Quality control of the new proteomic data from timsTOF machine

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Last updated: 2020-08-06

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Knit directory: Proteomics/analysis/

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Test association with RNA expression

Dimension of the inputed data

dim(protCLL)

[1] 4977   50

Process both datasets

colnames(dds) <- dds$PatID
dds <- estimateSizeFactors(dds)
sampleOverlap <- intersect(colnames(protCLL), colnames(dds))
geneOverlap <- intersect(rowData(protCLL)$ensembl_gene_id, rownames(dds))
ddsSub <- dds[geneOverlap, sampleOverlap]
protSub <- protCLL[match(geneOverlap, rowData(protCLL)$ensembl_gene_id), sampleOverlap]

#how many gene don't have RNA expression at all?
noExp <- rowSums(counts(ddsSub)) == 0
sum(noExp)

[1] 9

#remove those genes in both datasets
ddsSub <- ddsSub[!noExp,]
protSub <- protSub[!noExp,]

#remove proteins with duplicated identifiers
protSub <- protSub[!duplicated(rowData(protSub)$name)]

geneOverlap <- intersect(rowData(protSub)$ensembl_gene_id, rownames(ddsSub))

ddsSub.vst <- varianceStabilizingTransformation(ddsSub)

Calculate correlations between protein abundance and RNA expression

rnaMat <- assay(ddsSub.vst)
proMat.raw <- assays(protSub)[["count"]]
proMat.qrilc <- assays(protSub)[["QRILC"]]
rownames(proMat.qrilc) <- rowData(protSub)$ensembl_gene_id
rownames(proMat.raw) <- rowData(protSub)$ensembl_gene_id

corTab <- lapply(geneOverlap, function(n) {
  rna <- rnaMat[n,]
  pro.q <- proMat.qrilc[n,]
  pro.raw <- proMat.raw[n,]
  res.q <- cor.test(rna, pro.q)
  res.raw <- cor.test(rna, pro.raw, use = "pairwise.complete.obs")
  tibble(id = n, impute=c("No Imputation","QRILC"),
         p = c(res.raw$p.value, res.q$p.value),
         coef = c(res.raw$estimate, res.q$estimate))
}) %>% bind_rows() %>%
  arrange(desc(coef)) %>% mutate(p.adj = p.adjust(p, method = "BH"),
                                 symbol = rowData(dds[id,])$symbol)

Plot the distribution of correlation coefficient

ggplot(corTab, aes(x=coef, fill = impute)) + geom_histogram(position = "identity", col = "grey50", alpha =0.3, bins =100) +
  geom_vline(xintercept = 0, col = "red", linetype = "dashed")

Warning: Removed 2 rows containing non-finite values (stat_bin).

Most of the correlations are positive, which is reasonable.

Number of significant positive and negative correlations (10% FDR)

sigTab <- corTab %>% filter(p.adj < 0.1) %>% mutate(direction = ifelse(coef > 0, "positive", "negative")) %>%
  group_by(impute, direction) %>% summarise(number = length(id)) %>% ungroup() %>%
  mutate(ratio = format(number/length(geneOverlap), digits = 2)) %>% arrange(number)

`summarise()` regrouping output by 'impute' (override with `.groups` argument)

DT::datatable(sigTab)

Number of significant correlations VS FDR cut-off

plotTab <- lapply(seq(0,0.1, length.out = 100), function(fdr) {
  filTab <- dplyr::filter(corTab, p.adj < fdr, coef > 0) %>%
    group_by(impute) %>% summarise(n = length(id)) %>% mutate(fdr = fdr)
}) %>% bind_rows()

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ggplot(plotTab, aes(x=fdr, y = n, col = impute))+ geom_line() +
  ylab("Number of significant correlations") +
  xlab("FDR cut-off")

List of proteins that significantly correlated with RNA expression (10 %FDR, no imputation)

sigTab <- filter(corTab, p.adj < 0.1, impute == "No Imputation") %>% mutate_if(is.numeric, format, digits=2) 
DT::datatable(sigTab)

