# RNA-Seq data distribution

In the papers I read, it is usually claimed that since RNA-Seq is count data, a Poisson or negative binomial distribution would be the most suitable ones to model the RNA-Seq data. However, as a computational biologist, none of the RNA-Seq data I have seen so far is composed of integers. All RNA-Seq datasets I have seen contain decimals, which is probably because there is a standard normalization process applied to the raw read counts, which is crucial. This normalization process usually adjusts for sequencing depth and also for overdispersion. So, my question is, how come we can model those decimal numbers with Poisson or negative binomial? As I said, I have never seen processed (or normalized) RNA-Seq data that contain integers. What am I missing?

Well.. If you are using the standard count-based RNASeq differential expression analysis methods, then they really take counts as input. As far as I recall, some of the Bioconductor packages, e.g. DESeq2 [1], return the normalized counts by default to facilitate exploratory analysis, however the underlying object also stores the counts and the statistical analysis is also based on the counts.

To make things more concrete, in the DESeq2 paper [1], you will see that the counts are modelled as follows:

Let $K_{ij}$ be the counts of gene $i$ in sample $j$, then:

$$K_{ij} \sim \text{NegativeBinomial}( \text{mean} = \mu_{ij}, \text{dispersion} = \alpha_{i})$$ $$\mu_{ij} = q_{ij} s_{ij}$$

and $q_{ij}$ is connected to the predictors by using $\ln(\cdot)$ as the link function. Here $s_{ij}$ are the normalization factors you described.

In any case, both the counts $K_{ij}$ and the normalization factors $s_{ij}$ are used as data input into the model to do inference e.g. on the coefficients of the linear predictors of $\ln(q_{ij})$. In other words, the input does not consist of "normalized counts" or whatever else you might use for exploratory analysis.

[1] Love, M. I., Huber, W., & Anders, S. (2014). Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2. Genome biology

• Thanks for the reply. Also, I did not know negative binomial distribution could take a decimal number as its mean parameter; modeling this way makes much sense. – user5054 Oct 11 '16 at 17:29
• Yes! Similar also to e.g. the Poisson where the mean $\lambda$ can be an arbitrary real value $>0$. – air Oct 12 '16 at 5:03