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Abstract:
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Multi-state models are used to understand disease progression but the choice of state structure, for example to merge or separate two adjacent states of disease severity, can be uncertain. Important model outputs can be very sensitive to the choice of state structure, which depends on the data available, the purpose of the model, and how well the model fits the data. Formal statistical comparison between structures has received limited attention in the literature. A particular difficulty is that such models are estimated from differently aggregated data so likelihood methods, including Akaike Information Criterion (AIC), cannot be applied. We propose two approaches to the comparison of state-structures. The first is the Difference in Restricted AIC (DRAIC), a modification of the AIC, that compares models fit to different overlapping datasets on the data that they share. The second is to constrain the transition rates of the larger model to obtain equivalent predictions to the smaller and assess the constraints using standard statistical techniques. We will illustrate and compare these approaches with an example of disability progression modelling in psoriatic arthritis.
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