2"))
print(sim_design)
#> condition
#> 1 g1
#> 2 g1
#> 3 g1
#> 4 g1
#> 5 g2
#> 6 g2
#> 7 g2
dcats_GLM(sim_count, sim_design, similarity_mat = simil_mat)
#> $ceoffs
#> condition
#> cell_type_1 0.03661816
#> cell_type_2 -0.06993872
#> cell_type_3 0.05830053
#>
#> $coeffs_err
#> condition
#> cell_type_1 0.04897174
#> cell_type_2 0.02251655
#> cell_type_3 0.01511024
#>
#> $LR_vals
#> condition
#> cell_type_1 0.02731556
#> cell_type_2 0.21580226
#> cell_type_3 0.21884571
#>
#> $LRT_pvals
#> condition
#> cell_type_1 0.8687282
#> cell_type_2 0.6422572
#> cell_type_3 0.6399208
#>
#> $fdr
#> condition
#> cell_type_1 0.8687282
#> cell_type_2 0.8687282
#> cell_type_3 0.8687282The ceoffs indicates the estimated values of coefficients, the coeffs_err indicates the standard errors of coefficients, the LRT_pvals indicates the p-values calculated from the likelihood ratio test, and the fdr indicates the adjusted p-values given by Benjamini & Hochberg method.
Noted: You might sometime receive a warning like Possible convergence problem. Optimization process code: 10 (see ?optim). It is caused by the low number of replicates and won’t influence the final results.
When doing the differential abundance analysis in DCATS, we used generalized linear model assuming the cell counts follow beta-binomial distribution. DCATS provides p-values for each cluster considering each factor in the design matrix. The default model is comparing a model with only the tested factor and the null model. In this case, factors are tested independently.
We can also choose to compare the full model and a model without the tested factor. In this case, factors are tested when controlling the rest factors.
## add another factor for testing
set.seed(123)
sim_design = data.frame(condition = c("g1", "g1", "g1", "g1", "g2", "g2", "g2"),
gender = sample(c("Female", "Male"), 7, replace = TRUE))
dcats_GLM(sim_count, sim_design, similarity_mat = simil_mat, base_model='FULL')
#> $ceoffs
#> condition gender
#> cell_type_1 0.1948918 -0.38905567
#> cell_type_2 -0.1003737 0.06189625
#> cell_type_3 -0.1723674 0.40591227
#>
#> $coeffs_err
#> condition gender
#> cell_type_1 0.0386976000 0.0385575207
#> cell_type_2 0.0284446849 0.0283368344
#> cell_type_3 0.0007620465 0.0006001116
#>
#> $LR_vals
#> condition gender
#> cell_type_1 0.9040969 3.0970425
#> cell_type_2 0.3443648 0.1313372
#> cell_type_3 3.0111465 12.3540360
#>
#> $LRT_pvals
#> condition gender
#> cell_type_1 0.34168556 0.0784346670
#> cell_type_2 0.55732056 0.7170496021
#> cell_type_3 0.08269378 0.0004400341
#>
#> $fdr
#> condition gender
#> cell_type_1 0.5125283 0.165387560
#> cell_type_2 0.6687847 0.717049602
#> cell_type_3 0.1653876 0.002640205When fitting the beta binomial model, we have a parameter \(\phi\) to describe the over-dispersion of data. The default setting of DCATS is to fit \(\phi\) for each cell type. This might leads to over-fitting. Here we can use the getPhi function to estimate a global \(\phi\) for all cell types and set fixphi = TRUE to apply this global \(\phi\) to all cell types.
In this case, coeffs_err is not available.
sim_design = data.frame(condition = c("g1", "g1", "g1", "g1", "g2", "g2", "g2"))
phi = DCATS::getPhi(sim_count, sim_design)
dcats_GLM(sim_count, sim_design, similarity_mat = simil_mat, fix_phi = phi)
#> $ceoffs
#> condition
#> cell_type_1 0.02732541
#> cell_type_2 -0.06575758
#> cell_type_3 0.05803205
#>
#> $coeffs_err
#> condition
#> cell_type_1 NA
#> cell_type_2 NA
#> cell_type_3 NA
#>
#> $LR_vals
#> condition
#> cell_type_1 0.04776539
#> cell_type_2 0.27685545
#> cell_type_3 0.21489868
#>
#> $LRT_pvals
#> condition
#> cell_type_1 0.8269983
#> cell_type_2 0.5987697
#> cell_type_3 0.6429547
#>
#> $fdr
#> condition
#> cell_type_1 0.8269983
#> cell_type_2 0.8269983
#> cell_type_3 0.8269983The LRT_pvals can be used to define whether one cell type shows differential proportion among different conditions by setting threshold as 0.05 or 0.01.
