Differential Correlation across Ranked Samples
DCARS is a flexible statistical approach which uses local weighted correlations to build a powerful and robust statistical test to identify significant variation in levels of concordance across a ranking of samples. This has the potential to discover biologically informative relationships between genes across a variable of interest, such as survival outcome. Read more about DCARS in Bioinformatics.
# Install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("shazanfar/DCARS")
library(DCARS)The following example calculates the DCARS test statistic using the skin cutaneous melanoma (SKCM) TCGA dataset, along survival ranking. First it does so for a single gene pair, SKP1 and SKP2, and then EIF3C and EIF5B. Then DCARS selects the top 10 gene pairs after calculating statistics across the STRING network.
data(STRING)
data(SKCM)
SKCM_rank = t(apply(SKCM,1,rank))
# highly significantly DCARS gene pair: SKP1 and SKP2
# calculates p-value based on permutation
DCARS(SKCM_rank,"SKP1","SKP2",plot=TRUE)
# extract only the test statistic
DCARS(SKCM_rank,"SKP1","SKP2", extractTestStatisticOnly = TRUE)
# examine the weighted correlation vector
wcor = DCARS(SKCM_rank,"SKP1","SKP2", extractWcorSequenceOnly = TRUE)
plot(wcor, type = "l", ylim = c(-1,1)); abline(h = 0, lty = 2)
# plot scatterplot split into five groups by survival ranking
plotColouredExpression(SKCM, genepair = c("SKP1","SKP2"), n = 5)
# plot ribbon plot of genes along sample ranking
plotOrderedExpression(SKCM, gene = c("SKP1", "SKP2"), facet = FALSE)
# not significantly DCARS gene pair: EIF3C and EIF5B
# calculates p-value based on permutation
DCARS(SKCM_rank,"EIF3C","EIF5B",plot=TRUE)
# extract only the test statistic
DCARS(SKCM_rank,"EIF3C","EIF5B", extractTestStatisticOnly = TRUE)
# examine the weighted correlation vector
wcor = DCARS(SKCM_rank,"EIF3C", "EIF5B",extractWcorSequenceOnly = TRUE)
plot(wcor, type = "l", ylim = c(-1,1)); abline(h = 0, lty = 2)
# build weight matrix
W = weightMatrix(ncol(SKCM_rank), type = "triangular", span = 0.5, plot = TRUE)
# extract DCARS test statistics
# should take about 30 seconds
SKCM_stats = DCARSacrossNetwork(SKCM_rank,edgelist = STRING,
W = W, extractTestStatisticOnly = TRUE,
verbose = FALSE)
sort(SKCM_stats,decreasing=TRUE)[1:10]To calculate p-values associated with these tests quickly, we use permutation tests over a stratified sample of gene pairs
globalCors = apply(STRING, 1, function(x) cor(SKCM_rank[x[1],], SKCM_rank[x[2],]))
# first take a stratified sample of gene pairs
sampleindices = stratifiedSample(abs(globalCors), length = 50)
# set number of permutations, roughly 1000 or so
niter = 1000
# calculate a large number of permutation statistics from these stratified sample pairs
# this should take about 3-4 minutes
permstats = DCARSacrossNetwork(SKCM_rank,
edgelist = STRING[sampleindices,],
W = W,
niter = niter,
weightedConcordanceFunction = weightedPearson_matrix,
weightedConcordanceFunctionW = "matrix",
verbose = TRUE,
extractPermutationTestStatistics = TRUE)
res = estimatePvaluesSpearman(stats = SKCM_stats,
globalCors = globalCors, permstats = permstats,
usenperm = TRUE, nperm = 5000, plot = TRUE, verbose = FALSE)
# plot DCARS statistic against estimated (unadjusted) p-value
# note if there are not enough iterations then the top-most may flatten out
plot(SKCM_stats, -log10(res$pval), col = "red", pch = 16)
# highlight FDR adjusted points
pval_FDR = p.adjust(res$pval, method = "BH")
FDR_sig = pval_FDR < 0.3
sum(pval_FDR < 0.3)
points(SKCM_stats[FDR_sig], -log10(res$pval)[FDR_sig], col = "blue", pch = 16, cex = 1.2)
