Chronic disease projections in heterogeneous ageing populations: approximating multi-state models of joint distributions by modelling marginal distributions.

To quantify the effects of changes in risk factors for chronic diseases on morbidity and mortality, Markov-type multi-state models are used. However, with multiple risk factors and many diseases relating to these risk factors, these models contain a large number of states. In this paper, we present an alternative modelling methodology implemented in the National Institute for Public Health and the Environment chronic disease model. This model includes multiple states based on risk factor levels and disease stages but only keeps track of the marginal probability values. Starting from the multi-state model, differential equations are derived that describe the change of the marginal distribution for each risk factor class and disease stage, taking into account population heterogeneity and competing mortality risks. The model is illustrated by presenting results of a scenario affecting disease incidence by altering the risk factor distribution of the population. To show the strength of the approximating model, we compare its results to those of the multi-state Markov model.