In Oshlack/speckle: Statistical methods for analysing single cell RNA-seq data

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Introduction

The r BiocStyle::Biocpkg("speckle") package contains functions to analyse differences in cell type proportions in single cell RNA-seq data. As our research into specialised analyses of single cell data continues we anticipate that the package will be updated with new functions.

The analysis of single cell RNA-seq data consists of a large number of steps, which can be iterative and also depend on the research question. There are many R packages that can do some or most of these steps. The analysis steps are described here briefly.

Once the sequencing data has been summarised into counts over genes, quality control is performed to remove poor quality cells. Poor quality cells are often characterised as having very low total counts (library size) and very few genes detected. Lowly expressed and uninformative genes are filtered out, followed by appropriate normalisation. Dimensionality reduction and clustering of the cells is then performed. Cells that have similar transcriptional profiles cluster together, and these clusters (hopefully) correspond to something biologically relevant, such as different cell types. Differential expression between each cluster compared to all other clusters can highlight genes that are more highly expressed in each cluster. These marker genes help to determine the cell type each cluster corresponds to. Cell type identification is a process that often uses marker genes as well as a list of curated genes that are known to be expressed in each cell type. It is always helpful to visualise the data in a lot of different ways to aid in interpretation of the clusters using tSNE/UMAP plots, clustering trees and heatmaps of known marker genes.

Installation

library(devtools)
install_github("/Oshlack/speckle")

Finding significant differences in cell type proportions using propeller

In order to determine whether there are statistically significant compositional differences between groups, there must be some form of biological replication in the experiment. This is so that we can estimate the variability of the cell type proportion estimates for each group. A classical statistical test for differences between two proportions is typically very sensitive to small changes and will almost always yield a significant p-value. Hence propeller is only suitable to use in single cell experiments where there are multiple groups and multiple biological replicates in at least one of the groups. The absolute minimum sample size is 2 in one group and 1 in the other group/s. Variance estimates are obtained from the group with more than 1 biological replicate which assumes that the cell type proportion variances estimates are similar between experimental conditions.

The propeller test is performed after initial analysis of the single cell data has been done, i.e. after clustering and cell type assignment. The propeller function can take a SingleCellExperiment or Seurat object and extract the necessary information from the metadata. The basic model for propeller is that the cell type proportions for each sample are estimated based on the clustering information provided by the user or extracted from the relevant slots in the data objects. The proportions are then transformed using either an arcsin square root transformation, or logit transformation. For each cell type $i$, we fit a linear model with group as the explanatory variable using functions from the R Bioconductor package r BiocStyle::Biocpkg("limma"). Using r BiocStyle::Biocpkg("limma") to obtain p-values has the added benefit of performing empirical Bayes shrinkage of the variances. For every cell type we obtain a p-value that indicates whether that cell type proportion is statistically significantly different between two (or more) groups.

Load the libraries

library(speckle)
library(SingleCellExperiment)
library(CellBench)
library(limma)
library(ggplot2)
library(scater)
library(patchwork)
library(edgeR)
library(AnnotationDbi)
library(org.Hs.eg.db)

Loading data into R

We are using single cell data from the r BiocStyle::Biocpkg("CellBench") package to illustrate how propeller works. This is an artificial dataset that is made up of an equal mixture of 3 different cell lines. There are three datasets corresponding to three different technologies: 10x genomics, CelSeq and DropSeq.

sc_data <- load_sc_data()

The way that propeller is designed to be used is in the context of a designed experiment where there are multiple biological replicates and multiple groups. Comparing cell type proportions without biological replication should be done with caution as there will be a large degree of variability in the cell type proportions between samples due to technical factors (cell capture bias, sampling, clustering errors), as well as biological variability. The r BiocStyle::Biocpkg("CellBench") dataset does not have biological replication, so we will create several artificial biological replicates by bootstrapping the data. Bootstrapping has the advantage that it induces variability between bootstrap samples by sampling with replacement. Here we will treat the three technologies as the groups, and create artifical biological replicates within each group. Note that bootstrapping only induces sampling variability between our biological replicates, which will almost certainly be much smaller than biological variability we would expect to see in a real dataset.