# What are the most significant (FDR < 0.3) edges?
SKCM_signif_edges_FDR = STRING[FDR_sig,]
SKCM_signif_edges_FDRThresholding on unadjusted DCARS p-values (P-value < 0.05) to explore an unweighted network
# extract these significant edges
SKCM_signif_edges = STRING[res$pval < 0.05,]
# and graph them as a network
library(igraph)
SKCM_signif_graph = graph.edgelist(SKCM_signif_edges, directed = FALSE)
V(SKCM_signif_graph)$size = 0.01
V(SKCM_signif_graph)$label.cex = 0.6
plot(SKCM_signif_graph)
# plot network with pathway information overlaid
# pathway information downloaded from MSigDB REACTOME pathways
plotNetworkPathway(SKCM_signif_graph)
# extract network communities and plot
cm = walktrap.community(SKCM_signif_graph)
plot(cm, SKCM_signif_graph)
plot(induced_subgraph(SKCM_signif_graph, V(SKCM_signif_graph)[cm$membership==1]))
plot(induced_subgraph(SKCM_signif_graph, V(SKCM_signif_graph)[cm$membership==2]))
plot(induced_subgraph(SKCM_signif_graph, V(SKCM_signif_graph)[cm$membership==3]))
plot(induced_subgraph(SKCM_signif_graph, V(SKCM_signif_graph)[cm$membership==4]))Treating DCARS statistics as a network edge weight
library(igraph)
SKCM_graph = graph.edgelist(STRING, directed = FALSE)
E(SKCM_graph)$weight = SKCM_stats
E(SKCM_graph)$pvalweight = -log10(permpvals)
# Graph the Ego network associated with SKP1 with
plotEgoNetwork(hubnode = c("SKP1"), network = SKCM_graph, weight = "weight")
# only display unadjusted P < 0.05 significant pairs
plotEgoNetwork(hubnode = c("SKP1"), network = SKCM_graph, weight = "pvalweight", subset = TRUE, thresh = -log10(0.05))
SKCM_meanStrength = strength(SKCM_graph, weights = E(SKCM_graph)$weight)/degree(SKCM_graph)
topNodes = names(degree(SKCM_graph))[order(SKCM_meanStrength, decreasing = TRUE)[1:20]]
plot(degree(SKCM_graph), SKCM_meanStrength)
text(degree(SKCM_graph)[topNodes], SKCM_meanStrength[topNodes],
names(degree(SKCM_graph)[topNodes]))
library(ggplot2)
library(ggrepel)
df = data.frame(node = names(degree(SKCM_graph)),
degree = degree(SKCM_graph),
meanStrength = SKCM_meanStrength,
topNodes = (names(degree(SKCM_graph)) %in% topNodes))
g = ggplot(df, aes(x = degree, y = meanStrength)) +
geom_point() +
geom_text_repel(data = subset(df,topNodes==TRUE), aes(label = node)) +
theme_minimal() +
NULL
g
# this shows that the strongest genes are IMPDH1 and SKP2, these genes have the highest mean edge weightsFurther interrogation
Examine the weighted correlation vector for given genepairs. e.g. we observe a positive association between SKP1 and SKP2, which deteriorates along the sample rankings.
# calculate the weighted correlation vectors across the network
SKCM_wcor = t(DCARSacrossNetwork(SKCM_rank,
edgelist = STRING,
W = W,
verbose = FALSE,
extractWcorSequenceOnly = TRUE))
plotWCorLine(SKCM_wcor, gene = "SKP1")Examine the significant weighted correlations in terms of clustered pathways
SKCM_signif_wcor = t(DCARSacrossNetwork(SKCM_rank,
edgelist = SKCM_signif_edges,
W = W,
verbose = FALSE,
extractWcorSequenceOnly = TRUE))
plotWcorsClusterPathway(SKCM_signif_wcor,cluster = TRUE, cutk = 6)- Shila Ghazanfar - @shazanfar