Title: Bayesian analysis of RNA sequencing data

Abstract:
Massive parallel sequencing is quickly replacing microarrays as a technique to quantify genomic features on the level
of DNA or mRNA.We focus on the analysis of mRNA sequencing (RNAseq) data, which are counts of pieces of RNA (tags).
RNAseq is believed to be less prone to background noise than microarray data, and hence is particularly promising for
lowly abundant tags. We present a novel approach to model and analyze these data.

RNAseq data is still expensive, so sample sizes are usually small.
However, the number of tags measured is often enormous, so shrinkage of variance-related parameters may lead to more
stable estimates and inference. Methodology and software to do so are available, using a negative binomial (i.e.
Poisson-Gamma), but only for  restrictive study designs, e.g. two-group comparisons. Moreover, there is no consensus
on what model fits best to RNAseq data, and this may depend on the technology used. Usually, some generalization of
the Poisson or Binomial distribution that accounts for overdispersion is applied.

We developed a framework that allows for various count models, flexible study designs, random effects and shrinkage
across tags. Moreover, it incorporates a Bayesian-type of multiplicity correction.

Integrated nested Laplace approximations (INLA) for latent Gaussian models provide the desired model and design
flexibility: it covers a large variety of Bayesian additive models and the Laplace approximations avoid
computationally intensive MCMC. However, its standard implementation does currently not allow for estimating
parameters that depend on all tags, which is typically needed for shrinkage. Here, we discuss methods to apply INLA
using Bayesian shrinkage, which amounts to estimating parameters of hyperpriors. A hyperprior may correspond to a
prior that is used to model an overdispersion parameter or to a prior on the parameter of interest. In the first
case, it should lead to more stable variance estimates, while in the latter case it is used to shrink the posterior
towards the null-domain to deal with multiplicity.

We illustrate our approach on two data sets. After considering these, we suggest use of the zero-inflated negative
binomial as a powerful alternative to the negative binomial, because it leads to a better fit and less bias of the
overdispersion parameters for the low count tags.