Medical diagnostic test based on the potential test result approach: Bounds and identification

Evaluating the performance of a medical diagnostic test is an important issue in disease diagnosis. Youden [Index for rating diagnostic tests, Cancer 3 (1950), pp. 32-35] stated that the ideal measure of performance is to ensure that the control group resembles the diseased group as closely as possible in all respects except for the presence of the disease. To achieve this aim, this paper introduces the potential test result approach and proposes a new measure to evaluate the performance of medical diagnostic tests. This proposed measure, denoted as pr(T_d1 ≥ t, T_d0 < t), can be interpreted as a probability that a test result T would respond to a disease status D (d∈{d ₀, d ₁}) for a given threshold t, and therefore evaluates both the sufficiency and necessity of the performance of a medical diagnostic test. This new measure provides a total different interpretation for the Youden index and thus helps us to better understand the essence of the Youden index and its properties. We further propose non-parametric bounds on the proposed measure based on a variety of assumptions and illustrate our results with an example from the neonatal audiology study.