A Bayesian Mixture of Exponential Family Factor Models for Uncovering Disease Progression Subtypes

Patients affected by neurological disorders usually present substantial heterogeneity in multi-domain biomarkers and clinical measures. This heterogeneity arises from differences in disease stage, unique characteristics, and membership in distinct latent subtypes. Exploring such complex heterogeneity and identifying disease progression-related markers is crucial for early diagnosis and developing timely and targeted interventions. This paper proposes a mixture exponential family trajectory model to integrate markers from multiple modalities to learn the disease progression. We incorporate continuous neuroimaging and microRNA sequencing biomarkers, categorical clinical symptoms, and ordinal cognitive markers using appropriate exponential family distributions with lower-dimensional latent factors. The mixture model assigns subtype-specific parameters to these distributions for each mixture component, enabling the characterization of patients in heterogeneous latent subgroups. The proposed model can also describe the nonlinear trajectory of disease deterioration and provide a temporal sequence of decline for each marker. We develop a Bayesian estimation procedure coupled with efficient Markov chain Monte Carlo (MCMC) sampling schemes to perform statistical inference for the mixture model. The proposed method is assessed through extensive simulation studies and an application to Parkinson's Progression Markers Initiative (PPMI) to learn the temporal ordering and subtypes of neurodegeneration of Parkinson's disease (PD).