An early- and late-stage convolution model for disease natural history

The standard convolution model of disease natural history posits an asymptomatic (preclinical) and a symptomatic (clinical) state. An augmented model includes, in both the preclinical and clinical states, an early and late stage of disease. In the case of cancer, the early stage would generally correspond to the organ-confined stages before there is evidence of cancer spread. We compute the number of screen-detected (preclinical) and clinical cases in the early and late stages expected under a given screening program and show how the model can be fit to data from a screening trial using maximum likelihood. We also develop expressions for sojourn time, lead time, and overdiagnosis in the context of the model, where each of the above concepts incorporates disease stage. As an example, we fit the model to data from the Mayo Lung Cancer Screening trial.