Natural History

The natural history component of the model pertains to any aspect of CRC development (non-clinical or clinical) and death from any cause. At the start of the simulation, each individual is assigned a maximum lifespan using U.S. life tables, taking into account his or her sex and race. Simulated people either die at the end of this assigned lifespan from reasons unrelated to CRC, or die from CRC earlier than the assigned lifespan. Polyps can begin to grow from birth, progressing to pre-clinical or clinical cancer, with event rates dependent on age, race, and gender. If individuals are screened, polyps and preclinical cancer can be identified earlier, affecting cancer and cancer deaths.

Maximum CRC-Free Lifespan

A random number is generated from the uniform distribution for each simulated person. The maximum lifespan is the age at which the random number is less than the cumulative probability of death from the sex- and race-specific life table of 2004 [1]. The death rates for black females and black males are applied to all individuals in the population whose race is not white. If the simulated individual does not die from CRC (an event determined later), he or she dies from other causes at the age of the maximum (CRC-free) lifespan. The model assumes that the life table and survival experience remains constant for all simulated cohorts.

Lesion Incidence

A lesion is defined as a spot on the colon that develops into either a polyp or a cancer. Two types of lesions are defined:

• Type 0 lesion – starts as a polyp and may later develop into cancer
• Type 1 lesion – starts immediately as cancer

Each individual in the model may develop no lesions or multiple lesions of each type during his or her lifetime. The set of moments when an individual develops each lesion type is controlled by overall lesion incidence rates and individual risk factor values. The user can control the overall incidence rate and allow for individual variation in the probability of lesion development.

Development of Polyps

Polyps develop progressively through three different sizes: small, medium, and large. In this model, medium and large polyps may develop into a cancer. However, small polyps cannot progress directly into cancer; they must first develop into medium or large polyps.. The transition of a polyp from one size to another or into a cancer is controlled by random waiting times taken from an exponential distribution. For example, since a medium polyp may develop into either a large-sized polyp or a cancer, a waiting time is generated for each of these two possibilities. The shorter of the two waiting times dictates both the time of the transition and the new state into which the small polyp will transition.

Development of Cancer

Cancerous lesions develop through four stages. These stages can represent any specifications of the user. In the current model we used the clinical stages defined by the American Joint Committee on Cancer [2] that correspond to the extent of the malignancy. The time spent in each stage before progression to the next stage is taken from an exponential distribution. A cancer in the fourth stage cannot progress to any further stage. As a consequence, cancers that reach the fourth stage remain in the fourth stage.

Clinical Detection of Cancer

In each of the four cancer stages, symptoms of a cancerous lesion may lead a provider to suspect cancer and recommend a diagnostic test. To determine whether this happens, when a person enters a cancer stage, the model uses an exponential distribution to compute a random waiting time until the emergence of symptoms. If the time until symptom emergence is shorter than the time until progression to the next cancer stage, the person will exhibit symptoms in that cancer stage and become eligible for a diagnostic test. Otherwise, the person does not exhibit symptoms and the cancerous lesion eventually progresses to the next cancer stage. If the person exhibits symptoms, elects to take a diagnostic test, and the result is positive, the cancerous lesion is considered to be clinically detected. At this point, the model stops tracking its progression to more severe stages, and the person remains in the state represented by his or her stage at diagnosis until death. If the person elects not to take the diagnostic test or the result is negative, the cancerous lesion remains undetected and eventually progresses to the next cancer stage.

Death from Cancer

A person may die from cancer before or after clinical detection. The model first determines whether the person will survive the cancer with certainty. This determination is made using a survival probability for each stage at detection. If the person will not survive the cancer with certainty, the model then calculates the time from cancer until death. This waiting time is chosen randomly from an exponential distribution, where the parameters of the distribution vary based on the stage at diagnosis. The waiting time is shortened if the person elects not to receive cancer treatment. If the waiting time until death from cancer expires before the person reaches his or her expected lifespan, he or she is considered to have died from CRC. Otherwise, the individual is considered to have died from other causes. In this model, all CRC deaths are preceded by clinical detection, and death from CRC does not affect the expected age at death from other causes. 

Sources:

1. Arias E. United States life tables, 2002. National vital statistics reports; 2004. Vol. 53, No. 6. Hyattsville (MD): National Center for Health Statistics.
2. Edge SB, Compton CC. The American Joint Committee on Cancer: the 7^thedition of the AJCC cancer staging manual and the future of TNM. Ann Surg Oncol. 2010;17(6):1471-1474. DOI: 10.1245/s10434-010-0985-4