Current diagnosis of neurological disorders often relies on late-stage clinical symptoms, which poses barriers to developing effective interventions at the premanifest stage. Recent research suggests that biomarkers and subtle changes in clinical markers may occur in a time-ordered fashion and can be used as indicators of early disease. In this article, we tackle the challenges to leverage multidomain markers to learn early disease progression of neurological disorders. We propose to integrate heterogeneous types of measures from multiple domains (e.g., discrete clinical symptoms, ordinal cognitive markers, continuous neuroimaging, and blood biomarkers) using a hierarchical Multilayer Exponential Family Factor (MEFF) model, where the observations follow exponential family distributions with lower-dimensional latent factors. The latent factors are decomposed into shared factors across multiple domains and domain-specific factors, where the shared factors provide robust information to perform extensive phenotyping and partition patients into clinically meaningful and biologically homogeneous subgroups. Domain-specific factors capture remaining unique variations for each domain. The MEFF model also captures nonlinear trajectory of disease progression and orders critical events of neurodegeneration measured by each marker. To overcome computational challenges, we fit our model by approximate inference techniques for large-scale data. We apply the developed method to Parkinson's Progression Markers Initiative data to integrate biological, clinical, and cognitive markers arising from heterogeneous distributions. The model learns lower-dimensional representations of Parkinson's disease (PD) and the temporal ordering of the neurodegeneration of PD.
