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Alternative splicing produces multiple functional transcripts from a single gene. Dysregulation of splicing is known to be associated with disease and as a hallmark of cancer. Existing tools for differential transcript usage (DTU) analysis either lack in performance, cannot account for complex experimental designs or do not scale to massive single-cell transcriptome sequencing (scRNA-seq) datasets. We introduce satuRn, a fast and flexible quasi-binomial generalized linear modelling framework that is on par with the best performing DTU methods from the bulk RNA-seq realm, while providing good false discovery rate control, addressing complex experimental designs, and scaling to scRNA-seq applications.