Misclassification multi-state models with two timescales with application to estimating trends in dementia prevalence

Music City Center 

Multi-state models offer a versatile framework for modelling complex event history data, including panel observed data subject to misclassification error and left truncation. The state occupied by a patient is governed by a continuous-time discrete-state stochastic process, defined by transition intensities. The main computational challenge to fitting the models to panel observed data is the evaluation of the transition probabilities. Under a Markov assumption, subject-specific transition probabilities can be computed by directly solving the Kolmogorov Forward equations as a system of ordinary differential equations. However, the presence of continuous covariates makes this approach computationally unattractive for large datasets since a separate system must be solved for each unique covariate pattern in the data. To address this issue, the transition probabilities can be considered as a function of both time (for instance age) and continuous covariates (for instance calendar date of birth), where the function can be defined as the solution to a system of partial differential equations (PDEs). Standard approaches for obtaining approximate solutions to PDEs can then be applied to obtain solutions.

The method is illustrated through modelling of cognitive decline in the elderly population using the Health and Retirement Study (HRS). A four-state progressive process is assumed, consisting of normal cognition, mild cognitive impairment, dementia and death, where backward transitions in the observed trajectories are accounted for by allowing misclassification to adjacent cognition states. HRS aims to have a representative sample of the older population leading to subjects entering the study at various ages over 50. To account for this late entry, subjects can be assumed to be representative of living subjects of the same age and covariate pattern, with their initial state distribution inferred from the state distribution at age 50 and the transition probabilities between age 50 and their age at entry. However, HRS has run for over 30 years meaning cohort effects are present which affects the validity of standard left-truncation assumptions. To accommodate the cohort effect, calendar time is introduced as a second timescale which affects the magnitude of transition intensities and interacts with key covariates. The resulting model can be used to explore trends in prevalence and incidence of cognitive impairment.