Approximate Bayesian computation for the natural history of breast cancer, with application to data from a Milan cohort study

We explore models for the natural history of breast cancer, where the main events of interest are the start of asymptomatic detectability of the disease (through screening) and the time of symptomatic detection (through symptoms). We develop several parametric specifications based on a cure rate structure, and present the results of the analysis of data collected as part of a motivating study from Milan. Participants in the study were part of a regional breast cancer screening program, and their ten-year trajectories were obtained from administrative data available from the Italian national health care system. We first present a tractable model for which we develop the likelihood contributions of the observed trajectories and perform maximum likelihood inference on the latent process. Likelihood based inference is not feasible for more flexible models, and we implement approximate Bayesian computation (ABC) for inference. Issues that arise from the use of ABC for model choice and parameter estimation are discussed, including the problem of choosing appropriate summary statistics. The estimated parameters of the underlying disease process allow for the study of the effect of different examination schedules (age range and frequency of screening examinations) on a population of asymptomatic subjects.