Fitting a progressive 3-state colorectal cancer model to interval-censored surveillance data under outcome-dependent sampling using a weighted likelihood approach

To optimize colorectal cancer (CRC) surveillance, accurate information on the risk of developing CRC from premalignant lesions is essential. However, directly observing this risk is challenging since precursor lesions, that is, advanced adenomas (AAs), are removed upon detection. Statistical methods for multistate models can estimate risks, but estimation is challenging due to low CRC incidence. We propose an outcome-dependent sampling (ODS) design for this problem in which we oversample CRCs. More specifically, we propose a 3-state model for jointly estimating the time distributions from baseline colonoscopy to AA and from AA onset to CRC accounting for the ODS design using a weighted likelihood approach. We applied the methodology to a sample from a Norwegian adenoma cohort (1993-2007), comprising 1495 individuals (median follow-up $6.8$ years; IQR, 1.1-12.8) of whom 648 did and 847 did not develop CRC. We observed a 5-year AA risk of 13% and 34% for individuals having nonadvanced adenoma (NAA) and AA removed at baseline colonoscopy, respectively. Upon AA development, the subsequent risk to develop CRC in 5 years was 17% and age-dependent. These estimates provide a basis for optimizing surveillance intensity and determining the optimal trade-off between CRC prevention, costs, and use of colonoscopy resources.