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Array properties

Get the array annotation data.

ann <- loadAnnotation(arrayType="EPIC")

Associate CpGs to genes (ENTREZ ID) using the Illumina annotation information.

flatAnn <- loadFlatAnnotation(ann)

The number of CpGs annotated to a gene is highly variable.

numCpgsPerGene <- as.vector(table(flatAnn$entrezid))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1.00   10.00   20.00   27.25   33.00 1485.00 
dat <- data.frame(table(table(flatAnn$entrezid)))
numCpgsPerGene <- as.vector(table(flatAnn$entrezid))
med <- median(numCpgsPerGene)
mod <- getMode(numCpgsPerGene)

p <- ggplot(dat, aes(x=Var1, y=Freq)) +
    geom_segment(aes(x=Var1, xend=Var1, y=0, yend=Freq), color="darkgrey") +
    geom_point( color="black", size=1) +
    geom_vline(xintercept = med, linetype = "dashed", color = "red") +
    annotate("text", x = med + 2, label=glue("median = {med}"), y=720, colour="red", 
             size = 3, hjust="left") +
    geom_vline(xintercept = mod, linetype = "dashed", color = "blue") +
    annotate("text", x = mod + 2, label=glue("mode = {mod}"), y=780, colour="blue", 
             size = 3, hjust="left") +
    scale_x_discrete(breaks = c(1,10,20,30,45,55,70,80,90,100,120,135,150,160,180,
                                200,215,250,330,429,1485)) +
    theme(axis.text.x=element_text(angle=45, hjust=1)) +
    xlab("No. CpGs per gene") +


Version Author Date
e66c39a JovMaksimovic 2020-08-14

Save figure for use in manuscript.

outDir <- here::here("output/figures")
if (!dir.exists(outDir)) dir.create(outDir)

fig <- here("output/figures/Fig-1A.rds")
saveRDS(p, fig, compress = FALSE)

The number of genes a CpG maps to can also vary, although the majority of CpGs only map to one gene.

dat <- data.frame(table(table(flatAnn$cpg)))
dat$Split <- ifelse(dat$Freq > 2500, "A", 
                    ifelse(dat$Freq < 2500 & dat$Freq > 65,"B","C"))

a <- ggplot(dat[dat$Split == "A",], aes(x=Var1, y=Freq)) +
    geom_bar(stat = "identity") +
    theme(axis.title.x = element_blank(), 
          axis.text.y=element_text(angle=90, hjust=0.5)) +

b <- ggplot(dat[dat$Split == "B",], aes(x=Var1, y=Freq)) +
    geom_bar(stat = "identity") +
          axis.title.y = element_blank())

c <- ggplot(dat[dat$Split == "C",], aes(x=Var1, y=Freq)) +
    geom_bar(stat = "identity") +
    theme(axis.title.y = element_blank(),
          axis.title.x = element_blank()) 

p <- a + b + c + plot_layout(widths = c(1,2,6)) + 
   plot_annotation(caption = "No. genes mapped to a CpG",
                   theme = theme(plot.caption = element_text(hjust = 0.5,
                                                             size = 12)))

Version Author Date
e66c39a JovMaksimovic 2020-08-14

Save figure for use in manuscript.

fig <- here("output/figures/Fig-1D.rds")
saveRDS(p, fig, compress = FALSE)

Explore the distribution of the average number of CpGs per gene, per GO category.

ann450 <- loadAnnotation("450k")
flatAnn450 <- loadFlatAnnotation(ann450)

cpgEgGoEPIC <- cpgsEgGoFreqs(flatAnn)
cpgEgGoEPIC$Array <- "EPIC"

cpgEgGo450 <- cpgsEgGoFreqs(flatAnn450)
cpgEgGo450$Array <- "450k"

cpgEgGoEPIC %>% bind_rows(cpgEgGo450) %>% 
    group_by(Array, GO) %>%
    summarise(avg = mean(Freq)) -> datSum
`summarise()` has grouped output by 'Array'. You can override using the `.groups` argument.
maxEPIC <- max(datSum$avg[datSum$Array == "EPIC"])
max450 <- max(datSum$avg[datSum$Array == "450k"])

