Abstract
We propose a parametric model for describing chronic disease mortality from cohort data and illustrate its use for Type 2 diabetes. The model uses ideas from accelerated life testing in reliability theory and conceptualizes the occurrence of a chronic disease as putting the observational unit to an enhanced stress level, which is supposed to shorten its lifetime. It further addresses the issue of semi-competing risk, that is, the asymmetry of death and diagnosis of disease, where the disease can be diagnosed before death, but not after. With respect to the cohort structure of the data, late entry into the cohort is taken into account and prevalent as well as incident cases inform the analysis. We finally give an extension of the model that allows age at disease diagnosis to be observed not exactly, but only partially within an interval. Model parameters can be straightforwardly estimated by Maximum Likelihood, using the assumption of a Gompertz distribution we show in a small simulation study that this works well. Data of the Cardiovascular Disease, Living and Ageing in Halle (CARLA) study, a population-based cohort in the city of Halle (Saale) in the eastern part of Germany, are used for illustration.