DCATS also supports the use of known unchanged cell types as reference cell types. We recommend using 1) more than one cell type; 2) more than 20% of total cells as the reference group. Here, we named three simulated cell types as A, B, C, and use the cell type A, B as the reference cell types.
colnames(sim_count) = c("A", "B", "C")
dcats_GLM(sim_count, sim_design, similarity_mat = simil_mat, reference = c("A", "B"))
#> $ceoffs
#> condition
#> A 0.04318527
#> B -0.02668661
#> C 0.05748545
#>
#> $coeffs_err
#> condition
#> A 0.01600641
#> B 0.01633854
#> C 0.01529722
#>
#> $LR_vals
#> condition
#> A 0.11817121
#> B 0.04383267
#> C 0.21072459
#>
#> $LRT_pvals
#> condition
#> A 0.7310265
#> B 0.8341652
#> C 0.6462001
#>
#> $fdr
#> condition
#> A 0.8341652
#> B 0.8341652
#> C 0.8341652Even though it is not recommended, DCATS allows the use of one cell type as the reference cell type. Especially when we are interested in the ratio relationship between two cell types (for eaxmple A and B).
dcats_GLM(sim_count, sim_design, similarity_mat = simil_mat, reference = c("A"))
#> Warning in aod::betabin(formula_fm1, ~1, data = df_tmp, warnings = FALSE):
#> Possible convergence problem. Optimization process code: 10 (see ?optim).
#> $ceoffs
#> condition
#> A -0.004533535
#> B -0.083349329
#> C 0.008707148
#>
#> $coeffs_err
#> condition
#> A 0.00485482
#> B 0.05644594
#> C 0.05138848
#>
#> $LR_vals
#> condition
#> A -0.005172729
#> B 0.122209029
#> C 0.001515344
#>
#> $LRT_pvals
#> condition
#> A 1.0000000
#> B 0.7266509
#> C 0.9689483
#>
#> $fdr
#> condition
#> A 1
#> B 1
#> C 1When we have no idea which cell types can be used as reference cell types, DCATS supports detection of reference cell types automatically using the function detect_reference. This function returns a vector with ordered cell types and a meesage indicating how many cell types should be selected as the reference group. Cell types are ordered by an estimation of their proportion difference. The order indicating how they are recommended to be selected as reference cell types. We recommend to select top cell types.
Nonetheless, this kind of tasks is challenging and we suggest users perform the reference cell selection with caution.
reference_cell = detect_reference(sim_count, sim_design, similarity_mat = simil_mat)
#> Please check the 'min_celltypeN' for the number of minimum cell types recommend.
print(reference_cell)
#> $min_celltypeN
#> [1] 2
#>
#> $ordered_celltype
#> [1] "A" "B" "C"
dcats_GLM(sim_count, sim_design, similarity_mat = simil_mat, reference = reference_cell$ordered_celltype[1:2])
#> $ceoffs
#> condition
#> A 0.04423357
#> B -0.02718748
#> C 0.05830053
#>
#> $coeffs_err
#> condition
#> A 0.01611672
#> B 0.01641139
#> C 0.01511024
#>
#> $LR_vals
#> condition
#> A 0.12191851
#> B 0.04545546
#> C 0.21884571
#>
#> $LRT_pvals
#> condition
#> A 0.7269629
#> B 0.8311687
#> C 0.6399208
#>
#> $fdr
#> condition
#> A 0.8311687
#> B 0.8311687
#> C 0.8311687sessionInfo()
#> 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] SeuratObject_4.1.4 sp_2.1-1 DCATS_1.0.0 BiocStyle_2.30.0
#>
#> loaded via a namespace (and not attached):
#> [1] Matrix_1.6-1.1 future.apply_1.11.0 jsonlite_1.8.7
#> [4] compiler_4.3.1 BiocManager_1.30.22 Rcpp_1.0.11
#> [7] MatrixModels_0.5-2 parallel_4.3.1 jquerylib_0.1.4
#> [10] globals_0.16.2 splines_4.3.1 yaml_2.3.7
#> [13] fastmap_1.1.1 lattice_0.22-5 coda_0.19-4
#> [16] R6_2.5.1 MCMCpack_1.6-3 robustbase_0.99-0
#> [19] knitr_1.44 MASS_7.3-60 future_1.33.0
#> [22] bookdown_0.36 bslib_0.5.1 rlang_1.1.1
#> [25] cachem_1.0.8 xfun_0.40 sass_0.4.7
#> [28] aod_1.3.2 cli_3.6.1 progressr_0.14.0
#> [31] mcmc_0.9-7 digest_0.6.33 grid_4.3.1
#> [34] quantreg_5.97 DEoptimR_1.1-3 evaluate_0.22
#> [37] SparseM_1.81 listenv_0.9.0 codetools_0.2-19
#> [40] survival_3.5-7 parallelly_1.36.0 rmarkdown_2.25
#> [43] matrixStats_1.0.0 tools_4.3.1 htmltools_0.5.6.1