A Blockwise Mixed Membership Model for Multivariate Longitudinal Data: Discovering Clinical Heterogeneity and Identifying Parkinson's Disease Subtypes

Current diagnosis and prognosis for Parkinson's disease (PD) face formidable challenges due to the heterogeneous nature of the disease course, including that (i) the impairment severity varies hugely between patients, (ii) whether a symptom occur independently or co-occurs with related symptoms differs significantly, and (iii) repeated symptom measurements exhibit substantial temporal dependence. To tackle these challenges, we propose a novel blockwise mixed membership model (BM3) to systematically unveil between-patient, between-symptom, and between-time clinical heterogeneity within PD. The key idea behind BM3 is to partition multivariate longitudinal measurements into distinct blocks, enabling measurements within each block to share a common latent membership while allowing latent memberships to vary across blocks. Consequently, the heterogeneous PD-related measurements across time are divided into clinically homogeneous blocks consisting of correlated symptoms and consecutive time. From the analysis of Parkinson's Progression Markers Initiative data (n=1,531), we discover three typical disease profiles (stages), four symptom groups (i.e., autonomic function, tremor, left-side and right-side motor function), and two periods, advancing the comprehension of PD heterogeneity. Moreover, we identify several clinically meaningful PD subtypes by summarizing the blockwise latent memberships, paving the way for developing more precise and targeted therapies to benefit patients. Our findings are validated using external variables, successfully reproduced in validation datasets, and compared with existing methods. Theoretical results of model identifiability further ensures the reliability and reproducibility of latent structure discovery in PD.