Background: Breast cancer (BC) screening, primarily age-based, is a major public health program in many wealthy countries. At the same time, there is a dramatic increase in using genetics to support personalized medicine. These two approaches would seem antithetical. However, they can join powerfully with the possibility of using genetic information as the basis for a major shift from age-based to a risk-based BC screening programs. Aim: To assess the prospective cost-effectiveness of such a shift to risk-based BC screening requires representative population data on the relationships among a woman's age when a risk assessment is done, her family history of cancer in the context of pedigree data, and specific features of her genotype - comprising both the presence of rare genetic mutations like BRCA1/2 and recently derived polygenic risk scores. We use our newly developed Genetic Mixing Model (GMM) to estimate this joint distribution as the initial step in assessing the prospective cost-effectiveness of risk stratified BC screening in Canada. Methods: BOADICEA is a BC risk stratification algorithm already in wide use around the world, and in particular in Ontario, for high risk screening. A new version of BOADICEA incorporating a polygenic risk score has recently (will have) been published. We embedded the new core BOADICEA algorithm into the GMM. GMM thus provides the empirical foundation for assessing risk stratification for a representative population by constructing an estimate of the multivariate joint distribution of family history, presence of rare genetic mutations including BRCA1/2, and a polygenic risk score, derived from genome-wide association studies. Results: Using a polygenic risk score (PRS) would be far more useful for stratifying women according to their risk of breast cancer than the two most commonly used indicators at present: family history and rare genetic mutations. We have assessed a variety of combinations of these genetic indicators, in combination with offering universal risk assessment to women in Canada at various ages, and using different thresholds for categorizing women as being at high risk. The optimal age for risk assessment is in the 35 to 40 range. And the PRS is substantially more useful than family history or rare mutations for stratifying women for screening intensity by their risk of BC. Conclusion: Shifting from the current public health approach of primarily age-based screening for breast cancer, to one based on risk stratification, especially making use of recent advances in assessing polygenic risk, offers major potential benefits.