The three single cell experiment objects in sc_data all have differing numbers of genes. The first step is to find all the common genes between all three experiments in order to create one large dataset.

commongenes1 <- rownames(sc_data$sc_dropseq)[rownames(sc_data$sc_dropseq) %in% 
                                               rownames(sc_data$sc_celseq)]
commongenes2 <-  commongenes1[commongenes1 %in% rownames(sc_data$sc_10x)]

sce_10x <- sc_data$sc_10x[commongenes2,]
sce_celseq <- sc_data$sc_celseq[commongenes2,] 
sce_dropseq <- sc_data$sc_dropseq[commongenes2,] 

dim(sce_10x)
dim(sce_celseq)
dim(sce_dropseq)

table(rownames(sce_10x) == rownames(sce_celseq))
table(rownames(sce_10x) == rownames(sce_dropseq))

Bootstrap additional samples

This dataset does not have any biological replicates, so we will bootstrap additional samples and pretend that they are biological replicates. Bootstrapping won't replicate true biological variation between samples, but we will ignore that for the purpose of demonstrating how propeller works. Note that we don't need to simulate gene expression measurements; propeller only uses cluster information, hence we simply bootstrap the column indices of the single cell count matrices.

i.10x <- seq_len(ncol(sce_10x))
i.celseq <- seq_len(ncol(sce_celseq))
i.dropseq <- seq_len(ncol(sce_dropseq))

set.seed(10)
boot.10x <- sample(i.10x, replace=TRUE)
boot.celseq <- sample(i.celseq, replace=TRUE)
boot.dropseq <- sample(i.dropseq, replace=TRUE)

sce_10x_rep2 <- sce_10x[,boot.10x]
sce_celseq_rep2 <- sce_celseq[,boot.celseq]
sce_dropseq_rep2 <- sce_dropseq[,boot.dropseq]

Combine all SingleCellExperiment objects

The SingleCellExperiment objects don't combine very easily, so I will create a new object manually, and retain only the information needed to run propeller.

sample <- rep(c("S1","S2","S3","S4","S5","S6"), 
              c(ncol(sce_10x),ncol(sce_10x_rep2),ncol(sce_celseq),
                ncol(sce_celseq_rep2), 
                ncol(sce_dropseq),ncol(sce_dropseq_rep2)))
cluster <- c(sce_10x$cell_line,sce_10x_rep2$cell_line,sce_celseq$cell_line,
             sce_celseq_rep2$cell_line,sce_dropseq$cell_line,
             sce_dropseq_rep2$cell_line)
group <- rep(c("10x","celseq","dropseq"),
             c(2*ncol(sce_10x),2*ncol(sce_celseq),2*ncol(sce_dropseq)))

allcounts <- cbind(counts(sce_10x),counts(sce_10x_rep2), 
                   counts(sce_celseq), counts(sce_celseq_rep2),
                   counts(sce_dropseq), counts(sce_dropseq_rep2))

sce_all <- SingleCellExperiment(assays = list(counts = allcounts))
sce_all$sample <- sample
sce_all$group <- group
sce_all$cluster <- cluster

Visualise the data

Here I am going to use the Bioconductor package r BiocStyle::Biocpkg("scater") to visualise the data. The r BiocStyle::Biocpkg("scater") vignette goes quite deeply into quality control of the cells and the kinds of QC plots we like to look at. Here we will simply log-normalise the gene expression counts, perform dimensionality reduction (PCA) and generate PCA/TSNE/UMAP plots to visualise the relationships between the cells.

sce_all <- scater::logNormCounts(sce_all)
sce_all <- scater::runPCA(sce_all)
sce_all <- scater::runUMAP(sce_all)

Plot PC1 vs PC2 colouring by cell line and technology:

pca1 <- scater::plotReducedDim(sce_all, dimred = "PCA", colour_by = "cluster") +
  ggtitle("Cell line")
pca2 <- scater::plotReducedDim(sce_all, dimred = "PCA", colour_by = "group") +
  ggtitle("Technology")
pca1 + pca2

Plot UMAP highlighting cell line and technology:

umap1 <- scater::plotReducedDim(sce_all, dimred = "UMAP", 
                                colour_by = "cluster") + 
  ggtitle("Cell line")
umap2 <- scater::plotReducedDim(sce_all, dimred = "UMAP", colour_by = "group") +
  ggtitle("Technology")
umap1 + umap2

For this dataset UMAP is a little bit of an overkill, the PCA plots show the relationships between the cells quite well. PC1 separates cells based on technology, and PC2 separates cells based on the cell line (clusters). From the PCA plots we can see that 10x is quite different to CelSeq and DropSeq, and the H2228 cell line is quite different to the remaining 2 cell lines.

Test for differences in cell line proportions in the three technologies

In order to demonstrate propeller I will assume that the cell line information corresponds to clusters and all the analysis steps have beeen performed. Here we are interested in testing whether there are compositional differences between the three technologies: 10x, CelSeq and DropSeq. Since there are more than 2 groups, propeller will perform an ANOVA to determine whether there is a significant shift in the cell type proportions between these three groups.

