Application of global removal of unwanted variation
RUV is a data-driven method that removes systematic noise from gene expression datasets. The particular version of RUV is dependent on the goal of the analysis. We have developed a method, RUVNaiveRidge, for the removal of unwanted variation that focuses on retrieving the true underlying gene-gene correlations, but at the cost of the specification of the absolute values of gene expression.The application of RUVNaiveRidge requires the analyst to make several descisions, which should be informed by the ultimate research goal. Here we will demonstrate some of the principles using a dataset on gene expression in 57 samples from the bladder as described in Dyrskjot et al. The dataset can be found in the Bioconductor package bladderbatch. Note that this dataset is small and co-expression analysis should ideally be performed on studies with at least 100 samples.
Investigating the dataset design and getting data into the correct format
For the application of RUVNaiveRidge it is important to be familar with the experiment design of the dataset. If the accompanying metadata of the samples is available the experiment design can be visualized using the function plotDesign.
library(bladderbatch)
data(bladderdata)
expr.meta <- pData(bladderEset)
plotDesign(expr.meta, c("cancer", "outcome", "batch"),
c("Diagnosis", "Outcome", "Batch"), orderby="batch")
Every line in each of the bars represents a sample, which is colored according to the factor displayed on the left-hand side. The samples in each bar are in the same order
The figure illustrates that batches, diagnosis and eventual outcome were substantially confounded; ie. not all factors could be fully randomized. Thus, it is likely that the data contains some systematic noise.
The gene expression data needs to be a matrix with its columns containing the genes and its rows containing the samples.
## GSM71019.CEL GSM71020.CEL GSM71021.CEL GSM71022.CEL GSM71023.CEL
## 1007_s_at 10.115170 8.628044 8.779235 9.248569 10.256841
## 1053_at 5.345168 5.063598 5.113116 5.179410 5.181383
## 117_at 6.348024 6.663625 6.465892 6.116422 5.980457
## 121_at 8.901739 9.439977 9.540738 9.254368 8.798086
## 1255_g_at 3.967672 4.466027 4.144885 4.189338 4.078509## [1] 22283 57Selecting negative control genes
Ideally, negative control genes should be selected with the help of a priori information. Unfortunately, when the aim is estimating gene coexpression and the factor of interest is unknown, a suitable set of negative control genes is seldomly known. Because of this it is advisable to choose negative control genes empirically. Using the RUVcorr package this can be accomplished using the function empNegativeControls. Note that it is necessary to exclude the genes that pertain to your research question from being selected as negative controls. For demonstration purposes let us assume we are interested in the following 10 random genes:
na_genes <- c("SCN1A", "SCN3A", "SCN4A", "SCN5A", "SCN7A", "SCN8A", "SCN11A",
"SCN1B", "SCN2B", "SCN3B", "SCN4B")Since the genes in the dataset is uing Affymetrix identifiers, we have to find the corresponding Affymetrix probe names for our genes of interest.
na_affy <- names(which(unlist(lapply(xx, function(x) is.element(x, na_genes)[1]))))
na_index <- which(is.element(colnames(expr),na_affy))
nc_index <- empNegativeControls(expr, exclude=na_index, nc=3000)Usefully, the selection can also be visualized:
This figure shows the inter-quantile range vs. mean plot of the expression of all genes. The genes highlighted in red are the empirically chosen negative control genes.
Effective application of RUVNaiveRidge
Besides negative control genes the application of RUVNaiveRidge also requires the input of two user-selected parameters, the ridge parameter \(\nu\) and the dimensionality of \(\hat{W}\), \(\hat{k}\). Since these parameters determine the strength of the cleaning, the user is adviced to carefully assess her choices. It is recommended to run RUVRidgeNaive with several different choices of the parameters and then assess the results. In order to do this efficiently it is advisable to RUVNaiveRidge in parallel. This can be achieved with a package such as snowfall.