bw <- 2
pal <- paletteer::paletteer_d("RColorBrewer::Set1", 2)
platform <- c("EPIC" = pal[1], "450k" = pal[2])
p <- ggplot(datSum, aes(x=avg)) +
    geom_histogram(dat = subset(datSum, Array == "450k"),
                   alpha = 0.5, aes(fill = "450k"), binwidth = bw) +
    geom_histogram(dat = subset(datSum, Array == "EPIC"),
                   alpha = 0.5, aes(fill = "EPIC"), binwidth = bw) +
    geom_vline(xintercept = maxEPIC, linetype="dashed", colour = pal[1]) +
    geom_vline(xintercept = max450, linetype="dashed", colour = pal[2]) +
    labs(x="Mean no. CpGs per gene per GO category", y = "Frequency",
         fill = "Platform") +
    annotate("text", x = maxEPIC - 4, label=glue("Max. EPIC = {maxEPIC}"),
             y = 1500, colour=pal[1], size = 2.5, hjust="right") +
    annotate("text", x = max450 - 4, label=glue("Max. 450k = {max450}"),
             y = 2500, colour=pal[2], size = 2.5, hjust="right") +
    scale_fill_manual(values = platform)

Version Author Date
e66c39a JovMaksimovic 2020-08-14

Save figure for use in manuscript.

fig <- here("output/figures/Fig-1C.rds")
saveRDS(p, fig, compress = FALSE)

Null simulations

We randomly select 50, 100, 500, 1000, 5000 and 10000 sets of CpGs and perform GO testing on each set 100 times, with and without adjusting for the various biases on the array.

The code used to produce the simulation results can be found in the code/random-cpg-sims directory. It consists of three scripts: genRandCpgSimJobs.R, randomCpgSim.R and processRandCpgSim.R. The genRandCpgSimJobs.R script creates and submits Slurm job scripts that run the randomCpgSim.R script, in parallel, on a HPC. Each job executes one of the 100 simulations, for a fixed number of randomly selected CpGs, using either the 450K or EPIC array annotation. The results of each job are saved as an RDS file named {arrayType}.{noCpgs}.{simNo}.rds in the output/random-cpg-sims directory. Once all simulation jobs are complete, the processRandCpgSim.R must be executed to collate the results into a single object for each array type, which are then saved as 450K.rds and EPIC.rds in the output/random-cpg-sims directory. The intermediate RDS files are moved into output/random-cpg-sims/.bin, which can then be deleted, if no longer required. The subsequent section requires EPIC.rds to be present in the output/random-cpg-sims directory for downstream analysis and plotting.


The following boxplots show what proportion of the 100 simulations, at each level of CpGs sampled, had a raw p-value less than 0.05. This gives us an idea of the false discovery rate with and without adjustment for the number of CpGs annotated to a gene.

dat <- readRDS(here("output/random-cpg-sims/EPIC.rds"))

dat %>% filter(method %in% names(dict)) %>%
    mutate(method = unname(dict[method])) %>%
    group_by(simNo, noCpgs, method) %>% 
    summarise(pSig = sum(P.DE < 0.05)/length(P.DE)) -> sigDat
`summarise()` has grouped output by 'simNo', 'noCpgs'. You can override using the `.groups` argument.
p <- ggplot(sigDat, aes(x=noCpgs, y=pSig, fill=method)) + 
    geom_violin(size = 0.3) +
    geom_hline(yintercept=0.05, linetype="dashed", color = "red") +
    labs(y="Prop. GO cat. with p-value < 0.05", x="No. randomly sampled CpGs",
         fill="Method") +
    scale_fill_manual(values = methodCols)  +
    facet_grid(cols = vars(noCpgs), scales = "free_x") + 
    theme(strip.background = element_blank(), 
          strip.text = element_blank())

Version Author Date
e66c39a JovMaksimovic 2020-08-14
fig <- here("output/figures/Fig-3A.rds")
saveRDS(p, fig, compress = FALSE)

QQ plots of randomly selected simulations at each level of CpGs sampled.

s <- sample(1:100, 3)
dat %>% filter(simNo %in% s) %>%
    filter(method %in% names(dict)) %>%
    mutate(method = unname(dict[method])) %>%
    arrange(simNo, noCpgs, method, P.DE) %>%
    group_by(simNo, noCpgs, method) %>%
    mutate(exp = 1:n()/n()) -> subDat

p <- ggplot(subDat, aes(x=-log10(exp), y=-log10(P.DE), color=method)) + 
    geom_point(shape = 1, size = 0.5) + 
    facet_grid(noCpgs ~ simNo, scales = "free_y") +
    scale_color_manual(values = methodCols)

p + geom_line(aes(x=-log10(exp), y=-log10(exp)),
              linetype="dashed", color = "black") +
         color="Method") +
    theme(legend.position="bottom", strip.text.x = element_blank())

