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.

翻译：连续时间多状态模型被广泛用于分析随时间推移疾病进展的区间删失数据。有时，疾病的表现形式不同，看似一致的症状集合可能是多种不同疾病亚型的表现。为应对这种复杂性，我们提出了一种混合隐马尔可夫模型，其中观测过程包含代表这些疾病间共同症状阶段的各状态，而每个潜在过程对应一种独特的疾病亚型。我们的方法同时对总体及特定类型的疾病发病率/患病率进行建模，并考虑了抽样条件和精确观测的死亡时间。此外，该方法能够利用部分可用的疾病类型信息（这些信息提供了对疾病过程中特定隐藏状态通路的洞察）来辅助估计。我们提出了获取估计值的频率学派和贝叶斯学派两种方法。通过模拟研究评估了有限样本下的性能。我们利用修女研究展示了我们的方法，并对痴呆症（包括阿尔茨海默病和非阿尔茨海默病性痴呆）的发生和发展进行了建模。