Question: DESeq2 modelling and Wald's test
2
Uday Rangaswamy120 wrote:

Hi all,

Can you please explain to me the relation between Wald's test and Negative binomial generalized linear model? As for my understanding, the count data is modeled using negative binomial generalized linear model after which Wald's test is applied to figure out whether a particular gene is significant or not. Please correct me if I'm wrong.

rna-seq deseq2 • 1.9k views
modified 19 months ago by Kevin Blighe51k • written 19 months ago by Uday Rangaswamy120
8
Kevin Blighe51k wrote:

RNA-seq raw count data 'naturally' follows a negative binomial distribution (Poisson-like), so, the DESeq2 authors model the data as such. By 'model the data', we merely imply that we build a regression model of the data such that we can make statistical inferences from it [the data].

So, after normalising the raw counts, the following occurs:

For each gene, a logistic regression model with the negative binomial as family is fit:

``````require(MASS)
gene1.model <- glm.nb(gene1 ~ CaseControl + ..., data=MyData)
gene2.model <- glm.nb(gene2 ~ CaseControl + ..., data=MyData)
*et cetera*
``````

Once we have modeled each gene, a simple way to derive a P value for each model coefficient (i.e. CaseControl, etc) is by applying the Wald Test and selecting the coefficient of interest:

``````require(aod)
wald.test(b=coef(gene1.model), Sigma=vcov(gene1.model), Terms=c(2)) #term '2' would be CaseControl
``````

The Wald test is a standard way to extract a P value from a regression fit.

Kevin

NB - this is not the exact code used by DESeq2, of course. This is just giving you a broad overview with some simple R functions. For one, DESeq2 models dispersion in addition to everything that I have mentioned above, and the Wald test is not used in each case to derive p-values in DESeq2.

1

Thank you so much for that.

Kevin, thanks for your explanation. Let me one naive question please? Why we need to make a `GLM` model before performing a `Wald test` itself (as i can understand it's just a simple `t-test` in rough approximation?)? Why not just perform a `Wald test` on count data?

2

A Wald test requires a coefficient and its standard deviation, which are tested for difference from 0. Yes, in a way that's sort of like a single group T-test, but you'd still need to perform a fit first in order to derive the coefficient.

Sorry, but it's stiil not quite clear for me. I thought that `T-test` for two (in majority experiments) independent groups would be more intuitive and obvious. So, why a single group `T-test`? In addition, when i perform `T-test` for example in `R` i don't need anything except trait observations in two groups. In particular, no coefficiets are required for that. So why in `DESeq2` i need to estimate some coefficient before the test itself? Could you elaborate on this please (just for understanding)? Finally, as i understand the `GLM` output already contains p-values. So why just not use these ones to test for `DE` genes?

1

We're talking about different things with the single-group T-test, just ignore that.

You can do a standard T-test for RNAseq data, your power will just be terrible. Packages like limma were developed to get around this and can be used with RNAseq. You estimate a coefficient with a T-test too (a T-test is a kind of GLM), you're just not aware of it. The p-values from the GLM (in particular, `summary()`) are from a Wald test. You don't have to explicitly run that separately, but it can be convenient to do so to more easily extract the information you want (it also allows more flexibility, wherein you can use contrasts).