Version Author Date
e66c39a JovMaksimovic 2020-08-14

Explore the relationship between the median, average number of CpGs, per gene, per GO category and the various sources of bias on the array.

goFreq <- as_tibble(unique(cpgEgGoEPIC[,c("GO","Freq")]))

dat %>% filter(method %in% names(dict)) %>%
    mutate(method = unname(dict[method])) %>% 
    filter(P.DE < 0.05) %>%
    inner_join(goFreq, by=c("GO" = "GO")) %>%
    group_by(simNo, noCpgs, method, GO) %>%
    summarise(avgFreq=mean(Freq)) %>% 
    group_by(simNo, noCpgs, method) %>%
    summarise(medAvgFreq=median(avgFreq)) -> medAvgDat
`summarise()` has grouped output by 'simNo', 'noCpgs', 'method'. You can override using the `.groups` argument.
`summarise()` has grouped output by 'simNo', 'noCpgs'. You can override using the `.groups` argument.
goFreq %>% group_by(GO) %>% 
    summarise(med = median(Freq)) %>%
    dplyr::select(med) %>%
    summarise(med = median(med)) -> medPerGO

dat_text <- data.frame(
  label = c(rep("",4),
            "Med. Med. # Genes", 
            glue("per GO Cat. = {round(medPerGO$med, 2)}")),
  method = "GOmeth",
  noCpgs = unique(medAvgDat$noCpgs),
  x = unique(medAvgDat$noCpgs),
  y = rep(medPerGO$med + 1, 6)

p <- ggplot(medAvgDat, aes(x=noCpgs, y=medAvgFreq, fill=method)) +
    geom_violin(size = 0.3, scale = "area") +
    stat_summary(geom="point", size = 0.5, color="white",
                 position = position_dodge(0.9),
                 show.legend = FALSE, fun = median) +
    labs(y="Median avg. no. CpGs/gene/GO cat.",
         x="No. randomly sampled CpGs",
         fill="Method")  +
    scale_fill_manual(values = methodCols) +
    geom_hline(yintercept = medPerGO$med, linetype="dashed", color = "red") +
    geom_text(data = dat_text, colour="red", size = 2.5, hjust="left", 
              mapping = aes(x = -Inf, y = y, label = label)) +
    facet_grid(cols = vars(noCpgs), scales = "free_x") +
    theme(strip.background = element_blank(),
          strip.text = element_blank())

Version Author Date
bbf77e1 JovMaksimovic 2020-08-21
e66c39a JovMaksimovic 2020-08-14

Save figure for use in manuscript.

fig <- here("output/figures/Fig-3B.rds")
saveRDS(p, fig, compress = FALSE)

R version 4.0.3 (2020-10-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Mojave 10.14.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

[1] en_AU.UTF-8/en_AU.UTF-8/en_AU.UTF-8/C/en_AU.UTF-8/en_AU.UTF-8

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

other attached packages:
 [1] dplyr_1.0.5                                        
 [2] tibble_3.1.0                                       
 [3] ggplot2_3.3.3                                      
 [4] patchwork_1.1.1                                    
 [5] GO.db_3.12.1                                       
 [7] AnnotationDbi_1.52.0                               
 [8] missMethyl_1.24.0                                  
 [9] IlluminaHumanMethylation450kanno.ilmn12.hg19_0.6.0 
[10] IlluminaHumanMethylationEPICanno.ilm10b4.hg19_0.6.0
[11] minfi_1.36.0                                       
[12] bumphunter_1.32.0                                  
[13] locfit_1.5-9.4                                     
[14] iterators_1.0.13                                   
[15] foreach_1.5.1                                      
[16] Biostrings_2.58.0                                  
[17] XVector_0.30.0                                     
[18] SummarizedExperiment_1.20.0                        
[19] Biobase_2.50.0                                     
[20] MatrixGenerics_1.2.1                               
[21] matrixStats_0.58.0                                 
[22] GenomicRanges_1.42.0                               
[23] GenomeInfoDb_1.26.7                                
[24] IRanges_2.24.1                                     
[25] S4Vectors_0.28.1                                   
[26] BiocGenerics_0.36.0                                
[27] glue_1.4.2                                         
[28] here_1.0.1                                         
[29] workflowr_1.6.2                                    

