A progressive three-state model to estimate time to cancer: a likelihood-based approach

Abstract

Background: To optimize colorectal cancer (CRC) screening and surveillance, information regarding the time-dependent risk of advanced adenomas (AA) to develop into CRC is crucial. However, since AA are removed after diagnosis, the time from AA to CRC cannot be observed in an ethically acceptable manner. We propose a statistical method to indirectly infer this time in a progressive three-state disease model using surveillance data.

Methods: Sixteen models were specified, with and without covariates. Parameters of the parametric time-to-event distributions from the adenoma-free state (AF) to AA and from AA to CRC were estimated simultaneously, by maximizing the likelihood function. Model performance was assessed via simulation. The methodology was applied to a random sample of 878 individuals from a Norwegian adenoma cohort.

Results: Estimates of the parameters of the time distributions are consistent and the 95% confidence intervals (CIs) have good coverage. For the Norwegian sample (AF: 78%, AA: 20%, CRC: 2%), a Weibull model for both transition times was selected as the final model based on information criteria. The mean time among those who have made the transition to CRC since AA onset within 50 years was estimated to be 4.80 years (95% CI: 0; 7.61). The 5-year and 10-year cumulative incidence of CRC from AA was 13.8% (95% CI: 7.8%;23.8%) and 15.4% (95% CI: 8.2%;34.0%), respectively.

Conclusions: The time-dependent risk from AA to CRC is crucial to explain differences in the outcomes of microsimulation models used for the optimization of CRC prevention. Our method allows for improving models by the inclusion of data-driven time distributions.

Keywords: Adenoma; Adenoma surveillance; Adenoma-carcinoma sequence; Colorectal cancer; Colorectal cancer surveillance; Interval-censored data; Maximum likelihood; Progressive three-state disease model; Simulation.

Fig. 1

Multi-state model of colorectal cancer. (A) Natural history process, (B) Observed transition pathways

Fig. 2

Schematic representation of 3 possible observation process leading to right-censoring (A) and interval- censoring (B and C). From top to bottom, all individuals are AF at time zero prior to start of surveillance (A) and remain AF until the end of their follow-up v_m, (B) detected to be AA, or (C) detected to be CRC

Fig. 3

Flow chart of inclusion and exclusion criteria from the adenoma cohort [34, 35]. Never colonoscopy: single entry with non-colonoscopic polypectomy at baseline, or because there was no colonoscopic examination in all visits including baseline. No findings at baseline colonoscopy, and no findings later: a single (i.e., baseline) entry as no finding, or all entries as no findings. CRC at baseline colonoscopy: a single (i.e., baseline) entry as CRC

Fig. 4

Comparison between survival curves from NPMLE estimate and Weibull model for the first transition time to AA

Fig. 5

Estimated cumulative incidence curves. (A) Cumulative distribution function (CDF) for patients treated with AA (red solid line) and NAA (blue dashed lines) since baseline. (B) CDF of CRC (black solid line) since AA onset, with 1000 bootstrapped CDF curves (grey lines)