List of proteins that significantly correlated with RNA expression (10 %FDR, QRILC imputed)

sigTab <- filter(corTab, p.adj < 0.1, impute == "QRILC") %>% mutate_if(is.numeric, format, digits=2) 
DT::datatable(sigTab)

Correlation plot of top 9 most correlated protein-rna pairs

plotList <- lapply(sigTab$id[1:9], function(n) {
  plotTab <- tibble(pro = proMat.qrilc[n,], gene = rnaMat[n,])
  symbol <- filter(sigTab, id == n)$symbol
  ggplot(plotTab, aes(x=pro, y=gene)) + geom_point() + geom_smooth(method = "lm") +
    ggtitle(symbol) + ylab("RNA expression") + xlab("Protein abundance")
})

cowplot::plot_grid(plotlist = plotList, ncol =3)

`geom_smooth()` using formula 'y ~ x'
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Assocation with technical factors

Are thechnical variables confounded with major genomic variabes?

# A tibble: 4 x 4
  genomic     technical       pval p.adj
  <chr>       <chr>          <dbl> <dbl>
1 IGHV.status processDate   0.0219 0.437
2 SF3B1       freeThawCycle 0.0229 0.437
3 del11q      freeThawCycle 0.0369 0.437
4 trisomy12   processDate   0.0416 0.437

No Significant assocations

Association between technical variables and priciple components of protein expression

plotMat <- assays(protCLL)[["QRILC"]]
pcRes <- prcomp(t(plotMat), center =TRUE, scale. = FALSE)$x

testRes <- lapply(colnames(pcRes), function(pc) {
  lapply(colnames(techTab), function(tech) {
    pcVar <- pcRes[,pc]
    techVar <- techTab[[tech]]
    res <- summary(aov(pcVar ~ techVar))
    p <- res[[1]][1,4]
    tibble(component = pc, technical = tech, pval = p)
  }) %>% bind_rows()
}) %>% bind_rows() %>% mutate(p.adj = p.adjust(pval, method = "BH")) %>%
  arrange(pval)
filter(testRes, p.adj < 0.1)

# A tibble: 3 x 4
  component technical         pval  p.adj
  <chr>     <chr>            <dbl>  <dbl>
1 PC28      proteinConc   0.000102 0.0306
2 PC37      freeThawCycle 0.000298 0.0447
3 PC42      proteinConc   0.000575 0.0575

There are some principle components correlated with technical variables. But the PCs are not top PCs, suggesting the know technical factor do not have impact on the major trends of the dataset.

Associations between technical variables and individual protein expressions

Association test

techTab <- colData(protCLL)[,c("operator", "viability","batch","processDate","proteinConc","freeThawCycle")] %>%
  data.frame() %>%rownames_to_column("patID") %>% as_tibble() %>% mutate(processDate = as.character(processDate)) %>%
  mutate_if(is.character, as.factor)%>% mutate_at(vars(-patID), as.numeric)
testTab <- assays(protCLL)[["QRILC"]] %>% data.frame() %>% 
  rownames_to_column("id") %>% mutate(name = rowData(protCLL)[id,]$hgnc_symbol) %>%
  gather(key = "patID", value = "expr", -id, -name) %>%
  left_join(techTab, by ="patID") %>% gather(key = technical, value = value, -id, -name, -patID, -expr)

testRes <- filter(testTab, !is.na(value)) %>% 
  group_by(name, technical) %>% nest() %>%
  mutate(m = map(data, ~lm(expr~value,.))) %>%
  mutate(res = map(m, broom::tidy)) %>%
  unnest(res) %>% filter(term=="value") %>%
  mutate(p.adj = p.adjust(p.value, method = "BH"))

sumTab <- filter(testRes, p.adj < 0.1) %>% group_by(technical) %>% summarise(n=length(name)) 

`summarise()` ungrouping output (override with `.groups` argument)

ggplot(sumTab, aes(x=technical, y = n)) + geom_bar(stat = "identity") + coord_flip() +
  xlab("") + ylab("Number of significantly associated proteins")

Assocation P value histogram for each technical factor

ggplot(testRes, aes(x=p.value)) + geom_histogram() + facet_wrap(~technical) +xlim(0,1)

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Warning: Removed 12 rows containing missing values (geom_bar).

