USING MULTI-STATE MODELS FOR ANALYSIS

Abstract

Multi-state models as shown in figure 1 have several strengths for the analysis and summary of a subject's traversal of the path from cognitively normal (CN) through dementia. We will discuss some of these, along with examples and details of their implementation. The Mayo Clinic Study of Aging multi-state transition model. All states can transition to death. The underlying model is a simple diagram of the patient states and possible transitions between them. Software for fitting the models is freely available but not yet widely utilized. The methods fall into two disjoint classes. The first applies to cases where the actual transitions between states are observed, e.g., competing risks (Putter http://dx.doi.org/10.1002/sim.2712). The second applies to cases where a subject’s state is recorded at regular visits but the exact event times are unknown (Satten, Applied Statistics 1996). We fit models of both types using the survival, mstate, and msm packages in R. A primary advantage of this approach is that it views the disease process in toto, and as such can generate results on multiple levels, e.g., the predicted future path for a subject given their starting age and state, the population prevalence across states of living subjects, the lifetime probability of ever being demented, and perhaps most useful, estimates of the underlying event rates. Figures 1-3 below are from the Mayo Clinic Study of Aging (MCSA), a population based study of cognitive aging. Figure 1 shows the underlying multi-state model that was assumed. Figure 2 shows the estimated progression rates from the model as a function of age, and figure 3 the fitted model's predicted distribution of states for living subjects. We see the following: (1) Rates increase exponentially with age, only one plateaus; (2) Simple biology (figure 2) can generate a complex interplay of observed frequency (figure 3); amd (3) Stage 1 NIA-AA pre-clinical AD (A+N-) is not benign. It carries an elevated risk for transition to A+N+ which in turn has the highest rate of transition to dementia. Estimated biomarker transition rates by age. Estimated percentage of participants in each state at a given age among those who are alive. Multi-state models are a worthwhile addition to the analysis toolbox, and can give further insight into underlying disease processes. Computational tools to fit the models are increasingly available.