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176 Ho et al.A different measure is needed to capture shifts, as in shift patterns one can havejoint differential expression even though the two class-conditional correlationsare very close. The quantityS shift= ρ + ρ −αρ1 2(3)with values of α between one and two, produces good empirical results indetecting shifts. When α =2, it is proportional to the difference between theaverage of the conditional correlations, and the combined correlation. Forillustration, α=2 is used throughout the chapter. In Fig. 1, if the grey and blacklines overlap, then S shjft= 0. When one of the two parallel lines for the twoclasses shifts up or down, the combined correlation, which is computed afterpooling the two classes, decreases whereas the class-conditional ones remainthe same. In this way, S shiftwill capture shifting patterns.For example, in Fig. 1, the two correlation-based scores are S cross= |–0.82 –(–0.83)| = 0.01 and S shift= |–0.82 + (−0.83) − 2 ⋅ (–0.68)| = 0.29 whereas in Fig. 2S cross= |0.85 − (−0.80)| = 1.64, and S shift= |0.85 + (−0.80) − 2 ⋅ (0.08)| = 0.11.These two correlation-based scores can be used to capture joint differentialexpression. They are intuitive and are computationally feasible in large searchspace. The same ideas can be extended straightforwardly to other kinds ofassociation measures for pairs of genes, such as Spearman’s correlation.Generalizations to searching for joint differential expression of groups of morethan three genes are not readily available, because of the pair-wise nature ofcorrelations. The implementation of these measures is straightforward in anyprogramming language with matrix manipulation functionality. The CorScor Rpackage provides tools for fast evaluation of S crossand S shift, as well as visualizationof interesting pairs and significance analysis. Use of the functions in theCorScor package requires previous installation of R and Bioconductor (seeSubheading 2.), and assumes that appropriate preprocessing of expression datais been carried out before joint differential-expression analysis. Bioconductorpackages affy (for Affymetrix chip experiments) and limma (for a variety ofother experiments including most two-channel arrays), include state-of-the-arttools and produce normalized data sets that are stored into objects of the classexprSet, that can be used as input to CorScor.Normalization of expression data can affect gene–gene correlations.Specifically, artifacts in gene–gene correlations can be caused by flooring ofexpression levels, and by exclusion of low-level readings followed by missing dataimputation. The latter combination can result in marking genes with similarly lowvalues as missing, and then replacing missing values with values with little variabilitybut very high correlation across genes. This generates falsely high correlationsand can impact the joint differential-expression analysis. The minimal