Also based on the p-value histogram, only overall protein concentration may have potential impact on protein abundance detection.

Will the correlation with RNA expression improve if we adjust for total protein concentration?

proteinConc <- techTab[match(colnames(proMat.qrilc), techTab$patID),]$proteinConc
corTab <- lapply(geneOverlap, function(n) {
  rna <- rnaMat[n,]
  pro.q <- proMat.qrilc[n,]
  p.single <- anova(lm(rna ~ pro.q))$`Pr(>F)`[1]
  p.multi <- car::Anova(lm(rna ~ pro.q + proteinConc))$`Pr(>F)`[1]
  tibble(name = n, corrected = c("no","yes"),
         p = c(p.single, p.multi))
}) %>% bind_rows() %>% mutate(p.adj = p.adjust(p, method = "BH")) %>% arrange(p)

Number of significant correlations VS FDR cut-off

plotTab <- lapply(seq(0,0.1, length.out = 100), function(fdr) {
  filTab <- dplyr::filter(corTab, p.adj < fdr) %>%
    group_by(corrected) %>% summarise(n = length(name)) %>% mutate(fdr = fdr)
}) %>% bind_rows()

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ggplot(plotTab, aes(x=fdr, y = n, col = corrected))+ geom_line() +
  ylab("Number of significant correlations") +
  xlab("FDR cut-off")

Seems to improve the correlation a little, but not much. We can include this factor in association test later.

Check data structure

Hierarchical clustering

plotMat <- assays(protCLL)[["QRILC"]]

colAnno <- colData(protCLL)[,c("gender","IGHV.status","trisomy12")] %>%
  data.frame()

plotMat <- jyluMisc::mscale(plotMat, censor = 6)
pheatmap(plotMat, scale = "none", annotation_col = colAnno, clustering_method = "ward.D2",
         show_rownames = FALSE, color = colorRampPalette(c("navy","white","firebrick"))(100),
         breaks = seq(-6,6, length.out = 101))

No clear separation can be observed

PCA

pcOut <- prcomp(t(plotMat), center =TRUE, scale. = FALSE)
pcRes <- pcOut$x
eigs <- pcOut$sdev^2
varExp <- structure(eigs/sum(eigs),names = colnames(pcRes))

plotTab <- pcRes[,1:2] %>% data.frame() %>% cbind(colAnno[rownames(.),]) %>%
  rownames_to_column("patID") %>% as_tibble()

ggplot(plotTab, aes(x=PC1, y=PC2, col = IGHV.status, shape = trisomy12)) + geom_point(size=4) +
  xlab(sprintf("PC1 (%1.2f%%)",varExp[["PC1"]]*100)) +
  ylab(sprintf("PC2 (%1.2f%%)",varExp[["PC2"]]*100))

PC2 separates trisomy12

Correlation PCs with trisomy12 and IGHV status

corTab <- lapply(colnames(pcRes),  function(pc) {
  ighvCor <- t.test(pcRes[,pc] ~ colAnno$IGHV.status)
  tri12Cor <- t.test(pcRes[,pc] ~ colAnno$trisomy12)
  tibble(PC = pc, 
         feature=c("IGHV", "trisomy12"),
         p = c(ighvCor$p.value, tri12Cor$p.value))
}) %>% bind_rows() %>% mutate(p.adj = p.adjust(p, method = "BH")) %>%
  filter(p <= 0.05) %>% arrange(p)
corTab

# A tibble: 7 x 4
  PC    feature             p     p.adj
  <chr> <chr>           <dbl>     <dbl>
1 PC2   trisomy12 0.000000234 0.0000234
2 PC5   IGHV      0.000142    0.00708  
3 PC6   trisomy12 0.00207     0.0691   
4 PC4   trisomy12 0.00420     0.105    
5 PC7   IGHV      0.0201      0.402    
6 PC1   IGHV      0.0355      0.566    
7 PC5   trisomy12 0.0396      0.566    