The propeller function can take a SingleCellExperiment object or Seurat object as input and extract the three necessary pieces of information from the cell information stored in colData. The three essential pieces of information are

• cluster
• sample
• group

If these arguments are not explicitly passed to the propeller function, then these are extracted from the SingleCellExperiment or Seurat object. Upper or lower case is acceptable, but the variables need to be named exactly as stated in the list above. For a Seurat object, the cluster information is extracted from Idents(x).

The default of propeller is to perform the logit transformation:

# Perform logit transformation
propeller(sce_all)

An alternative variance stabilising transformation is the arcsin square root transformation.

# Perform arcsin square root transformation
propeller(sce_all, transform="asin")

The results from using the two different transforms are a little bit different, with the H1975 cell line being statistically significant using the arc sin square root transform, and not significant after using the logit transform.

Another option for running propeller is for the user to supply the cluster, sample and group information explicitly to the propeller function.

propeller(clusters=sce_all$cluster, sample=sce_all$sample, group=sce_all$group)

The cell lines were mixed together in roughly equal proportions (~0.33) and hence we don't expect to see significant differences between the three clusters. However, because bootstrapping the samples doesn't incorporate enough variability between the samples to mimic true biological variability, we can see that the H1975 cluster looks significantly different between the three technologies. The proportion of this cell line is closer to 0.4 for CelSeq and DropSeq, and 0.34 for the 10x data.

Visualise the results

In the r BiocStyle::Biocpkg("speckle") package there is a plotting function plotCellTypeProps that takes a Seurat or SingleCellExperiment object, extracts sample and cluster information and outputs a barplot of cell type proportions between the samples. The user also has the option of supplying the cluster and sample cell information instead of an R object. The output is a ggplot2 object that the user can then manipulate however they please.

plotCellTypeProps(sce_all)

Alternatively, we can obtain the cell type proportions and transformed proportions directly by running the getTransformedProps function which takes the cluster and sample information as input. The output from getTransformedProps is a list with the cell type counts, transformed proportions and proportions as elements.

props <- getTransformedProps(sce_all$cluster, sce_all$sample, transform="logit")
barplot(props$Proportions, col = c("orange","purple","dark green"),legend=TRUE, 
        ylab="Proportions")

Call me old-school, but I still like looking at stripcharts to visualise results and see whether the significant p-values make sense.

par(mfrow=c(1,3))
for(i in 1:3){
stripchart(props$Proportions[i,]~rep(c("10x","celseq","dropseq"),each=2),
           vertical=TRUE, pch=16, method="jitter",
           col = c("orange","purple","dark green"),cex=2, ylab="Proportions")
title(rownames(props$Proportions)[i])
}

If you are interested in seeing which models best fit the data in terms of the cell type variances, there are two plotting functions that can do this: plotCellTypeMeanVar and plotCellTypePropsMeanVar. For this particular dataset it isn't very informative because there are only three cell "types" and no biogical variability.

par(mfrow=c(1,1))
plotCellTypeMeanVar(props$Counts)
plotCellTypePropsMeanVar(props$Counts)

Fitting linear models using the transformed proportions directly

If you are like me, you won't feel very comfortable with a black-box approach where one function simply spits out a table of results. If you would like to have more control over your linear model and include extra covariates then you can fit a linear model in a more direct way using the transformed proportions that can be obtained by running the getTransformedProps function.

We have already obtained the proportions and transformed proportions when we ran the getTransformedProps function above. This function outputs a list object with three elements: Counts, TransformedProps and Proportions. These are all matrices with clusters/cell types in the rows and samples in the columns.

names(props)

props$TransformedProps

First we need to set up our sample information in much the same way we would if we were analysing bulk RNA-seq data. We can pretend that we have pairing information which corresponds to our original vs bootstrapped samples to make our model a little more complicated for demonstration purposes.

group <- rep(c("10x","celseq","dropseq"),each=2)
pair <- rep(c(1,2),3)
data.frame(group,pair)

We can set up a design matrix taking into account group and pairing information. Please note that the way that propeller has been designed is such that the group information is always first in the design matrix specification, and there is NO intercept. If you are new to design matrices and linear modelling, I would highly recommend reading the r BiocStyle::Biocpkg("limma") manual, which is incredibly extensive and covers a variety of different experimental set ups.

design <- model.matrix(~ 0 + group + pair)
design

In our example, we have three groups, 10x, CelSeq and DropSeq. In order to perform an ANOVA to test for cell type composition differences between these 3 technologies, we can use the propeller.anova function. The coef argument tells the function which columns of the design matrix correspond to the groups we are interested in testing. Here we are interested in the first three columns.

propeller.anova(prop.list=props, design=design, coef = c(1,2,3), 
                robust=TRUE, trend=FALSE, sort=TRUE)

Note that the p-values are smaller here than before because we have specified a pairing vector that states which samples were bootstrapped and which are the original samples.

