To evaluate various ages to begin periodic breast cancer screening, we propose a method of analysis that can be applied to either a nonrandomized or a randomized study involving only a few screenings at regular intervals. For the analysis of data from a nonrandomized study, we assume (i) once breast cancer can be detected on screening and confirmed by biopsy, it will stay that way; (ii) given age, the probability of breast cancer detection does not depend on year of birth; and (iii) subjects who refuse screening have the same rates of breast cancer mortality following diagnosis as screened subjects had they not received screening. The key idea is that older screened subjects are controls for younger screened subjects. For the analysis of data from a randomized study, we relax assumption (iii). Based on the HIP randomized trial and assumptions (i) and (ii), we estimate that starting periodic breast cancer screening with mammography and physical examination at age 40 instead of age 50 reduces breast cancer mortality by 14 per 10,000 with a 95% confidence interval of (-4/10,000, 32/10,000). This must be weighed against an estimated increase in the number of biopsies that do not detect cancer of 580 per 10,000 with a 95% confidence interval of (520/10,000, 650/10,000).