Parallel designs with an end-of-treatment analysis are commonly used for randomised trials, but they remain challenging to conduct in rare diseases due to small sample size and heterogeneity. A more powerful alternative could be to use model-based approaches. We investigated the performance of longitudinal modelling to evaluate disease-modifying treatments in rare diseases using simulations. Our setting was based on a model describing the progression of the standard clinician-reported outcome SARA score in patients with ARCA (Autosomal Recessive Cerebellar Ataxia), a group of ultra-rare, genetically defined, neurodegenerative diseases. We performed a simulation study to evaluate the influence of trials settings on their ability to detect a treatment effect slowing disease progression, using a previously published non-linear mixed effect logistic model. We compared the power of parallel, crossover and delayed start designs, investigating several trial settings: trial duration (2 or 5 years); disease progression rate (slower or faster); magnitude of residual error (=2 or =0.5); number of patients (100 or 40); method of statistical analysis (longitudinal analysis with non-linear or linear models; standard statistical analysis), and we investigated their influence on the type 1 error and corrected power of randomised trials. In all settings, using non-linear mixed effect models resulted in controlled type 1 error and higher power (88% for a parallel design) than a rich (75% for a parallel design) or sparse (49% for a parallel design) linear mixed effect model or standard statistical analysis (36% for a parallel design). Parallel and delayed start designs performed better than crossover designs. With slow disease progression and high residual error, longer durations are needed for power to be greater than 80%, 5 years for slower progression and 2 years for faster progression ataxias. In our settings, using non-linear mixed effect modelling allowed all three designs to have more power than a standard end-of-treatment analysis. Our analysis also showed that delayed start designs are promising as, in this context, they are as powerful as parallel designs, but with the advantage that all patients are treated within this design.