We consider the assessment of the overall diagnostic accuracy of a sequence of tests (e.g. repeated screening tests). The complexity of diagnostic choices when two or more continuous tests are used in sequence is illustrated, and different approaches to reducing the dimensionality are presented and evaluated. For instance, in practice, when a single test is used repeatedly in routine screening, the same screening threshold is typically used at each screening visit. One possible alternative is to adjust the threshold at successive visits according to individual-specific characteristics. Such possibilities represent a particular slice of a receiver operating characteristic surface, corresponding to all possible combinations of test thresholds. We focus in the development and examples on the setting where an overall test is defined to be positive if any of the individual tests are positive ('believe the positive'). The ideas developed are illustrated by an example of application to screening for prostate cancer using prostate-specific antigen.