Conditional Relative Odds Ratio and Comparison of Accuracy of Diagnostic Tests Based on 2×2 Tables

In order to evaluate the accuracy of diagnostic tests based on 2×2 tables, a number of indices were used, some of which are occasionally used inappropriately. This paper demonstrates the characteristics and problems with those indices, and introduces several methods to compare the accuracy of two diagnostic tests. The author summarizes existing indices based on 2×2 tables, agreement rate, kappa (κ), and odds ratio, and reviews their characteristics to find better indices by which to compare two diagnostic tests using hypothetical examples. Because only the odds ratio is not affected by prevalence, the relative odds ratio is the most appropriate index for comparing diagnostic accuracy. In order to decrease selection bias, giving the two tests to the same individuals is preferred. However, no standard method has been established to obtain the standard error of relative odds ratios. In this case, using the newly proposed conditional relative odds ratio (CROR), based on McNemar’s odds ratio, the standard error is available. The CROR is a less biased index when the two tests were given to the same individuals, and it is also preferable in light of its ethical and economic advantages. However, a large base population is required for the two tests to be highly accurate and produce few discordant results.