The abundance of medical imaging data from various healthcare organisations and concerns about patient data privacy have made it challenging to share data across institutions. Federated learning offers a promising solution for collaborative model training while preserving data privacy. In this work, we use our previous proposed pFedMTL approach to analyse diabetic retinopathy images using personalised multi-task federated learning. Our approach operates under the assumption that the data distribution of each client is a composite of unknown underlying distributions, effectively tackling issues associated with data heterogeneity and imbalance. We evaluate our method on six diverse medical imaging datasets: DDR, IDRID, FGADR, balanced DDR dataset, synthetic dataset, and balanced synthetic dataset, where our method is optimised to improve efficiency and accelerate convergence. Experimental results show that our approach is promising to be effective in analysing medically sensitive image data.