Studies for assessing non-inferiority or superiority of a new diagnostic or screening test relative to a standard test use a complete matched-pairs design in which results for both tests are obtained for all subjects. We present alternative tests for the situation where results on the standard test are obtained for all subjects but results on the new test are obtained for a subset of those subjects only. This situation is common when results for the standard test are available from a large biobank. We present a stratified random sampling procedure for drawing the subsample of subjects that receive the new diagnostic test with strata defined by the two outcome categories of the standard test. We derive appropriate statistical tests for non-inferiority and superiority of the new diagnostic test. We will show how the number of subjects that receive the new test can be minimized by non-proportional stratified random sampling. Copyright © 2012 John Wiley & Sons, Ltd.