PC6 is for IGHV

PCA plot using PC2 and PC7

plotTab <- pcRes[,1:10] %>% data.frame() %>% cbind(colAnno[rownames(.),]) %>%
  rownames_to_column("patID") %>% as_tibble()

ggplot(plotTab, aes(x=PC2, y=PC6, col = IGHV.status, shape = trisomy12, label = patID)) + geom_point() + ggrepel::geom_text_repel() +
  xlab(sprintf("PC2 (%1.2f%%)",varExp[["PC2"]]*100)) +
  ylab(sprintf("PC6 (%1.2f%%)",varExp[["PC6"]]*100))

Using PC3 and PC4 better seperates IGHV and trisomy12.

Biological annotation of PC1

Annotate PC1

Correlation test

Assocation test

proMat <- assays(protCLL)[["QRILC"]]
pc <- pcRes[,1][colnames(proMat)]
designMat <- model.matrix(~1+pc)
fit <- lmFit(proMat,  designMat)
fit2 <- eBayes(fit)
corRes.pc1 <- topTable(fit2, number ="all", adjust.method = "BH", coef = "pc") %>% rownames_to_column("id") %>%
    mutate(symbol = rowData(protCLL[id,])$hgnc_symbol)

Number of significant associations (10% FDR)

hist(corRes.pc1$P.Value,breaks=100)

Table of significant associations (5% FDR)

resTab.sig <- filter(corRes.pc1, adj.P.Val < 0.05) %>% 
  select(symbol, id,logFC, P.Value, adj.P.Val) %>%
  arrange(P.Value)
resTab.sig %>% mutate_if(is.numeric, formatC, digits=2, format= "e") %>%
  DT::datatable()

Heatmap of associated genes

colAnno <- tibble(patID = colnames(proMat), PC1 = pcRes[colnames(proMat),1]) %>%
  arrange(PC1) %>% data.frame() %>% column_to_rownames("patID")

plotMat <- proMat[resTab.sig$id[1:100],rownames(colAnno)]
plotMat <- jyluMisc::mscale(plotMat, censor = 6)

pheatmap(plotMat, scale = "none", annotation_col = colAnno, clustering_method = "ward.D2",
         cluster_cols = FALSE,
         labels_row = resTab.sig$symbol[1:100], color = colorRampPalette(c("navy","white","firebrick"))(100),
         breaks = seq(-6,6, length.out = 101))

Enrichment using Camera

Hallmarks

gmts = list(H= "../data/gmts/h.all.v6.2.symbols.gmt",
            C6 = "../data/gmts/c6.all.v6.2.symbols.gmt",
            KEGG = "../data/gmts/c2.cp.kegg.v6.2.symbols.gmt")

res <- runCamera(proMat, designMat, gmts$H, id = rowData(protCLL[rownames(proMat),])$hgnc_symbol)
res$enrichPlot

C6

res <- runCamera(proMat, designMat, gmts$C6, id = rowData(protCLL[rownames(proMat),])$hgnc_symbol)
res$enrichPlot

KEGG

res <- runCamera(proMat, designMat, gmts$KEGG, id = rowData(protCLL[rownames(proMat),])$hgnc_symbol)
res$enrichPlot

Association with lymphocyte count (potential contamination?)

load("~/CLLproject_jlu/ShinyApps/sampleTimeline//timeline.RData")
plotTab <- pcRes[,1:9] %>% data.frame()  %>%
  rownames_to_column("patID") %>% as_tibble() %>%
  mutate(sampleID = protCLL[,patID]$sampleID) %>%
  mutate(lymCount = sampleTab[match(sampleID, sampleTab$sampleID),]$leukCount) %>%
  gather(key = "pc", value = "val",-patID,-sampleID,-lymCount)

ggplot(plotTab, aes(x=val, y=lymCount)) + geom_point() + geom_smooth(method = "lm") +
  facet_wrap(~pc, ncol =3, scale = "free")

