We derive mathematical expressions for the size distribution of screen-detectable pre-malignant lesions, both conditional and unconditional on no prior detection of cancer in the tissue of interest, based on a general multistage clonal expansion model of carcinogenesis. We apply these expressions to simulate the natural history of colorectal cancer and to evaluate the effect of a screen for adenomatous polyps and concomitant intervention on cancer risk. Our approach allows the efficient simulation of multiple screens and interventions and determination of the optimal timing of the screens. We further demonstrate the utility of our approach by computing the benefits of up to two colonoscopies on the lifetime risk of colorectal cancer.