Estimation of progression of multi-state chronic disease using the Markov model and prevalence pool concept

Estimation of progression rates in the multi-state model is performed using the E-M algorithm. This approach is applied to data on Type 2 diabetes screening.Good convergence of estimations is demonstrated. In contrast to previous Markov models, the major advantage of our proposed method is that integrating the prevalence pool equation (that the numbers entering the prevalence pool is equal to the number leaving it) into the likelihood function not only simplifies the likelihood function but makes estimation of parameters stable.This approach may be useful in quantifying the progression of a variety of chronic diseases.While the relationship between exposure and outcome is explored in traditional epidemiology, the status of the disease in question is usually expressed as a dichotomous state: disease and non-disease. Categorizing the disease of interest into two states, more often than not, may not only widen the gap between epidemiologists, who are interested in the occurrence of disease, and clinicians, who are concerned with the prognosis of disease, but also limit investigation of the disease progression for the majority of chronic diseases. As a matter of fact, chronic diseases usually have a multi-state property for which a dynamic progression from the early stage to the late stage proceeds under the influence of a range of internal and external risk factors. In order to elucidate the mechanism of disease progression quantifying the multi-state natural history of the disease becomes important in the new era of epidemiology.Multi-state models are increasingly used to model the progression of chronic diseases [1,2]. Such models are useful for study of both natural history and progression of the related disease [3,4]. Examples include the estimation of transition rates of growth, spread of breast cancer [4], and outcomes of cardiac transplantation [2]. Quantifying the progression of chronic diseases from mild state to advanced state is also relevant to prevention a