Epidemiological studies of dementia often use two-stage designs because of the relatively low prevalence of the disease and the high cost of ascertaining a diagnosis. The รฟrst stage of a two-stage design assesses a large sample with a screening instrument. Then, the subjects are grouped according to their performance on the screening instrument, such as poor, intermediate and good performers. The second stage involves a more extensive diagnostic procedure, such as a clinical assessment, for a particular subset of the study sample selected from each of these groups. However, not all selected subjects have the clinical diagnosis because some subjects may refuse and others are unable to be clinically assessed. Thus, some subjects screened do not have a clinical diagnosis. Furthermore, whether a subject has a clinical diagnosis depends not only on the screening test result but also on other factors, and the sampling fractions for the diagnosis are unknown and have to be estimated. One of the goals in these studies is to assess the relative accuracies of two screening tests. Any analysis using only veriรฟed cases may result in veriรฟcation bias. In this paper, we propose the use of two bootstrap methods to construct conรฟdence intervals for the di erence in the accuracies of two screening tests in the presence of veriรฟcation bias. We illustrate the application of the proposed methods to a simulated data set from a real two-stage study of dementia that has motivated this research.