Progressive diseases worsen over time and can be characterised by sequences of events that correspond to changes in observable features of disease progression. Here we connect ideas from two formerly separate methodologies – event-based and hidden Markov modelling – to derive a new generative model of disease progression: the Temporal Event-Based Model (TEBM). TEBM can uniquely infer the most likely group-level sequence and timing of events (natural history) from mixed data types. Moreover, it can infer and predict individual-level trajectories (prognosis) even when data are missing, giving it high clinical utility. Here we derive TEBM and provide an inference scheme based on the expectation maximisation algorithm. We use imaging, clinical and biofluid data from the Alzheimer’s Disease Neuroimaging Initiative to demonstrate the validity and utility of our model. First, we train TEBM to uncover a new sequence and timing of events in Alzheimer’s disease, which are inferred to occur over a period of ∼17.6 years. Next, we demonstrate the utility of TEBM in predicting clinical progression, and that TEBM provides improved utility over a comparative disease progression model. Finally, we demonstrate that TEBM maintains predictive accuracy with up to $50%$ missing data. These results support the clinical validity of TEBM and its broader utility in real-world medical applications.