Abstract

   High-throughput (HT) RNA interference (RNAi) screens are increasingly
   used for reverse genetics and drug discovery. These experiments are
   laborious and costly, hence sample sizes are often very small. Powerful
   statistical techniques to detect siRNAs that potentially enhance
   treatment are currently lacking, because they do not optimally use the
   amount of data in the other dimension, the feature dimension.

   We introduce ShrinkHT, a Bayesian method for shrinking multiple
   parameters in a statistical model, where 'shrinkage' refers to
   borrowing information across features. ShrinkHT is very flexible in
   fitting the effect size distribution for the main parameter of
   interest, thereby accommodating skewness that naturally occurs when
   siRNAs are compared with controls. In addition, it naturally
   down-weights the impact of nuisance parameters (e.g. assay-specific
   effects) when these tend to have little effects across siRNAs. We show
   that these properties lead to better ROC-curves than with the popular
   limma software. Moreover, in a 3 + 3 treatment vs control experiment
   with 'assay' as an additional nuisance factor, ShrinkHT is able to
   detect three (out of 960) significant siRNAs with stronger enhancement
   effects than the positive control. These were not detected by limma. In
   the context of gene-targeted (conjugate) treatment, these are
   interesting candidates for further research.

Introduction

   Many clinical genomics studies suffer from low power and low
   reproducibility caused by small sample sizes. Small sample sizes may be
   due to high costs per sample, low availability of genomic material
   (e.g. for rare diseases) or even juridical restrictions (e.g. when
   administering an experimental drug to patients). The philosophy behind
   our method is to increase power and reproducibility by retrieving as
   much information as possible from the vertical data direction (feature
   space: genes, tags, small interference RNAs (siRNAs), etc.) for
   estimating differential treatment effects from the horizontal data
   direction (sample space).

   In statistical terms the latter is referred to as 'shrinkage'. In a
   classical setting, a shrinkage estimator is a weighted average between
   the estimator from the concerning feature and a pooled estimator from
   all features. Shrinkage of dispersion-related parameters, like σ^2 for
   the Normal distribution, is now commonly applied to genomics data and
   has been implemented in popular analysis software like limma [[30]1].
   We take a step further. We show that shrinking additional parameters,
   including the main parameter of interest, e.g. the treatment effect,
   may further enhance power and reproducibility. Our approach is an
   Empirical Bayes framework around a Full Bayes fitting method called
   Integrated Nested Laplace Approximation (INLA [[31]2]). Here, INLA
   provides a fast, flexible, versatile and accurate alternative to MCMC,
   whereas our framework uses the high-dimensional aspect of the data to
   estimate priors, which effectuates shrinkage.

   For the analysis of RNA-seq count data, we introduced ShrinkSeq
   [[32]3]. We showed its improved performance in terms of Receiver
   Operating Characteristic (ROC)-curves with respect to other methods
   like edgeR, baySeq and DESeq, in particular when the data contain many
   zeros and sample sizes are small. Here, we provide several extensions
   and new insights: 1) ability to handle high-dimensional Gaussian data;
   2) model selection properties when nuisance parameters are involved; 3)
   flexible and powerful inference with potentially asymmetric priors.

   High-throughput (HT) RNA interference (RNAi) screens [[33]4] are
   increasingly used for reverse genetics and drug discovery. Statistical
   methods used for HT screens data analysis are commonly borrowed from
   small-molecule screens or even other types of high-dimensional data
   methods. However, HT screens data differs from other high-dimensional
   data in fundamental ways. Firstly, HT screens data are more susceptible
   to technical effects, as the cell culture plates are handled several
   times over a multiple day period, and the various experimental steps
   are performed by a variety of equipment. Secondly, studies currently
   involve a very small (1-3) number of replicates per condition. Hence,
   statistical inference is often absent in HT RNAi studies: only fold
   changes and standard deviations are mentioned. Thirdly, HT screens data
   typically involve a large amount of observations for controls, which
   serve as references for condition effect but are not of primary