Hi,

I'm working on a differential methylation analysis on WGBS data, using the bsseq package.

I'm following the vignette to identify differentially methylated regions (DMRs) between two groups but I'm having troubles in understanding this step:

Once t-statistics have been computed, we can compute differentially methylated regions (DMRs) by thresholding the t-statistics. Here we use a cutoff of 4.6, which was chosen by looking at the quantiles of the t-statistics (for the entire genome).
> dmrs0 <- dmrFinder(BS.cancer.ex.tstat, cutoff = c(-4.6, 4.6)) 

So, my questions are:

• How was the 4.6 cutoff for the t-statitistic chosen and what does it mean to look at the quantiles of the t-statistic? Can you provide some code that shows how the choice was made?
   
• Would it be possible to filter by p-value instead? I would find it more intuitive but I don't see a p-value column in the results object. How would I go about adding a p-value column based on the values of the t-statistic?

Thank you!

Enrico

Hi Enrico,

1. The cutoff is chosen as follows: Compute the t-statistic for each CpG in your study and then form the distribution of these t-statistics. Compute the (alpha/2)-level lower and upper quantiles of this distribution; this can be done using the quantile() function in R. The choice of alpha is up to you - from memory, the numbers referred to in the vignette correspond to alpha = 0.05, i.e., the lower quantile is at the lower 2.5% of the data and the upper quantile as at the upper 97.5% of the data. This means we are selecting empirically the 5% of the most extreme t-statistics in your data. To emphasise, these numbers should be based on the distribution of t-statistics from your data.

2. Sure, you could filter by p-value. You can easily map the t-statistic to a p-value; see the pt() function in R. However, you will need to also compute and supply the appropriate degrees of freedom as well as accounting for the sign of the t-statistic. To me, this makes it simpler to just use the t-statistics themselves for setting the cutoff.

I hope this helps.

By the way, there's no need to notify the bsseq developers via Twitter of your question on this forum. We receive email notifications of posts tagged by packages we are involved with.

Cheers,

Pete

Edit: Technically the quantiles are the (0,25,50,75,100) percentiles of the data <- That is like, not correct.

Quantiles can be computed using the quantile function. Using the data from the vignette:

> library(bsseqData)

> data(BS.cancer.ex.tstat)

> ps <- getStats(BS.cancer.ex.tstat)[,"tstat.corrected"]

> quantile(ps)
         0%         25%         50%         75%        100%
-10.9073281  -0.5864714   0.1185087   0.8609352  14.3986699

But I doubt that you want to use any of those percentiles as a cutoff. More likely you want to look at the (95, 99, 99.5) percentiles instead.

> quantile(ps, c(0,0.005, 0.01, 0.05, 0.95,0.99, 0.995,1))
        0%       0.5%         1%         5%        95%        99%      99.5%
-10.907328  -4.115913  -3.447037  -1.998064   2.622552   5.918016   8.127983
      100%
 14.398670

And you could exclude all but about 2% of the regions under contention by using the cutoffs that are used in the vignette

> sum(ps < -4.6 | ps > 4.6)/length(ps)
[1] 0.01981683

You could use the p-value for those t-statistics, but it wouldn't be materially different than using the t-statistics directly.

The idea here is pretty simple - you just want to get a relatively small number of CpG sites that look to be differentially methylated, and then see if any of them are all together in one or more regions. How you select the CpG sites will necessarily be pretty ad hoc, and you just want to make sure you don't have too many (don't want too many false positives creeping in) or too few (you do want some results, no?). In the end you need some criterion to say if a CpG is in or out, and using the t-stat or the p-value will result in pretty much the same thing.

To see what I mean, you can make a 'volcano plot' of the data:

> plot(ps, -log10(pt(abs(ps), 8, lower.tail = FALSE)))

> abline(v = c(-4.6, 4.6))

The cutoff in the vignette is choosing all the CpG sites outside of those two vertical lines. Using a p-value cutoff would be the same as putting a horizontal line in there somewhere, at say

> abline(h = 3.1)

And taking all the CpG sites above that line. Which just so happens to be the same exact CpG sites.