Disease progression modelling of Alzheimer's disease using probabilistic principal components analysis

The recent biological redefinition of Alzheimer's Disease (AD) has spurred the development of statistical models that relate changes in biomarkers with neurodegeneration and worsening condition linked to AD. The ability to measure such changes may facilitate earlier diagnoses for affected individuals and help in monitoring the evolution of their condition. Amongst such statistical tools, disease progression models (DPMs) are quantitative, data-driven methods that specifically attempt to describe the temporal dynamics of biomarkers relevant to AD. Due to the heterogeneous nature of this disease, with patients of similar age experiencing different AD-related changes, a challenge facing longitudinal mixed-effects-based DPMs is the estimation of patient-realigning time-shifts. These time-shifts are indispensable for meaningful biomarker modelling, but may impact fitting time or vary with missing data in jointly estimated models. In this work, we estimate an individual's progression through Alzheimer's disease by combining multiple biomarkers into a single value using a probabilistic formulation of principal components analysis. Our results show that this variable, which summarises AD through observable biomarkers, is remarkably similar to jointly estimated time-shifts when we compute our scores for the baseline visit, on cross-sectional data from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Reproducing the expected properties of clinical datasets, we confirm that estimated scores are robust to missing data or unavailable biomarkers. In addition to cross-sectional insights, we can model the latent variable as an individual progression score by repeating estimations at follow-up examinations and refining long-term estimates as more data is gathered, which would be ideal in a clinical setting. Finally, we verify that our score can be used as a pseudo-temporal scale instead of age to ignore some patient heterogeneity in cohort data and highlight the general trend in expected biomarker evolution in affected individuals.