`geom_smooth()` using formula 'y ~ x'

corRes <- plotTab %>% group_by(pc) %>% nest() %>%
  mutate(m= map(data, ~cor.test(~ val+ lymCount,.))) %>%
  mutate(res = map(m, broom::tidy)) %>%
  unnest(res) %>% select(pc, estimate, p.value) %>%
  arrange(p.value)
corRes

# A tibble: 9 x 3
# Groups:   pc [9]
  pc    estimate p.value
  <chr>    <dbl>   <dbl>
1 PC2    -0.364  0.00927
2 PC6    -0.236  0.0987 
3 PC1    -0.226  0.115  
4 PC5    -0.145  0.315  
5 PC8    -0.131  0.364  
6 PC3     0.122  0.399  
7 PC9    -0.105  0.467  
8 PC7     0.0908 0.530  
9 PC4     0.0766 0.597  

Association wit %Lymphocyte PB

library(DBI)

con <- dbConnect(RPostgreSQL::PostgreSQL(),
                 dbname = "tumorbank",
                 host = "huber-vm01.embl.de",
                 user = "admin",
                 password = "bloodcancertumorbank")

PBtab <- tbl(con, "patient") %>% 
  left_join(tbl(con, "sample"), by = c(patid = "smppatidref")) %>% 
  left_join(tbl(con, "analysis"), by = c(smpid = "anlsmpidref")) %>%
  collect() %>%
  select(patpatientid, smpsampleid, smpleukocytes, smpsampledate, smppblymphocytes)

dbDisconnect(con)

[1] TRUE

plotTab <- pcRes[,1:9] %>% data.frame()  %>%
  rownames_to_column("patID") %>% as_tibble() %>%
  mutate(sampleID = protCLL[,patID]$sampleID) %>%
  mutate(perPB = PBtab[match(sampleID, PBtab$smpsampleid),]$smppblymphocytes) %>%
  gather(key = "pc", value = "val",-patID,-sampleID,-perPB)

ggplot(plotTab, aes(x=val, y=perPB)) + geom_point() + geom_smooth(method = "lm") +
  facet_wrap(~pc, ncol =3, scale = "free")

`geom_smooth()` using formula 'y ~ x'

corRes <- plotTab %>% group_by(pc) %>% nest() %>%
  mutate(m= map(data, ~cor.test(~ val+ perPB,.))) %>%
  mutate(res = map(m, broom::tidy)) %>%
  unnest(res) %>% select(pc, estimate, p.value) %>%
  arrange(p.value)
corRes

# A tibble: 9 x 3
# Groups:   pc [9]
  pc    estimate p.value
  <chr>    <dbl>   <dbl>
1 PC1    -0.382  0.00626
2 PC3     0.328  0.0199 
3 PC2    -0.260  0.0679 
4 PC6     0.103  0.475  
5 PC7     0.0967 0.504  
6 PC5    -0.0799 0.581  
7 PC8     0.0494 0.733  
8 PC9    -0.0334 0.818  
9 PC4     0.0131 0.928  

PC1 and PC2 both seem to correlation with %PB. But PC2 is also associate with trisomy12?

Will the correlation with transcriptomics increase if PC1 is regressed out?

pc1 <- pcRes[colnames(rnaMat),1]

corTab <- lapply(geneOverlap, function(n) {
  rna <- rnaMat[n,]
  pro.q <- proMat.qrilc[n,]
  p.single <- anova(lm(rna ~ pro.q))$`Pr(>F)`[1]
  p.multi <- car::Anova(lm(rna ~ pro.q + pc1))$`Pr(>F)`[1]
  tibble(name = n, corrected = c("no","yes"),
         p = c(p.single, p.multi))
}) %>% bind_rows() %>% mutate(p.adj = p.adjust(p, method = "BH")) %>% arrange(p)

Number of significant correlations VS FDR cut-off

plotTab <- lapply(seq(0,0.1, length.out = 100), function(fdr) {
  filTab <- dplyr::filter(corTab, p.adj < fdr) %>%
    group_by(corrected) %>% summarise(n = length(name)) %>% mutate(fdr = fdr)
}) %>% bind_rows()

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ggplot(plotTab, aes(x=fdr, y = n, col = corrected))+ geom_line() +
  ylab("Number of significant correlations") +
  xlab("FDR cut-off")

Seems to improve the correlation a little, but not much. We can include this factor in association test later.

