Early detection of cancer by screening advances the date of diagnosis, but may or may not affect survival. To assess the survival benefit associated with early detection, one must estimate the distribution of time survived post lead-time, that is, after the unknown date when clinical diagnosis would have occurred in the absence of screening. One can then compare the adjusted survival of screen-detected cancer cases to other groups of cases not diagnosed by screening. This paper describes a model for the survival of screen-detected cases, with a hazard function that depends on an individual's lead time, the duration of preclinical disease, and the time since diagnosis. The model is fitted to the ten year survival data from the 132 screen-detected cases of breast cancer in the well-known HIP (Health Insurance Plan of Greater New York) study. Comparison with the survival of several groups of cancer cases not detected by screening (interval cases arising clinically in persons previously screened, cases among persons who refuse screening, and cases among randomized controls not offered screening) yields various estimates of benefit. Use of the interval cases for comparison gives an estimate of about 21 breast cancer deaths prevented among 20, 166 women screened in the HIP study; use of the data from the randomized controls gives an estimate of about 25 prevented deaths. The former estimate derives from the screened group of women only, and so the same method of evaluation may also be applied to community screening programmes and other situations that do not entail randomization.