  The preclinical stage of many neurodegenerative diseases can span decades
before symptoms become apparent. Understanding the sequence of preclinical
biomarker changes provides a critical opportunity for early diagnosis and
effective intervention prior to significant loss of patients' brain functions.
The main challenge to early detection lies in the absence of direct observation
of the disease state and the considerable variability in both biomarkers and
disease dynamics among individuals. Recent research hypothesized the existence
of subgroups with distinct biomarker patterns due to co-morbidities and degrees
of brain resilience. Our ability to early diagnose and intervene during the
preclinical stage of neurodegenerative diseases will be enhanced by further
insights into heterogeneity in the biomarker-disease relationship. In this
paper, we focus on Alzheimer's disease (AD) and attempt to identify the
systematic patterns within the heterogeneous AD biomarker-disease cascade.
Specifically, we quantify the disease progression using a dynamic latent
variable whose mixture distribution represents patient subgroups. Model
estimation uses Hamiltonian Monte Carlo with the number of clusters determined
by the Bayesian Information Criterion (BIC). We report simulation studies that
investigate the performance of the proposed model in finite sample settings
that are similar to our motivating application. We apply the proposed model to
the BIOCARD data, a longitudinal study that was conducted over two decades
among individuals who were initially cognitively normal. Our application yields
evidence consistent with the hypothetical model of biomarker dynamics presented
in Jack et al. (2013). In addition, our analysis identified two subgroups with
distinct disease-onset patterns. Finally, we develop a dynamic prediction
approach to improve the precision of prognoses.
