There is evidence that the removal of adenomas, by endoscopy, from the large bowel can prevent the occurrence of colorectal cancer (CRC). However, the reduction in cancer incidence due to endoscopic surveillance is difficult to estimate. Studies of cohorts of adenoma patients typically rely on comparisons with groups of historical controls. We present a model for disease progression which enables estimation of this quantity without direct comparison to a reference group. Models are applied to data from the National Polyp Study. Rates of adenoma recurrence and progression to carcinoma are estimated based on study data and relevant literature. This allows calculation of the number of cancers expected in the absence of surveillance and, thus, the number of cancers prevented. Results are compared with the original analysis. Models estimate that surveillance reduced CRC incidence by at least 97% in this cohort. The majority of the effect was due to the initial removal of adenomas rather than the follow-up surveillance. These results are similar to those produced in the original analysis when using the most appropriate reference groups. They indicate that polypectomy and follow-up surveillance can lead to large reductions in cancer incidence which may have been under-estimated in previous studies.