Appendix 1c: Description of CRC-CPIN model for natural history and intervention
Model overview
For this analysis we will use the ColoRectal Cancer Simulated Population model for Incidence and Natural history (CRC-SPIN). CRC-SPIN is a semi-Markov microsimulation program to simulate the effect of screening and other interventions on colorectal cancer (CRC) incidence and mortality. With microsimulation we mean that each individual in the population is simulated separately. The model is semi-Markov in the sense that:
- Distributions other than exponential are possible in each disease state.
- Transitions can be age, location, and calendar time dependent.
All events in the model are discrete, but the durations in each state are continuous. Hence, there are no annual transitions in the model.
The CRC-SPIN model assumes that all colorectal cancers arise from an adenoma and models shifts from adenoma initiation to preclinical and clinically detectable CRC in continuous time using four components, described below. CRC-SPIN does not model adenomas <1mm, and implicitly assume that these are unobservable.
1. Adenoma Risk: CRC-SPIN models the occurrence of 1mm adenomas with a non-homogeneous Poisson process. Risk is modeled using a log-linear model. Baseline individual-level log-risk varies across individuals and has a Normal distribution. CRC-SPIN models systematic differences in the log-risk of adenomas for men and women, and by age. Age-effects are modeled using a piecewise linear age effect on log-risk with four age-risk intervals: [20,50), [50,60), [60,70), and (70. Under the CRC-SPIN model, individuals younger than 20 are not at risk of developing 1mm adenomas. Once initiated, adenomas are assigned a location using a multinomial distribution across 6 possible sites of the large intestine (from proximal to distal, with probabilities in parenthesis): 1) cecum (0.08); 2) ascending colon (0.23); 3) transverse colon (0.24); 4) descending colon (0.12); 5) sigmoid colon (0.24); and 6) rectum (0.09).
2. Adenoma Growth: CRC-SPIN models adenoma growth as a continuous process. We assume that adenoma growth varies independently across adenomas, both within and between individuals, and we allow different adenoma growth distributions for adenomas in the colon and rectum. The growth model used by CRC-SPIN is asymmetric, with exponential growth early that slows to allow an asymptote at 50mm, the maximum adenoma size. CRC-SPIN simulates adenoma growth by first simulating the time to reach 10mm using a type 2 extreme value distribution, and then solving for growth parameters. The type 2 extreme value distribution has a long right tail but does not heavily weight small values that indicate fast growth.
3. Transition from Adenoma to Invasive Cancer: CRC-SPIN models the cumulative probability of adenoma transition up to size s as a function of location (colon or rectum) and age at adenoma initiation. For an adenoma initiated at age a in the colon of a man, the probability of transition to preclinical cancer at or before size s is given by by (c(s,a) = (( [ln((1cms) + (2cm(a-50)]/ (3. where (( ) is the standard Normal cumulative distribution function. Cumulative transition probabilities for adenomas in the male rectum, and adenomas in the female colon and rectum have the same form, but with different parameters. For each adenoma, the size at transition is independently generated by simulating a Uniform[0,1] pseudodeviate and using an inverse cumulative distribution look-up.
4. Sojourn Time: Under the CRC-SPIN model, sojourn time is defined as the time from transition to preclincal cancer to clinical detection, defined as the onset of symptoms leading to detection in the absence of screening. We assume that the sojourn time of each preclinical cancer is independent and has a lognormal distribution that depends on adenoma location (colon or rectum).
Clinical Outcomes: Stage and Survival: Once a cancer becomes clinically detectable, CRC-SPIN simulates size and stage at clinical detection. We specify an overall (unconditional) distribution for tumor size at clinical detection using observed SEER size at detection from 1975-1979. We base the conditional distribution of stage given size on estimates from multinomial logistic regression models for the same SEER data. These models include linear and quadratic effects of tumor size on stage at detection. Given cancer size, we determine size during the preclinical period using an exponential model, which assumes a minimum cancer size of 0.5mm and replacement of adenoma cells with cancer cells until the cancer overtakes the adenoma.
Colorectal cancer relative survival probabilities are based on Cox proportional hazards models for relative survival applied to SEER survival data for cases diagnosed from 1975 to 1979, estimated using the CANSURV program (http://srab.cancer.gov/cansurv/). Proportional hazards models were stratified by location (colon or rectum) and AJCC stage. Age and sex were included as covariates. Age was treated as continuous, though people 25-34 were grouped with 35 year olds and people 90+ were grouped with 90 year olds due to small cell sizes. Other cause mortality uses survival probabilities based on product-limit estimates for age and birth-year cohorts from the National Center for Health Statistics Databases.
Simulation of screening
Individual life histories are simulated assuming there is no screening for colorectal cancer. After these life histories are simulated, screening is applied, to allow comparison of events with and without screening. The effectiveness of screening depends on the performance characteristics of the test performed: sensitivity, specificity and reach (for endoscopic tests). In the model, one minus the specificity is defined as the probability of a positive test result in an individual irrespective of any adenomas or cancers present. For a person without any adenomas or cancers, the probability of a positive test result is therefore equal to one minus the specificity. In individuals with adenomas or cancer the probability of a positive test result is dependent on the lack of specificity and the sensitivity of the test for the present lesions. Sensitivity in the model is lesion-specific, where each adenoma or cancer contributes to the probability of a positive test result.