Schematic overview of simulated life histories and effect of screening. The underlined words in the descriptions below refer to the words outlined in the figure. Sojourn time is the duration of the preclinical, screen-detectable phase of the tumor and lead time is the interval from screen detection to the time of clinical diagnosis, when the tumor would have surfaced without screening.
Model D is a state transition model where potential benefit from early detection arises because of a stage shift. The natural history of breast cancer is modeled analytically using stochastic models. The model assumes breast cancer (invasive) progresses from a no-disease state (S₀) to pre-clinical (S_p) state and to clinical state (S_c). Some cases will continue to the disease-specific death (S_d) state. Death due to other causes is treated as a competing risk. The S_p state begins when cancer is detectable at screening and S_c begins when cancer is diagnosed in absence of screening. For a given birth cohort, age-specific invasive breast cancer incidence rate and age-dependent sojourn time in pre-clinical state (published values) are used to estimate the transition probabilities from S₀ to S_p.The transition probabilities from S_p to S_c are estimated based on the age-specific breast cancer incidence rate. The other basic assumption is that any reduction in mortality associated with screening is from the stage-shift. That is screen-detected cases have a better stage distribution with a higher proportion of cases in earlier stages. The stage distribution data for screen-detected cases are obtained from BCSC and directly incorporated in constructing breast cancer specific survival. Also the lead time for screen-detected cases is treated as a random variable and adjusted in constructing the breast cancer specific survival for screen-detected cases. When cancer is diagnosed, a treatment is applied by age, stage and ER status and treatment reduces the hazard of breast cancer specific mortality by age, stage and ER status.
Model E is a microsimulation model based on continuous tumor growth. The natural history of breast-cancer is modeled as a continuously growing tumor from onset of cancer (starting with a tumor diameter of 0.1 mm). The moments that events happen are determined by tumor sizes. The screening threshold diameter determines the moment that the cancer is detectable at screening, and the diameter of clinical detection determines when the cancer will be diagnosed in the absence of screening. Each tumor has a size (the fatal diameter, which differs between tumors) at which diagnosis and treatment will no longer result in cure given available treatment options. If the tumor is diagnosed (either on the basis of clinical presentation with symptoms or by screening) and treated before the tumor reaches the fatal diameter, the woman will be cured and will die of non-breast cancer causes (death from other causes). Variation between tumors is modeled by probability distributions of parameters. Screening might detect tumors at a smaller tumor size with a larger probability of cure (because the tumor has not yet reached the fatal diameter) than when the cancer is diagnosed in the absence of screening.
Model G-E is a event-driven continuous time state transition model. Based on birth cohort-specific incidence curves, the date at which progressive breast cancer will appear clinically (if ever) is sampled, and the stage, ER and HER2 are then sampled based on age-period specific stage distributions for these parameters. A sojourn time is sampled from an age-specific distribution and the beginning of the sojourn period is defined as the clinical incidence date minus the sojourn time. If a screening event takes place during the sojourn period, it may detect the tumor with probability equal to the age-specific mammogram sensitivity. If the tumor is screen detected, a stage at detection is sampled from a probability distribution calculated from the observed lead time, the distributions of dwell times in the clinical stages, and the stage at the clinical detection date. Whether clinically or screen detected, treatment is sampled from an age-stage-ER-HER2-period specific distribution of possible treatment regimens. Each particular treatment regimen reduces the hazard of breast cancer mortality by a ratio that depends on age and stage at diagnosis, ER, and HER2. The date of breast cancer death (which may turn out to be after the date of death from other causes) is then sampled from the corresponding age-stage-ER-HER2-treatment regimen-specific survival function. Simulated women who do not have progressive breast cancer may have limited malignant potential (LMP) breast cancer. LMP breast cancer is modeled as never being clinically detected, and is never fatal. But it is screen-detectable for five years and, if screen-detected, its stage is always DCIS. These screen-detected LMP DCIS are then treated the same way as progressive breast cancer diagnosed during the DCIS stage, but treatment has no effect on mortality because these LMP tumors are never fatal.
Model W is a discrete-event, stochastic tumor growth simulation model. It simulates the natural history of breast-cancer using a continuous time growth model for tumor size and a Poisson process for tumor extent with a randomly assigned growth rate from a population level distribution. In the model breast cancer is assumed a progressive disease arising in the in situ stage. Model W further assumes a fraction of all tumors have “limited malignant potential” (LMP). This subtype is non-lethal, limited in size and stage to in situ and early localized disease and is predominately detected by screening mammography. If undetected for a fixed dwell period they are assumed to regress. Breast cancer can be detected by one of two methods: breast imaging (screen-detected), or by symptoms, where the likelihoods of detection are functions of a woman’s age and tumor size. Upon detection, a woman will receive standard treatment and depending on calendar year, and woman and tumor level characteristics, may also receive adjuvant treatment. Treatment effectiveness, a function of treatment type, is independent of the method of detection and is modeled as a “cure/no-cure” process.