3.1 Load example data

CellMixS uses the SingleCellExperiment class from the SingleCellExperiment Bioconductor package as the format for input data.

The package contains example data named sim_50, a list of simulated single-cell RNA-seq data with varying batch effect strength and unbalanced batch sizes.

Batch effects were introduced by sampling 0%, 20% or 50% of gene expression values from a distribution with variant mean (e.g. 0% - 50% of genes were affected by a batch effect).

All datasets consist of 3 batches, one with 300 cells and the others with half of its size (so 150 cells). The simulation is modified after (Büttner et al. 2019) and described in sim50.

# load required packages
suppressPackageStartupMessages({
    library(SingleCellExperiment)
    library(cowplot)
    library(limma)
    library(magrittr)
    library(dplyr)
    library(purrr)
})

# load sim_list example data
sim_list <- readRDS(system.file(file.path("extdata", "sim50.rds"), 
                                package = "CellMixS"))
names(sim_list)
#> [1] "batch0"  "batch20" "batch50"

sce50 <- sim_list[["batch50"]]
class(sce50)
#> [1] "SingleCellExperiment"
#> attr(,"package")
#> [1] "SingleCellExperiment"

table(sce50[["batch"]])
#> 
#>   1   2   3 
#> 300 150 150

3.2 Visualize batch effect

Often batch effects can already be detected by visual inspection and simple visualization (e.g. in a normal tSNE or UMAP plot) depending on the strength. CellMixS has different plotting functions to visualize group label and mixing scores aside without the need for using different packages. Results are ggplot objects and can be further customized using ggplot2. Other packages, such as scater, provide similar plotting functions and could be used as well.

#visualize batch distribution in sce50
visGroup(sce50, group = "batch")

#visualize batch distribution in other elements of sim_list 
batch_names <- c("batch0", "batch20")
  
vis_batch <- lapply(batch_names, function(name){
    sce <- sim_list[[name]]
    visGroup(sce, "batch") + ggtitle(paste0("sim_", name))
})

plot_grid(plotlist = vis_batch, ncol = 2)

4.1 Cellspecific Mixing scores

Not all batch effects or group differences are obvious using visualization. Also, in single-cell experiments celltypes and cells can be affected in different ways by experimental conditions causing batch effects (e.g. some cells are more robust to storing conditions than others).

Furthermore the range of methods for data integration and batch effect removal gives rise to the question of which method performs best on which data, and thereby a need to quantify batch effects.

The cellspecific mixing score cms tests for each cell the hypothesis that batch-specific distance distributions towards it’s k-nearest neighbouring (knn) cells are derived from the same unspecified underlying distribution using the Anderson-Darling test (Scholz and Stephens 1987). Results from the cms function are two scores cms and cms_smooth, where the latter is the weighted mean within each cell’s neighbourhood. They can be interpreted as the probability that batches within this cell’s neighbourhood are equally mixed. A high cms score refers to good mixing, while a low score indicates batch-specific bias. The test considers differences in the number of cells from each batch. This facilitates the cms score to differentiate between unbalanced batches (e.g. one celltype being more abundant in a specific batch) and a biased distribution of cells. The cms function takes an SingleCellExperiment object (described in SingleCellExperiment) as input and appends to the colData slot.

5.1 Cms parameter setting

The most important parameter to set to calculate cms is k, the number of knn cells to use in the Anderson-Darling test. The optimal choice depends on the application, as with a small k focus is on local mixing, while with a large k mixing with regard to more global structures is evaluated. If the overall dataset structure is very heterogeneous with large differences in the number of cells per celltypes, it might be useful to adapt the number of knn. This can be done by setting the k_min parameter to the minimum number of knn cells to include. Before performing the hypothesis test, cms will look for local minima in the overall distance distribution of it’s knn cells. Only cells within a distance smaller than the first local minimum are then included, but at least k_min cells. This can e.g. ensure that only cells from the same celltype cluster are included without relying on previous clustering algorithms.

For smoothing either k or if specified k_min cells are included to get a weighted mean of cms-scores. Weights are defined by the reciprocal distance towards the respective cell, with 1 as weight of the respective cell itself.

Another important parameter is the subspace to use to calculate cell distances. This can be set using the dim_red parameter. By default PCA subspace will be used and calculated if not present. Some data integration methods provide embeddings of a common subspace instead of “corrected counts”. cms scores can be calculated within these by defining them in dim_red (see 6.1). In general all reduced dimensional representations can be specified, but only PCA will be computed automatically, while other methods need to be precomputed.

5.2 Visualize the cell mixing score

An overall summary of cms can be visualized as histogram. As cms score are p.values from hypothesis testing, without any batch effect the p.value histogram should be flat. An increased number of very small p-values indicates the presence of a batch-specific bias within data.

#pval hist of cms50
visHist(sce50)

#pval hist sim30
#combine cms results in one matrix
batch_names <- names(sim_list)
cms_mat <- batch_names %>% 
  map(function(name) sim_list[[name]]$cms.unaligned) %>% 
  bind_cols() %>% set_colnames(batch_names)


visHist(cms_mat, n_col = 3)

Results of cms can be visualized in a cell-specific way and alongside any metadata.

