Algorithmic methods for interpreting the collective transcriptome (gene expression) patterns of disease cohorts in the context of biological networks are a cornerstone of systems medicine. The calibration of these algorithms using synthetic data with predefined statistical properties can be a relevant benchmarking procedure, facilitating the choice of the appropriate algorithm and the detailed mechanistic interpretation of the results. Here we present a generative model producing patterns of significantly up- and down-regulated genes for synthetic disease cohorts, in which the statistical agreement between the given biological network and the transcriptome patterns can be tuned. Parameters of this generative model are, among others, the size of the cohort, the number of disease-associated genes, the clustering of differentially expressed genes in the network and the network size. Several properties of the model can be analyzed analytically. In a first application of this generative model to produce test instances, we show that considering the subset of significant expression changes occurring in more than one patient of the cohort as an additional filtering step serves as an efficient noise suppression mechanism to enhance the recall of the signal contained in the data by the network connectivity.