loaded via a namespace (and not attached):
  [1] BiocFileCache_1.14.0      plyr_1.8.6               
  [3] splines_4.0.3             BiocParallel_1.24.1      
  [5] digest_0.6.27             htmltools_0.5.1.1        
  [7] fansi_0.4.2               magrittr_2.0.1           
  [9] memoise_2.0.0             paletteer_1.3.0          
 [11] limma_3.46.0              readr_1.4.0              
 [13] annotate_1.68.0           askpass_1.1              
 [15] siggenes_1.64.0           prettyunits_1.1.1        
 [17] colorspace_2.0-0          blob_1.2.1               
 [19] rappdirs_0.3.3            xfun_0.22                
 [21] prismatic_1.0.0           crayon_1.4.1             
 [23] RCurl_1.98-1.3            jsonlite_1.7.2           
 [25] genefilter_1.72.1         GEOquery_2.58.0          
 [27] survival_3.2-10           gtable_0.3.0             
 [29] zlibbioc_1.36.0           DelayedArray_0.16.3      
 [31] Rhdf5lib_1.12.1           HDF5Array_1.18.1         
 [33] scales_1.1.1              DBI_1.1.1                
 [35] rngtools_1.5              Rcpp_1.0.6               
 [37] xtable_1.8-4              progress_1.2.2           
 [39] bit_4.0.4                 mclust_5.4.7             
 [41] preprocessCore_1.52.1     httr_1.4.2               
 [43] RColorBrewer_1.1-2        ellipsis_0.3.1           
 [45] farver_2.1.0              pkgconfig_2.0.3          
 [47] reshape_0.8.8             XML_3.99-0.6             
 [49] sass_0.3.1                dbplyr_2.1.1             
 [51] utf8_1.2.1                reshape2_1.4.4           
 [53] labeling_0.4.2            tidyselect_1.1.0         
 [55] rlang_0.4.10              later_1.1.0.1            
 [57] munsell_0.5.0             tools_4.0.3              
 [59] cachem_1.0.4              generics_0.1.0           
 [61] RSQLite_2.2.5             evaluate_0.14            
 [63] stringr_1.4.0             fastmap_1.1.0            
 [65] yaml_2.2.1                rematch2_2.1.2           
 [67] knitr_1.31                bit64_4.0.5              
 [69] fs_1.5.0                  beanplot_1.2             
 [71] scrime_1.3.5              purrr_0.3.4              
 [73] nlme_3.1-152              doRNG_1.8.2              
 [75] sparseMatrixStats_1.2.1   whisker_0.4              
 [77] nor1mix_1.3-0             xml2_1.3.2               
 [79] biomaRt_2.46.3            compiler_4.0.3           
 [81] curl_4.3                  statmod_1.4.35           
 [83] bslib_0.2.4               stringi_1.5.3            
 [85] highr_0.8                 GenomicFeatures_1.42.3   
 [87] lattice_0.20-41           Matrix_1.3-2             
 [89] multtest_2.46.0           vctrs_0.3.7              
 [91] pillar_1.5.1              lifecycle_1.0.0          
 [93] rhdf5filters_1.2.0        jquerylib_0.1.3          
 [95] data.table_1.14.0         bitops_1.0-6             
 [97] httpuv_1.5.5              rtracklayer_1.50.0       
 [99] R6_2.5.0                  promises_1.2.0.1         
[101] codetools_0.2-18          MASS_7.3-53.1            
[103] assertthat_0.2.1          rhdf5_2.34.0             
[105] openssl_1.4.3             rprojroot_2.0.2          
[107] withr_2.4.1               GenomicAlignments_1.26.0 
[109] Rsamtools_2.6.0           GenomeInfoDbData_1.2.4   
[111] hms_1.0.0                 quadprog_1.5-8           
[113] tidyr_1.1.3               base64_2.0               
[115] rmarkdown_2.7             DelayedMatrixStats_1.12.3
[117] illuminaio_0.32.0         git2r_0.28.0