Causality and surrogate variable analysis

Abstract: Gene expression depends on thousands of factors and we usually only have access to tens or hundreds of observations of gene expression levels meaning we are in a high-dimensional setting. Additionally we don't always observe or care about all the factors. However, many different gene expression levels depend on a set of common factors. By observing the joint variance of the gene expression levels together with the observed primary variables (those we care about) Surrogate Variable Analysis (SVA) seeks to estimate the remaining unobserved factors. The ultimate goal is to assess whether the primary variable (or vector) has a significant effect on the different gene expression levels, but without estimating unobserved factors first the various regression models and hypothesis tests are dependent which complicates significance analysis. In this work we define a class of additive gene expression structural equation models (SEMs) which are convenient for modeling gene expression data and which provides a useful framework to understand the various steps of the SVA methodology. We justify the use of this class from a modeling viewpoint but also from a causality viewpoint by exploring the independence and causality properties of this class and comparing to the biologically driven data assumptions. For this we use some of the theory that has been developed elsewhere on graphical models and causality. We then give a detailed description of the SVA methodology and its implementation in the R package sva referring each step to different parts of the additive gene expression SEM defined previously.