Mammography screening programs are aimed at reducing mortality due to breast cancer by detecting tumors at an early stage. There is currently interest in moving away from the age‐based screening programs, and toward personalized screening based on individual risk factors. To accomplish this, risk prediction models for breast cancer are needed to determine who should be screened, and when. We develop a novel approach using a (random effects) continuous growth model, which we apply to a large population‐based, Swedish screening cohort. Unlike existing breast cancer prediction models, this approach explicitly incorporates each woman's individual screening visits in the prediction. It jointly models invasive breast cancer tumor onset, tumor growth rate, symptomatic detection rate, and screening sensitivity. In addition to predicting the overall risk of invasive breast cancer, this model can make separate predictions regarding specific tumor sizes, and the mode of detection (eg, detected at screening, or through symptoms between screenings). It can also predict how these risks change depending on whether or not a woman will attend her next screening. In our study, we predict, given a future diagnosis, that the probability of having a tumor less than (as opposed to greater than) 10‐mm diameter, at detection, will be, on average, 2.6 times higher if a woman in the cohort attends their next screening. This indicates that the model can be used to evaluate the short‐term benefit of screening attendance, at an individual level.