The Colorectal Cancer Simulated Population model for Incidence and Natural history (CRC-SPIN; Fred Hutchinson Cancer Center) describes discrete event state transitions in continuous time. State transitions can depend on the age and sex of the individual and lesion location within the large intestine. For each simulated individual, CRC-SPIN first generates a time of birth and a time of death from causes other than CRC. Next, CRC-SPIN generates adenomas within the individual using a non-homogeneous Poisson process. The log-risk of developing a new adenoma is based on a log-linear model. Each individual is assigned a baseline log-risk that is normally distributed. Adenoma risk depends systematically on sex and varies in a piecewise log-linear way with age, with cut points at 50, 60 and 70. Once initiated, CRC-SPIN adenomas are randomly assigned a location in the large intestine.
CRC-SPIN simulates continuous adenoma size and models adenoma growth with a minimum detectable adenoma size equal to 1 mm and a maximum (but rarely reached) adenoma size of 50mm.1,2 For each adenoma, CRC-SPIN simulates a time to reach 10 mm using a Type 2 extreme value distribution. The time to reach 10 mm depends on adenoma location (colon or rectum). The adenoma growth rate is a closed function based on the (randomly distributed) time to reach 10 mm. Adenomas of any size may progress to preclinical CRC, although most do not progress within an individual’s simulated lifetime and transition at a small size is rare. The size at transition is a function of sex, location, and age at adenoma initiation.
The CRC-SPIN 2.0 model has been updated to simulate duration in the preclinical cancer state (sojourn time) using a Weibull distribution with shape parameter fixed at 5 (to focus on distributions with a limited range of skewness) and scale parameter (which determines mean sojourn time) that depends on adenoma location (colon or rectum). Individuals can have multiple preclinical cancers, and, given location, the sojourn time of each preclinical cancer is independent. Once a cancer becomes clinically detectable, the size and stage at clinical detection is simulated based on observed SEER data from 1975-1979 (a period of no screening). Given cancer size at clinical detection, the size during the preclinical period is determined using an exponential model, which assumes a minimum cancer size of 0.5 mm and replacement of adenoma cells with cancer cells until the cancer overtakes the adenoma. Stage at screen detection is assigned based on tumor size, with the restriction that the screen-detected stage must be earlier or equal to stage at clinical detection. After clinical detection, CRC-SPIN simulates the survival time to death from CRC using relative survival estimates from SEER, following an approach that is common across the three models.3
CRC survival time depends on age, calendar year, stage at detection, cancer location (colon or rectum), and sex. For individuals with synchronous CRCs at the time of diagnosis, CRC-SPIN uses the stage-specific survival of the cancer with the highest stage present. For individuals with CRC, their death date is set to the earliest simulated death date (either due to CRC death or other causes).
Risk Factor Modeling: The CRC-SPIN model includes a risk factor input that can be incorporated to increase or decrease cancer risk in the overall population or in subgroups of the population. Risk factor inputs can affect each state transition via multiplicative effects similar to accelerated failure time models. That is, risk factors can affect adenoma incidence, adenoma growth, transition to preclinical cancer, and sojourn time. This approach allows inclusion of basic (essential) risk factors, such as race, in the model. The model currently incorporates this risk information as an input (estimated outside the model) rather than a calibrated parameter (chosen in conjunction with other parameters to match target data). The CRC-SPIN model is currently being revised to incorporate differences in CRC risk by race/ethnicity.
References
- Janoschek A. Das reakionskinetische Grundgesetz und seine Beziehungen zum Wachstums und Ertragsgesetz. Stat Vjschr. 1957;10:25-37.
- Gille U, Salomon FV. Brain growth in mallards, Pekin and Muscovy ducks (Anatidae). J Zoology. 2000;252:399-404.
- Rutter CM, Johnson EA, Feuer EJ, Knudsen AB, Kuntz KM, Schrag D. Secular trends in colon and rectal cancer relative survival. J Natl Cancer Inst. 2013;105(23):1806-13.