#cms only cms10
sce20 <- sim_list[["batch20"]]
metric_plot <- visMetric(sce20, metric_var = "cms_smooth.unaligned")

#group only cms10
group_plot <- visGroup(sce20, group = "batch")

plot_grid(metric_plot, group_plot, ncol = 2)

#add random celltype assignments as new metadata
sce20[["celltype"]] <- rep(c("CD4+", "CD8+", "CD3"), ncol(sce20)/3) %>% 
    as.factor 

visOverview(sce20, "batch", other_var = "celltype")

Systematic differences (e.g. celltype differences) can be further explored using visCluster. Here we do not expect any systematic difference as celltypes were randomly assigned.

visCluster(sce20, metric_var = "cms.unaligned", 
           cluster_var = "celltype")
#> Picking joint bandwidth of 0.103

6.1 Mixing after data integration

To remove batch effects when integrating different single-cell RNAseq datasets, a range of methods can be used. The cms function can be used to evaluate the effect of these methods, using a cell-specific mixing score. Some of them (e.g. fastMNN from the scran package) provide a “common subspace” with integrated embeddings. Other methods like limma give “batch-corrected data” as results. Both work as input for cms.

#MNN - embeddings are stored in the reducedDims slot of sce
reducedDimNames(sce20)
#> [1] "TSNE" "PCA"  "MNN"
sce20 <- cms(sce20, k = 30, group = "batch", 
             dim_red = "MNN", res_name = "MNN", n_dim = 3, cell_min = 4)

# run limma
limma_corrected <- removeBatchEffect(counts(sce20), batch = sce20$batch)
#add corrected counts to sce
assay(sce20, "lim_corrected") <- limma_corrected 

#run cms
sce20 <- cms(sce20, k = 30, group = "batch", 
             assay_name = "lim_corrected", res_name = "limma", n_dim = 3, 
             cell_min = 4)

names(colData(sce20))
#> [1] "batch"                "cms_smooth.unaligned" "cms.unaligned"       
#> [4] "celltype"             "cms_smooth.MNN"       "cms.MNN"             
#> [7] "cms_smooth.limma"     "cms.limma"

6.2 Compare data integration methods

To compare different methods summary plots from visIntegration (see 6.4) and p-value histograms from visHist can be used. Local patterns within single methods can be explored as described above.

# As pvalue histograms
visHist(sce20, metric_prefix = "cms.",  n_col = 3)

Here both methods limma and fastMNN from the scran package flattened the p.value distribution. So cells are better mixed after batch effect removal.

6.3 Remaining batch-specific structure - ldfDiff

Besides successful batch “mixing” data integration should also preserve the data’s internal structure and variability without adding new sources of variability or removing underlying structures. Especially for methods that result in “corrected counts” it is important to understand how much of the dataset internal structures are preserved.

ldfDiff calculates the differences between each cell’s local density factor before and after data integration (Latecki, Lazarevic, and Pokrajac 2007). The local density factor is a relative measure of the cell density around a cell compared to the densities within it’s neighbourhood. Local density factors are calculated on the same set of k cells from the cell’s kNN before integration. In an optimal case relative densities (according to the same set of cells) should not change by integration and the ldfDiff score should be close to 0. In general the overall distribution of ldfDiff should be centered around 0 without long tails.

#Prepare input 
# list with single SingleCellExperiment objects 
#(Important: List names need to correspond to batch levels! See ?ldfDiff)
sce_pre_list <- list("1" = sce20[,sce20$batch == "1"], 
                     "2" = sce20[,sce20$batch == "2"], 
                     "3" = sce20[,sce20$batch == "3"])

sce20 <- ldfDiff(sce_pre_list, sce_combined = sce20, 
                 group = "batch", k = 70, dim_red = "PCA", 
                 dim_combined = "MNN", assay_pre = "counts", 
                 n_dim = 3, res_name = "MNN")

sce20 <- ldfDiff(sce_pre_list, sce_combined = sce20, 
                 group = "batch", k = 70, dim_red = "PCA", 
                 dim_combined = "PCA", assay_pre = "counts", 
                 assay_combined = "lim_corrected",  
                 n_dim = 3, res_name = "limma")

names(colData(sce20))
#>  [1] "batch"                "cms_smooth.unaligned" "cms.unaligned"       
#>  [4] "celltype"             "cms_smooth.MNN"       "cms.MNN"             
#>  [7] "cms_smooth.limma"     "cms.limma"            "diff_ldf.MNN"        
#> [10] "diff_ldf.limma"

6.4 Visualize ldfDiff

Results from ldfDiff can be visualized in a similar way as results from cms.

#ldfDiff score summarized
visIntegration(sce20, metric_prefix = "diff_ldf") 
#> Picking joint bandwidth of 0.0768

ldfDiff shows a clear difference between both methods. While limma is able to preserve the batch internal structure within batches, fastMNN clearly changes it. Even if batches are well mixed (see 6.2), fastMNNdoes not work for batch effect removal on these simulated data. Again this is in line with expectations as due to the small number of genes in the example data. One of MNN’s assumptions is that batch effects should be much smaller than biological variation, which does not hold true in this small example dataset.