Inference of Onset Age of Preclinical State and Sojourn Time for Breast Cancer

Accurate estimation of the three key parameters (sensitivity, time duration in disease-free state and sojourn time in preclinical state) in cancer screening are critical. Likelihood method with a new link function was applied to the Health Insurance Plan of Greater New York (HIP) breast cancer screening data, to estimate the onset age of preclinical state and the sojourn time in the preclinical state for breast cancer.

A new link function to model sensitivity as a function of time in the preclinical state and the sojourn time was adopted. Markov Chain Monte Carlo simulations were used to obtain posterior samples and make inference on the three key parameters. Maximum likelihood estimate was also used for comparison.

The onset age of the preclinical state has a wide range for breast cancer; the peak onset age was 65.07 years (95% credible interval [C.I.], 55.76 to 73.02). The mean sojourn time was 2.00 years (95% C.I., 0.85 to 2.95). The 95 % C.I. for the sojourn time was 0.16 to 5.53 years. Sensitivity at onset of the preclinical state was 0.75 (95% C.I., 0.54 to 0.88); and sensitivity at the end of the preclinical state was 0.84 (95% C.I., 0.67 to 0.88).

The HIP study was the oldest breast cancer mass screening. The estimates reflect key parameters in those days with lower screening sensitivity. However, it is helpful to know other parameters in the planning for future breast cancer screening.