Screening for the early detection of cancer- III. Estimation of disease natural history

This paper concerns the statistical component of an overall investigation into screening. Its main focus is the estimation of a disease natural history described by a three-state model, with the following states: disease-free, preclinical, and clinical. Information to be used for estimation is that generated by an ongoing screening program. These data are used to provide maximum-likelihood estimates of the joint distribution of holding times in states, and this joint distribution is used to characterize a disease natural history. Classical descriptors of the natural history, such as age-specific preclinical prevalence, age-specific clinical incidence, and expected preclinical duration, can be computed from the joint distribution. Through a numerical example the estimates computed from the joint distribution are shown to be superior to those obtained by standard, epidemiologic methods. Also, the model-based approach enables estimation of important disease characteristics unattainable by the usual methods. A description of the likelihood maximization is included as is a demonstration of the inadequacy of age-specific prevalence and incidence information for estimating a disease natural history.