*Modelling*

To predict the expected number of cancers in a randomized trial of screening, we utilized the OncoSim-Breast model, a microsimulation tool, based partially on the NCI CISNET Wisconsin-Harvard model that has been described previously [25,26]. OncoSim Breast has been validated by comparing its estimates with empirical breast cancer incidence both in an era prior to the implementation of screening programs and after programs were in place. There is no explicit modelling of a mechanism for overdetection in the algorithm; however, a range of cancer progression and growth rates are incorporated in the software. This would provide a distribution of cancers with varying levels of aggressiveness in the simulated population. Some of the slower-growing cancers "created" in the model should exhibit the phenomenon of overdetection. In particular, the model treats in situ and invasive cancers as parallel, partially independent processes. As in situ cancers develop over time, they have a probability of either transitioning into the invasive phenotype or remaining in situ and this can also give rise to overdetection.

The modeling represents a study even more rigorous than the conditions of a randomized trial in that the characteristics of the simulated participants are not only statistically similar, but rather they are perfectly matched; essentially, the simulation creates a study in which each woman in one cohort is matched with her identical twin in the other. For CNBSS1, we simulated a set of birth cohorts of women equally distributed over birth years, such that women would be in the age range of 40–49 at the beginning of the trial. The model inputs assume that prior to the beginning of the trial there is no screening in either arm. For half of the women (MP arm), the model was configured to estimate the number of in situ and invasive breast cancers that would be detected each year if the women received annual screening mammography and clinical examination. For the other half (UC), the model simulated a single screen by clinical examination in the year of entrance to the study and then followed the cohort without any screening intervention, again estimating the number of in situ and invasive cancers that would surface.

For CNBSS2, the same approach was taken; however, the interventions for the two study arms included a total of 40,000 women who would be in their 50s at the onset of the trial. The MP group received clinical examination and mammography annually, while the PE group received only annual clinical breast examination.

For both studies, for the purpose of modelling, it was assumed that no screening occurred in either trial arm after the intervention period. To reduce stochastic noise in modeling, 32 million histories were run and the results were scaled down to the 25,000 women in each arm for CNBSS1 and 20,000 for CNBSS2.
