Frequency-Domain Evaluation and Estimation of Semi-Markov Disease Natural History Models

Introduction: Natural history models must often be estimated from data that do not directly capture disease transitions. Semi-Markov processes let the risk of progression depend on the time spent in a health state, which Markov models need extra states to represent. Their limitation is computational: discretizing time introduces approximation error, and simulating individuals introduces Monte Carlo error and a non-differentiable calibration objective. Methods: We show that the model-implied prevalence, incidence and cause-specific mortality of a continuous-time semi-Markov model satisfy convol

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