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Progressive diseases worsen over time and are characterised by monotonicchange in features that track disease progression. Here we connect ideas fromtwo formerly separate methodologies -- event-based and hidden Markov modelling-- to derive a new generative model of disease progression. Our model canuniquely infer the most likely group-level sequence and timing of events(natural history) from limited datasets. Moreover, it can infer and predictindividual-level trajectories (prognosis) even when data are missing, giving ithigh clinical utility. Here we derive the model and provide an inference schemebased on the expectation maximisation algorithm. We use clinical, imaging andbiofluid data from the Alzheimer's Disease Neuroimaging Initiative todemonstrate the validity and utility of our model. First, we train our model touncover a new group-level sequence of feature changes in Alzheimer's diseaseover a period of ${\sim}17.3$ years. Next, we demonstrate that our modelprovides improved utility over a continuous time hidden Markov model by areaunder the receiver operator characteristic curve ${\sim}0.23$. Finally, wedemonstrate that our model maintains predictive accuracy with up to $50\%$missing data. These results support the clinical validity of our model and itsbroader utility in resource-limited medical applications.

Learning transition times in event sequences: the Event-Based Hidden Markov Model of disease progression