Objective According to the Independent UK Panel on Breast Cancer Screening, the most reliable estimates of overdiagnosis for breast cancer screening come from stop-screen trials Canada 1, Canada 2, and Malmo. The screen-interval overdiagnosis fraction is the fraction of cancers in a screening program that are overdiagnosed. We used the cumulative incidence method to estimate screen-interval overdiagnosis fraction. Our goal was to derive confidence intervals for estimated screen-interval overdiagnosis fraction and adjust for refusers in these trials. Methods We first show that the UK Panel’s use of a 95% binomial confidence interval for estimated screen-interval overdiagnosis fraction was incorrect. We then derive a correct 95% binomial-Poisson confidence interval. We also use the method of latent-class instrumental variables to adjust for refusers. Results For the Canada 1 trial, the estimated screen-interval overdiagnosis fraction was 0.23 with a 95% binomial confidence interval of (0.18, 0.27) and a 95% binomial-Poisson confidence interval of (0.04, 0.41). For the Canada 2 trial, the estimated screen-interval overdiagnosis fraction was 0.16 with a 95% binomial confidence interval of (0.12, 0.19) and a 95% binomial-Poisson confidence interval of (−0.01, 0.32). For the Malmo trial, the estimated screen-interval overdiagnosis fraction was 0.19 with a 95% binomial confidence interval of (0.15, 0.22). Adjusting for refusers, the estimated screen-interval overdiagnosis fraction was 0.26 with a 95% binomial-Poisson confidence interval of (0.03, 0.50). Conclusion The correct 95% binomial-Poisson confidence interval s for the estimated screen-interval overdiagnosis fraction based on the Canada 1, Canada 2, and Malmo stop-screen trials are much wider than the previously reported incorrect 95% binomial confidence intervals. The 95% binomial-Poisson confidence intervals widen as follow-up time increases, an unappreciated downside of longer follow-up in stop-screen trials.