A Bayesian approach to modelling the natural history of a chronic condition from observations with intervention

To assess the costs and benefits of screening and treatment strategies, it is important to know what would have happened had there been no intervention. In today's ethical climate, however, it is almost impossible to observe this directly and therefore must be inferred from observations with intervention. In this paper, we illustrate a Bayesian approach to this situation when the observations are at separated and unequally spaced time points and the time of intervention is interval censored. We develop a discrete-time Markov model which combines a non-homogeneous Markov chain, used to model the natural progression, with mechanisms that describe the possibility of both treatment intervention and death. We apply this approach to a subpopulation of the Wisconsin Epidemiologic Study of Diabetic Retinopathy, a population-based cohort study to investigate prevalence, incidence, and progression of diabetic retinopathy. In addition, posterior predictive distributions are discussed as a prognostic tool to assist researchers in evaluating costs and benefits of treatment protocols. While we focus this approach on diabetic retinopathy cohort data, we believe this methodology can have wide application.