library(snowfall)
k <- c(1,2,3,4)
nu <- c(0,500,1000,5000)
k.nu.matrix <- cbind(rep(k, each=4), rep(nu, 4))
k.nu.matrix <- as.list(as.data.frame(t(k.nu.matrix)))
sfInit(parallel=TRUE, cpus=4)## R Version: R version 4.2.1 (2022-06-23)## Library RUVcorr loaded.Plotting options to help make parameter choices
Choosing the parameter values is not always easy and there might be more than one possible choice. It is therefore vital to thoroughly investigate different combinations of parameter choices using genes that are a prior} known to be uncorrelated with each other and a priori known to be correlated, also referred to as positive controls. Here, we will use the sodium channel genes as positive controls, because we expect some of these genes to be correlated with each other.
cor_AllRUV_na <- lapply(expr_AllRUV, function(x) cor(x[,na_index]))
cor_Raw_na <- cor(expr[,na_index])
lapply(1:4, function(i) histogramPlot(cor_AllRUV_na[seq(0,15,4)+i], cor_Raw_na,
title=paste("nu=", nu[i]), legend=c(paste("k=", k), "Raw")))
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## [1] 1.630746 1.565911 1.501075 1.436240 1.371404For the set of uncorrelated genes, the negative control genes cannot be used. This is because negative controls used during RUV will have zero correlation by definition. A good choice for a set of uncorrelated genes is a set of random genes. Picking these can be accomplished using the function background.
bg_index <- background(expr, nBG=100, exclude=na_index, nc_index=nc_index)
cor_AllRUV_bg <- lapply(expr_AllRUV, function(x) cor(x[,bg_index]))
cor_Raw_bg <- cor(expr[,bg_index])
lapply(1:4, function(i) histogramPlot(cor_AllRUV_bg[seq(0,15,4)+i], cor_Raw_bg,
title=paste("nu=", nu[i]), legend=c(paste("k=", k), "Raw")))
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## [1] 1.579056 1.516276 1.453495 1.390715 1.327935The figures show the impact of different parameter choices on the correlations of a set of sodium channel genes and random genes. Correlation densities for different parameter choices. The histogram in the background of each panel shows the denisty of the correlations of the random genes calculated using the raw data.
From the figures it seems a choice of \(\hat{k}=2\) corrects the wide range of the distribution of the correlations between random genes, but leaves some interesting non-zero correlations for the sodium-channel genes. Other plots that are informative for the choise of \(k\) include the eigenvaluePlot. The choice for the correct \(\nu\) however remains difficult because of the little change in the overall results. Further assessments are required.
Besides looking at histogram plots studying relative log expression (RLE) plots is useful. Specifically, parameter choices that overcorrect the data can be spotted. Such parameter choices will have gene expression variances that are too low. The RLE plots offered differ from the originally proposed RLE plot by combining all samples and are suited to large (\(>100\) arrays) gene expression data sets where visualisation of individual arrays becomes impractical. The option displayed here shows the boxplots for the 1st and 3rd quantile of the difference between the gene expression and the study median for all samples.
lapply(1:4, function(i) RLEPlot(expr, expr_AllRUV[[4+i]],
name=c("Raw", "RUV"), title=paste("nu=", nu[i]),
method="IQR.boxplots"))
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A parameter choice of \(\nu=500\) seems to offer the best choice. In order to check whether the selected parameter at least removes all the known sources of variation, there is yet another version of the RLE plot. Here we plot the median and the inter-quantile-range (IQR) of the difference between the gene expression and the study median for all samples. Furthermore, it is useful to color these plots according to a known source of unwanted variation, such as batches.
The fugure shows RLE plots for data cleaned with RUV using \(\nu=500\) for \(\hat{k}=2\). Every sample is represented by the median and inter-quantile-range of the difference between observed gene expressions and study mean. The samples are colored according to their batches.
Principal component plots (PCAPlot) provide a similar way of assessing parameter choices for RUV.
The figure demonstrates that at least most of the systematic noise introduced via the batch effect has been removed. Hence, it is now possible to examine gene-gene correlations, construct gene networks or else using this new dataset.