2D-ROC: a receiver operating surface and its illustrative application in clinical diagnostics

When there are multiple tests, the receiver operating characteristic (ROC) curve analysis does not answer the question of how the individual tests can be combined in medicine.

In this study, 2D-ROC analysis is considered to calculate the correct classification rate (CCR) by using two independent test results. To obtain the best combination of paired tests, results were combined as 'BOTH', 'ANY' or 'AVERAGE' for the final 2D-ROC decision.

When the combined model was 'AVERAGE', the CCR was better than individual test results. At every correlation level, the 2D-ROC was shown to have a better CCR compared to individual tests, and when the correlations were lower, the CCR of 2D-ROC was even better. For uncorrelated test pairs (r  =  0, p   <  0.0001), in healthy and diseased populations with normal distributions, the improvement in CCR compared to individual tests were from 2.6% to 6.5%, and leptokurtic distribution of diseased population (k  =  2, p   <  0.0001) was better by 1.3% to 5.3%. As a clinical application, multifrequency bioelectric impedance (BI) spectroscopy characteristic frequency (f _c) and body mass index (BMI) measurements from 53 post-menopausal women were used in finding the 2D-ROC decision matrix to determine the hip area bone mineral deficiency. Using the 'AVERAGE' combination model, the CCR of 2D-ROC was 1.6% better than BMI and 14.8% better than fc alone. In the second clinical application of prediction of metabolic syndrome (MeS), parameters such as BMI, waist circumference, abnormal fasting blood sugar, triglyceride and high-density lipoprotein cholesterol were measured from 5533 subjects and combined to assess individual and paired success rates. Using the 'AVERAGE' combination model, the CCR of pairs were up to 6.1% better compared to using each parameter alone.

Although the use of a simple 'AVERAGE' function was promising, the formulation for combining paired test results could be extended to include the deviations from ideal by weighted averaging of individual tests or by adding other parameters like their kurtosis or disease prevalence into the formulation.