Patients cured of ulcers, carcinomas or other recurrent conditions are randomized between two treatments designed to maintain their recovery. Spontaneous reporting of relapse is supplemented by periodic asymptomatic screening. Interest centres on the difference in times to relapse between the two treatments. However, the analysis is complicated by the times to diagnoses at screens being qualitatively different from the times to symptomatic diagnoses between screens. In this paper a number of approaches to the analysis of such data are explored, and one of them is recommended. An extensive example with data on ulcer recurrence is presented to illustrate the method.