Fitting models of carcinogenesis to a case-control study of breast cancer

Data from a case-control study of breast cancer in 441 cases and matched controls aged less than or equal to 38 in Los Angeles is fitted to two models of carcinogenesis: the two-stage model of Moolgavkar and Knudson; and a multistage adaptation of the log/log model proposed by Pike et al. In the two-stage model, risk factors (here age at menarche, age at first pregnancy, abortion, regularity of cycling, benign breast disease, and use of oral contraceptives (OCs] are postulated to act either by increasing the rate of mutation of normal to intermediate or of intermediate to malignant stage cells, or by increasing the proliferation rates of such cells. In the multistage model, it is postulated that all transition rates are equally determined by the rate of cell turnover, which is in turn influenced by risk factors. In both models, positive family history is modelled in two ways: (1) all cells may have started in an intermediate stage at birth, with probability depending on the number and degree of affected family members; or (2) as an event rate modifier in the same way as other covariates. With only menarche or menarche and family history included, the multistage and two-stage models both produced likelihoods very similar to those from a simple logistic model, though both fit better than the logistic model as more covariates were added to the model. The two stage models offer greater flexibility in modelling the time at which each factor is most effective. We found irregular menstrual cycling to reduce the rate of proliferation of normal cells or their mutation rate to intermediate cells by 50% (p less than 0.025) and use of OCs to increase these rates by 3.25 fold (p less than 0.01). Having completed a pregnancy of more than 26 weeks gestation appeared to reduce the rate of intermediate cell proliferation by 5% (p less than 0.05) relative to a baseline rate of 14% per year. Benign breast disease was associated with a 1.60 fold increased rate of the second mutation (p less than 0.025). In all models, family history was by far the strongest risk factor (RR = 4.44 from the logistic model, p less than 0.0001). Covariates showed similar effects in the multistage model, though their magnitudes were slightly different.