FDR calculation by combineTests in csaw
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renanec ▴ 20
@renanec-9080
Last seen 7.3 years ago
United States

Hi there,

Thanks for putting together a really nice tutorial for " From reads to regions: a Bioconductor workflow to detect differential binding in ChIP-seq data". I had a quick question regarding the function combineTests.

When I run the example piece of code I get the exact same FDR for very different p-values (see below). In the most extreme cases with some of my data all FDR values are equal independently of the p-value. Can somebody clarify this?

Many Thanks,

Renan

library(csaw)

ids <- round(runif(100, 1, 10))
tab <- data.frame(logFC=rnorm(100), logCPM=rnorm(100), PValue=rbeta(100, 1, 2))
head(tab)
combined <- combineTests(ids, tab)
head(combined)

Output

nWindows logFC.up logFC.down     PValue       FDR
1        3        0          1 0.29353630 0.4050539
2       11        4          3 0.06942862 0.3471431
3       14        8          4 0.23326239 0.3887707
4       11        6          2 0.51039737 0.5103974
5        9        1          2 0.14480150 0.3877034
6        6        1          4 0.35435897 0.4050539



Session Info

R version 3.2.2 (2015-08-14)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: OS X 10.11.1 (El Capitan)

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] stats4    parallel  stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] csaw_1.4.0                 SummarizedExperiment_1.0.1 Biobase_2.30.0             GenomicRanges_1.22.1       GenomeInfoDb_1.6.1
[6] IRanges_2.4.1              S4Vectors_0.8.2            BiocGenerics_0.16.1

loaded via a namespace (and not attached):
[1] AnnotationDbi_1.32.0    XVector_0.10.0          edgeR_3.12.0            zlibbioc_1.16.0         GenomicAlignments_1.6.1
[6] BiocParallel_1.4.0      tools_3.2.2             DBI_0.3.1               lambda.r_1.1.7          futile.logger_1.4.1
[11] rtracklayer_1.30.1      futile.options_1.0.0    bitops_1.0-6            biomaRt_2.26.0          RCurl_1.95-4.7
[16] RSQLite_1.0.0           limma_3.26.3            GenomicFeatures_1.22.4  Rsamtools_1.22.0        Biostrings_2.38.1
[21] XML_3.98-1.3
csaw • 879 views
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Entering edit mode
Aaron Lun ★ 28k
@alun
Last seen 19 hours ago
The city by the bay

This is a consequence of the BH method to control the FDR (or specifically, the reverse method in p.adjust` that computes the adjusted p-values corresponding to some FDR threshold). By itself, the raw FDR calculation is not a monotonic transformation of the p-values; it is defined as the p-value*N/r, where N is the total number of tests and r is the rank of the p-value (1 for the smallest p-value, N for the largest). You can easily imagine cases where this transformation results in a larger adjusted p-value for, e.g., the smallest p-value compared to the second-smallest p-value (if the latter is less than two-fold larger than the former). This would be silly, as you'd expect the smallest p-value to yield a smaller adjusted p-value/FDR than the second-smallest one.

To avoid such situations, a monotonic transformation is applied whereby the adjusted value for each p-value is replaced with the minimum of the adjusted p-values all of the larger p-values, if that minimum is smaller than its adjusted value. This results in what you observed, where blocks of tests (i.e., genes, regions, whatever) with different p-values have the same adjusted p-value/FDR. So in short, it's not a bug, it's just a little oddity stemming from how the FDR is calculated.

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