A Bayesian Approach to Multi-State Hidden Markov Models: Application to Dementia Progression.

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Jonathan P Williams, Curtis B Storlie, Terry M Therneau, Clifford R Jack Jr, Jan Hannig

People are living longer than ever before, and with this arise new complications and challenges for humanity. Among the most pressing of these challenges is to understand the role of aging in the development of dementia.This paper is motivated by the Mayo Clinic Study of Aging data for 4742subjects 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 hierarchicalBayesian 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 cutoff 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.

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