  Uncovering the heterogeneity in the disease progression of Alzheimer's is a
key factor to disease understanding and treatment development, so that
interventions can be tailored to target the subgroups that will benefit most
from the treatment, which is an important goal of precision medicine. However,
in practice, one top methodological challenge hindering the heterogeneity
investigation is that the true subgroup membership of each individual is often
unknown. In this paper, we aim to identify latent subgroups of individuals who
share a common disorder progress over time, to predict latent subgroup
memberships, and to estimate and infer the heterogeneous trajectories among the
subgroups. To achieve these goals, we propose a nonparametric fusion learning
method that can automatically identify subgroups and recover the heterogeneous
trajectories, which are represented by subject-specific unknown functions. We
approximate the unknown functions by B-splines, and apply a concave fusion
penalization method that can merge the estimated functions together for the
subjects belonging to the same subgroup. The resulting estimator of the disease
trajectory of each subgroup is supported by an asymptotic distribution. It
provides a sound theoretical basis for further conducting statistical inference
in subgroup analysis. Our method is applied to a longitudinal Alzheimer's
Disease data set.
