Background: It has been shown that a random-effects framework can be used to test the association between a gene's expression level and the number of DNA copies of a set of genes. This gene-set modelling framework was later applied to find associations between mRNA expression and microRNA expression, by defining the gene sets using target prediction information. Methods and results: Here, we extend the model introduced by Menezes et al. 2009 to consider the effect of not just copy number, but also of other molecular profiles such as methylation changes and loss-of-heterozigosity (LOH), on gene expression levels. We will consider again sets of measurements, to improve robustness of results and increase the power to find associations. Our approach can be used genome-wide to find associations and yields a test to help separate true associations from noise. We apply our method to colon and to breast cancer samples, for which genome-wide copy number, methylation and gene expression profiles are available. Our findings include interesting gene expression-regulating mechanisms, which may involve only one of copy number or methylation, or both for the same samples. We even are able to find effects due to different molecular mechanisms in different samples. Conclusions: Our method can equally well be applied to cases where other types of molecular (high-dimensional) data are collected, such as LOH, SNP genotype and microRNA expression data. Computationally efficient, it represents a flexible and powerful tool to study associations between high-dimensional datasets. The method is freely available via the SIM BioConductor package.