Analysis of the Natural History of Dementia Using Longitudinal Grade of Membership Models
We present a longitudinal form of the Grade of Membership (GoM) model for time-varying covariates, provide a self-contained description of its estimation, and illustrate its application with a substantively meaningful analysis of the progression of dementia among National Long Term Care Survey (NLTCS) respondents. The chapter has two goals—one methodological and the other substantive. Methodologically, we present the Kuhn-Tucker conditions for convergence of the maximum likelihood estimator and show how the associated estimates can be obtained using a new constrained form of the Newton-Raphson iteration algorithm that preserves the summation constraints at each update; we also present and discuss known results regarding the consistency and asymptotic normality of the longitudinal GoM model and offer a conjecture regarding how these results might be extended to the less restrictive cross-sectional form of the GoM model. Substantively, the natural history of dementia is modeled as a complex irreversible multidimensional process governed by a latent three-dimensional bounded state-space process. Individual dementia cases are initially widely dispersed in the latent state space. Over time, they move to state-space locations associated with severe cognitive and physical impairment and dramatically increased need for care. The application to the NLTCS data has been independently validated using Alzheimer’s disease data from the two cohorts of the Predictors Study.
