Models of cancer screening assume that cancers are detectable by screening before being diagnosed clinically through symptoms. The duration of this preclinical phase is called sojourn time, and it determines how much diagnosis might be advanced in time by the screening test (lead time). In the catch-up time method, mean sojourn time or lead time are estimated as the time needed for cumulative incidence in an unscreened population to catch up with the detection rate (prevalence) at a first screening test. The method has been proposed as a substitute of the prevalence/incidence ratio in the case of prostate cancer where incidence cannot be treated as a constant. A model is proposed to justify this estimator. It is shown that this model is different from classic Markov-type models developed for breast cancer screening. In both models, the catch-up time method results in biased estimates of mean sojourn time. Copyright © 2013 John Wiley & Sons, Ltd.