It should be clear that in this framework, the gene-set analysis models are a specific instance of a more general gene-level regression model of the formZ=β01→+C1β1+C2β2+…+ε. The variables C 1, C 2, …, in this generalized gene-set analysis model can reflect any gene property, from the binary indicators used for the competitive gene-set analysis to continuous variables such as gene size and expression levels. Any transformations of, and interactions between, such gene properties can also be added. This generalized gene-set analysis model thus allows for testing of conditional, joint and interaction effects of any combination of gene sets and other gene properties. In practice, the competitive gene-set analysis implemented in MAGMA in fact uses such a generalized model by default, performing a conditional test of β s corrected for the potentially confounding effects of gene size, gene density and (if applicable, e.g. in meta-analysis) difference in underlying sample size, if such effects are present. This is achieved by adding these variables, as well as the log of these variables, as covariates to the gene-level regression model. The gene density is
