One of the advantages of competitive gene set tests is that they can be applied just as easily to any genewise test statistic, no matter how complex. There is no need to be limited to two-group comparisons, for example. To be as general as possible, we assume throughout this article a linear model setup similar to that described previously (8 (link),24 ). Suppose that a gene expression experiment has been conducted resulting in log-expression values ygi for genes g = 1, … , G and RNA samples i = 1, … , n. We assume a linear model for the expected value of each expression value given the experimental design,
where the xij are covariates or design variables specifying which treatment condition is associated with each RNA sample, and the αgj are unknown regression coefficients representing expression log-fold changes (logFCs) between conditions in the experiment.
Each gene is assumed to have its own variance, . Expression values from different arrays are assumed to be independent, but expression values for different genes from the same RNA sample are generally not. The correlations cor(ygi,yg′i) = ρg,g′ are generally non-zero. Note that the ρg,g′ here represent residual correlations between genes across replicate samples, after the treatment effects μgi have been removed.
where the xij are covariates or design variables specifying which treatment condition is associated with each RNA sample, and the αgj are unknown regression coefficients representing expression log-fold changes (logFCs) between conditions in the experiment.
Each gene is assumed to have its own variance, . Expression values from different arrays are assumed to be independent, but expression values for different genes from the same RNA sample are generally not. The correlations cor(ygi,yg′i) = ρg,g′ are generally non-zero. Note that the ρg,g′ here represent residual correlations between genes across replicate samples, after the treatment effects μgi have been removed.
