Best way to call differencially methylated positions taking into account results from both Beta and M values

Question

[jeni]

Hi!

I have performed a probe wise differencial methylation analysis from a set of beta values downloaded from de TCGA. I have obtained a set of differencially methylated probes (dmp) for two groups of samples, but their log2 fold change (log2FC) range from -0.3 to 0.4. Then, I have performed exactly the same analysis, but transforming the Beta values to M values using beta2m from lumi package. Now, the log2FC range from -3 to 4.

So, looking to M values results, it seems that the effect size of the probes is quite big, but, when I look to the Beta values result, then the effect seems quite low.

So, I was thinking to filter those probes with abs (log2FC) < 1, using the results of M values, but I am worried about their low log2FC when Beta values are used. Do you think it would be okay this approach or that the better is to use the log2FC from the Beta values results (which in my case seems too low)?

Answer 1

[Papyrus]

There are a couple of things to consider here:

First, when interpreting effect size, I believe one should think of the biological meaning of the measurements. In the case of b-values, ranging from 0 to 1, this is more "straightforward" and they are usually interpreted as proportion (or percentage) of methylation (which could more or less reflect the mixture of cells with different methylation states which you have analyzed). M-values, on the other hand, being a logit transformation, are not so easily interpreted. Thus I would personally base the effect size filtering on b-value differences, even in you test using M-values, which is recommended because their distribution is more appropriate (they are more homoscedastic).

Secondly, different effect sizes may be observed for b- and M-values not just because of the scale, but because the relationship between b-values and M-values is non linear. This paper Pan Du, 2010 may help you understand the relationship: b-values are compressed at the extremes (0 and 1), so you could see that a "big" change in M-value may actually be a very small difference in betas. For example:

lumi::beta2m(0.002)
[1] -8.962896
lumi::beta2m(0.005)
[1] -7.636625

[jeni]

I see your point. However, if b-values are compressed at their extremes, then that wouldn't mean that a small change between extreme values of b-values (0.01 vs 0.02, for example) could actually be reflecting a higher biological effect?

[Papyrus]

No, I would not interpret it as such. When I said "compressed" I was referring to compressed with respect to M-values, not biologically.

These measurements arise from: hybridizing bisulfite-treated DNA to the probes of the array. Then, the b-value is computed as the ratio of methylated signal fluorescence with respect to total signal (meth + unmeth). Thus they reflect how much methylated DNA was detected by the array probes taking into account the total. Thus, in my opinion two similar and small proportions (such as your 0.01, 0.02 example) reflect mostly the same: that a very small proportion of the DNA was methylated. And to me, that would indicate that there is a very small biological difference between the samples (even if it were statistically significant).