Screening for the early detection of cancer- I. The temporal natural history of a progressive disease state

In this report, we characterize the natural history of a chronic disease state in terms of the distribution of X (a person's age at the time of entering the disease state), Y (the sojourn time in that disease state), and A (a person's present age) over a population of individuals. In terms of this distribution, we are able to define formally such traditional epidemiologic descriptors as age specific incidence and prevalence, lifetime attack rate, mean duration of the disease state, cohort effect. Length biased sampling and lead time due to screening can also be developed within this framework. By casting the description of a disease state's natural history in such a framework, we lay the groundwork for a statistical theory of estimation in epidemiology that has heretofore been lacking. Moreover, the present formulation casts light on conditions under which certain "classical" epidemiologic relationships actually obtain.