A Bayesian Approach to Multistate Hidden Markov Models: Application to Dementia Progression

Abstract

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.We formalize the discrete-state space exhibited in Figure 1 in which many of the states are defined by continuous biomarkers. The previous work of Jack et al. (2016) defined a state space similar to Figure 1, but in which the high/low burden biomarker states were defined by practitioner chosen, hard biomarker cut-points. Hard cut-points for discretizing continuous measurements of biological processes are practically and philosophically problematic, and have to be chosen more or less arbitrarily.Moreover, we illustrate a general and effective framework for fitting a continuoustime, discrete-state HMM within the Bayesian paradigm, and the infinitesimal generator matrix of the underlying Markov process is allowed to be truly time-inhomogeneous (as a function of an individual's age). Time must be treated as continuous because, as in much of medical research, subjects are often observed irregularly in time.Our final contribution is that in addition to the effect of age, the effects of the covariates gender, number of years of education, and presence of an APOE-ε4 allele on the infinitesimal transition rates are also estimated. The importance of these variables has been well documented in the medical literature but their effect on aging has not been studied in this context (i.e., how they affect the transition rates between states in Figure 1). In addition to the new insights these features bring to the medical community, flexible software to fit the models described below is provided at https://jonathanpw.github.io/software.html.Our analysis builds on the work of Jack et al. (2016) with more sophisticated modeling which allows for deeper insights. They found that a Markov model of disease progression for dementia is indeed a natural approach, that almost all rates are log-linear, and at age 5...

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