If we were interested in testing only 10x versus DropSeq we could alternatively use the propeller.ttest function and specify a contrast that tests for this comparison with our design matrix.

design
mycontr <- makeContrasts(group10x-groupdropseq, levels=design)
propeller.ttest(props, design, contrasts = mycontr, robust=TRUE, trend=FALSE, 
                sort=TRUE)

Finally note that the robust and trend parameters are parameters for the eBayes function in r BiocStyle::Biocpkg("limma"). When robust = TRUE, robust empirical Bayes shrinkage of the variances is performed which mitigates the effects of outlying observations. We set trend = FALSE as we don't expect a mean-variance trend after performing our variance stabilising transformation. There may also be an error when trend is set to TRUE because there are often not enough data points to estimate the trend.

More complex (or just different) experimental designs

Fitting a continuous variable rather than groups

Let us assume that we expect that the different technologies have a meaningful ordering to them, and we would like to find the cell types that are increasing or decreasing along this trend. In more complex scenarios beyond group comparisons I would recommend taking the transformed proportions from the getTransformedProps function and using the linear model fitting functions from the r BiocStyle::Biocpkg("limma") package directly.

Let us assume that the ordering of the technologies is 10x -> celseq -> dropseq. Then we can recode them 1, 2, 3 and treat the technologies as a continuous variable. Obviously this scenario doesn't make much sense biologically, but we will continue for demonstration purposes.

group
dose <- rep(c(1,2,3), each=2) 

des.dose <- model.matrix(~dose)
des.dose

fit <- lmFit(props$TransformedProps,des.dose)
fit <- eBayes(fit, robust=TRUE)
topTable(fit)

Here the log fold changes are reported on the transformed data, so they are not as easy to interpret directly. The positive logFC indicates that the cell type proportions are increasing (for example for H1975), and a negative logFC indicates that the proportions are decreasing across the ordered technologies 10x -> celseq -> dropseq.

You can get the estimates from the model on the proportions directly by fitting the same model to the proportions. Here the logFC is the slope of the trend line on the proportions, and the AveExpr is the average of the proportions across all technologies.

fit.prop <- lmFit(props$Proportions,des.dose)
fit.prop <- eBayes(fit.prop, robust=TRUE)
topTable(fit.prop)

You could plot the continuous variable dose against the proportions and add trend lines, for example.

fit.prop$coefficients

par(mfrow=c(1,3))
for(i in 1:3){
  plot(dose, props$Proportions[i,], main = rownames(props$Proportions)[i], 
       pch=16, cex=2, ylab="Proportions", cex.lab=1.5, cex.axis=1.5,
       cex.main=2)
  abline(a=fit.prop$coefficients[i,1], b=fit.prop$coefficients[i,2], col=4, 
         lwd=2)
}

What I recommend in this instance is using the p-values from the analysis on the transformed data, and the reported statistics (i.e. the coefficients from the model) obtained from the analysis on the proportions for visualisation purposes.

Including random effects

If you have a random effect that you would like to account for in your analysis, for example repeated measures on the same individual, then you can use the duplicateCorrelation function from the r BiocStyle::Biocpkg("limma").

For illustration purposes, let us assume that pair indicates samples taken from the same individual (or they could represent technical replicates), and we would like to account for this in our analysis using a random effect. Again, we fit our models on the transformed proportions in order to obtain the p-values.

We will formulate the design matrix with an intercept for this example, and test the differences in technologies relative to 10x. The block parameter will be the pair variable. Note that the design matrix now does not include pair as a fixed effect.

des.tech <- model.matrix(~group)

dupcor <- duplicateCorrelation(props$TransformedProps, design=des.tech,
                               block=pair)
dupcor

The consensus correlation is quite high (r dupcor$consensus.correlation), which we expect because we bootstrapped these additional samples.

# Fitting the linear model accounting for pair as a random effect
fit1 <- lmFit(props$TransformedProps, design=des.tech, block=pair, 
              correlation=dupcor$consensus)
fit1 <- eBayes(fit1)
summary(decideTests(fit1))

# Differences between celseq vs 10x
topTable(fit1,coef=2)

# Differences between dropseq vs 10x
topTable(fit1, coef=3)

For celseq vs 10x, H1975 and H2228 are significantly different, with a greater proportion of H1975 cells detected in celseq, and fewer H2228 cells. For dropseq vs 10x, there is a higher proportion of H1975 cells.

