Continuous-time multistate models are widely used for analyzing interval-censored data on disease progression over time. Sometimes, diseases manifest differently and what appears to be a coherent collection of symptoms is the expression of multiple distinct disease subtypes. To address this complexity, we propose a mixture hidden Markov model, where the observation process encompasses states representing common symptomatic stages across these diseases, and each underlying process corresponds to a distinct disease subtype. Our method models both the overall and the type-specific disease incidence/prevalence accounting for sampling conditions and exactly observed death times. Additionally, it can utilize partially available disease-type information, which offers insights into the pathway through specific hidden states in the disease process, to aid in the estimation. We present both a frequentist and a Bayesian way to obtain the estimates. The finite sample performance is evaluated through simulation studies. We demonstrate our method using the Nun Study and model the development and progression of dementia, encompassing both Alzheimer's disease (AD) and non-AD dementia.

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