Figure 4

For the hypothetical example of Figure 2, true and observed 2 × 2 tables. Numbers were rounded to the nearest whole number. All tables were calculated at specificity of about 0.82. This point was chosen because the maximum difference between the observed and true sensitivity for Test 1 occurs at this point. For Test 1, the true sensitivity is 0.34, withobserved sensitivity at 0.76. For Test 2, the true sensitivity is 0.43, withobserved sensitivity at 0.51. Each one of the four tables uses a slightly different ROC cutpoint. For the observed table, Test 1 is positive if it exceeds 2.511; for the true table, Test 1 is positive if it exceeds 2.515. For the observed table, Test 2 is positive if it exceeds 1.269; for the true table, Test 2 is positive if it exceeds 1.265. The tables have different ROC cutpoints because they were chosen to have the same specificity, not the same cutpoint. For this hypothetical example, the disease rate, r = 0.01; the chance that participants with disease would experience signs and symptoms within the year of follow-up, ψ = 0.1; the variance, σ ² = 1. The means of the ROC distributions for cases for Test 1 and Test 2 were 2.1 and 1.1, respectively, and the means for non-cases for Test 1 and Test 2 were 1.6 and 0.35. The correlation between test scores for cases was fixed at 0.1, as was the correlation for non-cases. All test scores above 2.5 on either test, or participants who had signs or symptoms had an infallible secondary test to determine disease status. For participants with scores below 2.5 on both tests, a less sensitive method was used to approximate disease status.