Reconstruct data with PC1 and PC2 removed

protMat <- t(assays(protCLL)[["QRILC"]])
mu <- colMeans(protMat)

Xpca <- prcomp(protMat, center = TRUE, scale. = FALSE)

#reconstruct without the first two components
protMat.new <- Xpca$x[,2:ncol(Xpca$x)] %*% t(Xpca$rotation[,2:ncol(Xpca$x)])
protMat.new <- scale(protMat.new, center = -mu, scale = FALSE)

protMat.new <- t(protMat.new)

Hierarchical clustering using reconstructed matrix

plotMat <- protMat.new

colAnno <- colData(protCLL)[,c("gender","IGHV.status","trisomy12")] %>%
  data.frame()

plotMat <- jyluMisc::mscale(plotMat, censor = 6)
pheatmap(plotMat, scale = "none", annotation_col = colAnno, clustering_method = "ward.D2",
         show_rownames = FALSE, color = colorRampPalette(c("navy","white","firebrick"))(100),
         breaks = seq(-6,6, length.out = 101))

Better separation for trisomy12 can be observed

PCA using reconstructed matrix

pcOut <- prcomp(t(plotMat), center =TRUE, scale. = FALSE)
pcRes.new <- pcOut$x
eigs <- pcOut$sdev^2
varExp <- structure(eigs/sum(eigs),names = colnames(pcRes.new))

plotTab <- pcRes.new[,1:2] %>% data.frame() %>% cbind(colAnno[rownames(.),]) %>%
  rownames_to_column("patID") %>% as_tibble()

ggplot(plotTab, aes(x=PC1, y=PC2, col = IGHV.status, shape = trisomy12)) + geom_point(size=4) +
  xlab(sprintf("PC1 (%1.2f%%)",varExp[["PC1"]]*100)) +
  ylab(sprintf("PC2 (%1.2f%%)",varExp[["PC2"]]*100))

Some outliers dominate the variance

Save the post process object

assays(protCLL)[["QRILC_re"]] <- protMat.new
protCLL$PC1 <- pcRes[colnames(protCLL),1]
protCLL$PC2 <- pcRes[colnames(protCLL),2]
save(protCLL, file = "../output/timsTOF_processed.RData")

timsTOF has some quality issues, and it's not very clear what the major variance in this dataset represents.

Session information

sessionInfo()

R version 3.6.0 (2019-04-26)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.15.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] parallel  stats4    stats     graphics  grDevices utils     datasets 
[8] methods   base     

other attached packages:
 [1] DBI_1.1.0                   forcats_0.5.0              
 [3] stringr_1.4.0               dplyr_1.0.0                
 [5] purrr_0.3.4                 readr_1.3.1                
 [7] tidyr_1.1.0                 tibble_3.0.3               
 [9] ggplot2_3.3.2               tidyverse_1.3.0            
[11] DESeq2_1.26.0               SummarizedExperiment_1.16.1
[13] DelayedArray_0.12.3         BiocParallel_1.20.1        
[15] matrixStats_0.56.0          Biobase_2.46.0             
[17] GenomicRanges_1.38.0        GenomeInfoDb_1.22.1        
[19] IRanges_2.20.2              S4Vectors_0.24.4           
[21] BiocGenerics_0.32.0         jyluMisc_0.1.5             
[23] pheatmap_1.0.12             piano_2.2.0                
[25] cowplot_1.0.0               limma_3.42.2               

