Believe the Extreme (BE) Strategy at the Optimal Point:What Strategy will it become?

The choice of what tests to sequence is essential in making a clinical decision. A variety of sequential techniques have been proposed to combine tests to increase the overall accuracy, including Believe the Positive (BP), Believe the Negative (BN), and the relatively new Believe the Extreme (BE). For a two test sequence, the BP strategy administers Test 2 only if the results on Test 1 are not positive. Similarly, the BN strategy administers Tests 2 only if the results on Test 1 are not negative. For both of these strategies (BP and BN), two thresholds are required. In the BE strategy, only those subjects who tested neither positive nor negative for disease with Test 1 are administered Test 2. Thus there are 3 thresholds for a two test BE strategy: 2 for the initial test, and 1 for the second test. The BE strategy can at times approximate the BP and BN strategies if the upper threshold on the first test is estimated very high or low. This paper explores the BE strategy while varying parameters associated with the features of each test to determine when the BE strategy behaves as a BP or BN strategy, as opposed to requiting all three thresholds. Two practical examples are presented: sleep apnea data and pancreatic cancer. The sleep apnea study shows that the BE strategy might actually function as a BN strategy. The cancer study shows how BE can display better accuracy and lower cost than either the BN or BP strategies.