  People are living longer than ever before, and with this arises new
complications and challenges for humanity. Among the most pressing of these
challenges is of understanding the role of aging in the development of
dementia. This paper is motivated by the Mayo Clinic Study of Aging data for
4742 subjects since 2004, and how it can be used to draw inference on the role
of aging in the development of dementia. We construct a hidden Markov model
(HMM) to represent progression of dementia from states associated with the
buildup of amyloid plaque in the brain, and the loss of cortical thickness. A
hierarchical Bayesian approach is taken to estimate the parameters of the HMM
with a truly time-inhomogeneous infinitesimal generator matrix, and response
functions of the continuous-valued biomarker measurements are cut-point
agnostic. A Bayesian approach with these features could be useful in many
disease progression models. Additionally, an approach is illustrated for
correcting a common bias in delayed enrollment studies, in which some or all
subjects are not observed at baseline. Standard software is incapable of
accounting for this critical feature, so code to perform the estimation of the
model described below is made available online.