loaded via a namespace (and not attached):
  [1] utf8_1.1.4             shinydashboard_0.7.1   tidyselect_1.1.0      
  [4] RSQLite_2.2.0          AnnotationDbi_1.48.0   htmlwidgets_1.5.1     
  [7] grid_3.6.0             maxstat_0.7-25         munsell_0.5.0         
 [10] codetools_0.2-16       DT_0.14                withr_2.2.0           
 [13] colorspace_1.4-1       knitr_1.29             rstudioapi_0.11       
 [16] ggsignif_0.6.0         labeling_0.3           git2r_0.27.1          
 [19] slam_0.1-47            GenomeInfoDbData_1.2.2 KMsurv_0.1-5          
 [22] bit64_0.9-7            farver_2.0.3           rprojroot_1.3-2       
 [25] vctrs_0.3.1            generics_0.0.2         TH.data_1.0-10        
 [28] xfun_0.15              sets_1.0-18            R6_2.4.1              
 [31] locfit_1.5-9.4         bitops_1.0-6           fgsea_1.12.0          
 [34] assertthat_0.2.1       promises_1.1.1         scales_1.1.1          
 [37] multcomp_1.4-13        nnet_7.3-14            gtable_0.3.0          
 [40] sandwich_2.5-1         workflowr_1.6.2        rlang_0.4.7           
 [43] genefilter_1.68.0      splines_3.6.0          rstatix_0.6.0         
 [46] acepack_1.4.1          broom_0.7.0            checkmate_2.0.0       
 [49] yaml_2.2.1             abind_1.4-5            modelr_0.1.8          
 [52] crosstalk_1.1.0.1      backports_1.1.8        httpuv_1.5.4          
 [55] Hmisc_4.4-0            tools_3.6.0            relations_0.6-9       
 [58] RPostgreSQL_0.6-2      ellipsis_0.3.1         gplots_3.0.4          
 [61] RColorBrewer_1.1-2     Rcpp_1.0.5             base64enc_0.1-3       
 [64] visNetwork_2.0.9       zlibbioc_1.32.0        RCurl_1.98-1.2        
 [67] ggpubr_0.4.0           rpart_4.1-15           zoo_1.8-8             
 [70] ggrepel_0.8.2          haven_2.3.1            cluster_2.1.0         
 [73] exactRankTests_0.8-31  fs_1.4.2               magrittr_1.5          
 [76] data.table_1.12.8      openxlsx_4.1.5         reprex_0.3.0          
 [79] survminer_0.4.7        mvtnorm_1.1-1          hms_0.5.3             
 [82] shinyjs_1.1            mime_0.9               evaluate_0.14         
 [85] xtable_1.8-4           XML_3.98-1.20          rio_0.5.16            
 [88] jpeg_0.1-8.1           readxl_1.3.1           gridExtra_2.3         
 [91] compiler_3.6.0         KernSmooth_2.23-17     crayon_1.3.4          
 [94] htmltools_0.5.0        mgcv_1.8-31            later_1.1.0.1         
 [97] Formula_1.2-3          geneplotter_1.64.0     lubridate_1.7.9       
[100] dbplyr_1.4.4           MASS_7.3-51.6          Matrix_1.2-18         
[103] car_3.0-8              cli_2.0.2              marray_1.64.0         
[106] gdata_2.18.0           igraph_1.2.5           pkgconfig_2.0.3       
[109] km.ci_0.5-2            foreign_0.8-71         xml2_1.3.2            
[112] annotate_1.64.0        XVector_0.26.0         drc_3.0-1             
[115] rvest_0.3.5            digest_0.6.25          rmarkdown_2.3         
[118] cellranger_1.1.0       fastmatch_1.1-0        survMisc_0.5.5        
[121] htmlTable_2.0.1        curl_4.3               shiny_1.5.0           
[124] gtools_3.8.2           lifecycle_0.2.0        nlme_3.1-148          
[127] jsonlite_1.7.0         carData_3.0-4          fansi_0.4.1           
[130] pillar_1.4.6           lattice_0.20-41        fastmap_1.0.1         
[133] httr_1.4.1             plotrix_3.7-8          survival_3.2-3        
[136] glue_1.4.1             zip_2.0.4              png_0.1-7             
[139] bit_1.1-15.2           stringi_1.4.6          blob_1.2.1            
[142] latticeExtra_0.6-29    caTools_1.18.0         memoise_1.1.0