If you want to do an ANOVA between the three groups:

topTable(fit1, coef=2:3)

Generally, you can perform any analysis on the transformed proportions that you would normally do when using limma (i.e. on roughly normally distributed data). For more complex random effects models with 2 or more random effects, you can use the `r BiocStyle::Biocpkg("lme4") package.

Tips for clustering

The experimental groups are likely to contribute large sources of variation in the data. In the r BiocStyle::Biocpkg("CellBench") data the technology effect is larger than the cell line effect. In order to cluster the data to produce meaningful cell types that will then feed into meaningful tests for proportions, the cell types should be represented in as many samples as possible. Users should consider using integration techniques on their single cell data prior to clustering, integrating on biological sample or perhaps experimental group. See methods such as Harmony, Liger and Seurat's integration technique for more information.

Cell type label assignment should not be too refined such that every sample has many unique cell types. The propeller function can handle proportions of 0 and 1 without breaking, but it is not very meaningful if every cell type difference is statistically significant. Consider testing cell type categories that are broader for more meaningful results, perhaps by combining clusters that are highly similar. The refined clusters can always be explored in terms of gene expression differences later on.

It may be appropriate to perform cell type assignment using classification methods rather than clustering. This allows the user to classify cells into known cell types, but you may run the risk of missing novel cell types. A combination of approaches may be necessary depending on the dataset. Good luck. The more heterogenous the dataset, the more tricky this becomes.

See also

Another approach is to model the counts directly using statistical models that can take into account biological variability, such as negative binomial. You can read the OSCA bookchapter on how to use the r BiocStyle::Biocpkg("edgeR") package to do this.

Classifying male and female cells from scRNA-seq data

A common quality control check in bulk RNA-seq is to check the sex of the samples. The simplest method to do this is to check expression of XIST, which is the gene responsible for X-inactivation. It is highly expressed in females, and not expressed in males. In experiments where the sex of the samples has not been recorded, the variation due to sex can often be captured by the top principal component in an MDS or PCA plot. It is important to know if the samples are a mix of males and females and to take this information into account in downstream analysis.

It turns out that for single cell data, it is not a simple matter to classify cells as male or female. The main reason for this is that the cells are much more lowly sequenced compared to bulk RNA-seq samples resulting in low or zero counts for many genes, including XIST and other X- and Y-chromosome genes. Thus simply trying to classify cells as male or female based on observed counts for XIST leave many cells unable to be classified.

There are a few reasons for wanting to classify male and female cells. First, it could form part of the analysis assessing quality of the cells, and if sex is not information that is easily available, it is an additional variable we can predict from the gene expression. This may then inform further analysis of the data, by allowing us to take sex into account in the analysis.

We have built a classifier to predict the sex of each cell based on logistic regression for human and mouse cells. The input is the matrix of counts where the genes are the rows and the cells are the columns. The rownames of the counts matrix needs to be gene symbol. The allcounts data object contains the counts for all the cells used in the propeller function, but the rownames are ENSEMBL IDs. The first step is thus converting the ENSEMBL IDs to gene symbol.

allcounts[1:5,1:5]
nc <- normCounts(allcounts, log=TRUE)
avgexp <- rowMeans(nc)
o <- order(avgexp, decreasing = TRUE)
allcounts2 <- allcounts[o,]
allcounts2[1:5,1:5]
ann <- AnnotationDbi::select(org.Hs.eg.db, keys=rownames(allcounts2),
              columns=c("ENSEMBL","SYMBOL"), keytype="ENSEMBL")
m <- match(rownames(allcounts2), ann$ENSEMBL)
symbol <- ann$SYMBOL[m]
table(duplicated(symbol))
allcounts2 <- allcounts2[!duplicated(symbol) & !is.na(symbol),]

rownames(allcounts2) <- symbol[!duplicated(symbol) & !is.na(symbol)]

table(duplicated(colnames(allcounts2)))
colnames(allcounts2) <- paste(colnames(allcounts2),1:ncol(allcounts2), sep=".")
table(duplicated(rownames(allcounts2)))

Now that the counts matrix is in the correct format we can call the classifySex function.

sex <- classifySex(allcounts2, genome="Hs", qc=FALSE)
table(sex$prediction)

The cell lines were all derived from females, so the sex of the cells is correctly classified as female.

Session Info

sessionInfo()

Oshlack/speckle documentation built on Oct. 16, 2022, 9:39 a.m.