Parametric estimation procedures for screening programmes: Stable and nonstable disease models for multimodality case finding

This paper develops methods for estimating the parameters associated with early detection programmes. Disease is considered to have three states: a disease-free state or a state in which the disease cannot be detected, a preclinical state and a clinical state. The natural history of the disease is assumed to be progressive. The parameters to be estimated are the sensitivity of one or two disease detection modalities and the characteristics of the preclinical sojourn time distribution under both the stable disease and nonstable disease models. The stable-disease model assumes that the incidence or prevalence of a disease is independent of age or chronological time, while the nonstable disease model allows these quantities to depend on time. With the nonstable disease model, the relevant parameters can be jointly estimated by a two-step iteration procedure from the likelihood function. For the stable disease model, the sensitivity and the parameters of the sojourn time distribution of the preclinical state can be obtained directly from a conditional likelihood function. Applications are made to recent clinical trials for the early detection of breast cancer.