BACKGROUND: Mutational processes of diverse origin leave their imprints in the genome during tumour evolution. These imprints are called mutational signatures and they have been characterised for point mutations, structural variants and copy number changes. Each signature has an exposure, or abundance, per sample, which indicates how much a process has contributed to the overall genomic change. Mutational processes are not static, and a better understanding of their dynamics is key to characterise tumour evolution and identify cancer cell vulnerabilities that can be exploited during treatment. However, the structure of the data typically collected in this context makes it difficult to test whether signature exposures differ between conditions or time-points when comparing groups of samples. In general, the data consists of multivariate count mutational data (e.g. signature exposures) with two observations per patient, each reflecting a group. RESULTS: We propose a mixed-effects Dirichlet-multinomial model: within-patient correlations are taken into account with random effects, possible correlations between signatures by making such random effects multivariate, and a group-specific dispersion parameter can deal with particularities of the groups. Moreover, the model is flexible in its fixed-effects structure, so that the two-group comparison can be generalised to several groups, or to a regression setting. We apply our approach to characterise differences of mutational processes between clonal and subclonal mutations across 23 cancer types of the PCAWG cohort. We find ubiquitous differential abundance of clonal and subclonal signatures across cancer types, and higher dispersion of signatures in the subclonal group, indicating higher variability between patients at subclonal level, possibly due to the presence of different clones with distinct active mutational processes. CONCLUSIONS: Mutational signature analysis is an expanding field and we envision our framework to be used widely to detect global changes in mutational process activity. Our methodology is available in the R package CompSign and offers an ample toolkit for the analysis and visualisation of differential abundance of compositional data such as, but not restricted to, mutational signatures.