This review provides the basic principle and rational for ROC analysis of rating and continuous diagnostic test results versus a gold standard. Derived indexes of accuracy, in particular area under the curve (AUC) has a meaningful interpretation for disease classification from healthy subjects. The methods of estimate of AUC and its testing in single diagnostic test and also comparative studies, the advantage of ROC curve to determine the optimal cut off values and the issues of bias and confounding have been discussed.

Dear Editor: We read with interest the article by Abu El Makarem MA et al. (1) entitled, “Platelet count/bipolar spleen diameter ratio for the prediction of esophageal varices: The special Egyptian situation.” This study evaluated noninvasive predictors of esophageal varices in cirrhotic patients by multivariate logistic regression and receiver operating characteristic (ROC) curve analysis. However, in our opinion, some aspects of the statistical analysis could be clarified. The first issue concerns the ROC analysis.The full area under the ROC curve (AUC) is a measure of the performance of the diagnostic test because it reflects the test performance at all possible cutoff levels.The AUC lies in the interval [0.5, 1], and the larger area, the better performance. A perfect test has an AUC of 1.0, whereas random chance gives an AUC of 0.5 (2, 3). In Abu El Makarem MA et al.’s paper, the AUC for age is 0.33, which is less than 0.5. Therefore, we think that something might have gone wrong when the authors performed the ROC analysis with the SPSS software. Because both the univariate analysis and multivariate logistic regression identified age as a valuable predictor of varices, older patients experienced a higher risk having varices. We presume that the AUC for age may be 0.67 (1-0.33) rather than 0.33. The second issue has to do with the odds ratio. The odds ratio refers to a ratio of the odds of the outcome occurring in one group divided by the odds of the outcome occurring in the other group with a 1-unit increase in x (4). The odds ratio for age was 1.205 in Abu El Makarem MA et al.’s (1) paper, but no statement such as “for a one year increase in age” was mentioned.

Multiple diagnostic tools are used by emergency physicians, every day. In addition, new tools are evaluated to obtain more accurate methods and reduce time or cost of conventional ones. In the previous parts of this educational series, we described diagnostic performance characteristics of diagnostic tests including sensitivity, specificity, positive and negative predictive values, and likelihood ratios. The receiver operating characteristics (ROC) curve is a graphical presentation of screening characteristics. ROC curve is used to determine the best cutoff point and compare two or more tests or observers by measuring the area under the curve (AUC). In this part of our educational series, we explain ROC curve and two methods to determine the best cutoff value.

Objective: To assess and compare the normal ranges of androgen hormones level, total testosterone (TT), free testosterone (FT), dehydrotestosterone (DHT), androstenedione (A4), dehydroepiandrosterone (DHEA), and dehydroepiandrosterone sulfate (DHEAS), in Iranian women based on different statistical methods. Materials and methods: This study was conducted on previous data collected in Iranian PCOS Prevalence Study, which details have been published before. A total of 1772 women of 18-45 years were recruited from urban areas of five randomly selected provinces in different geographic regions of Iran. The natural range of androgen hormones was determined and compared by two statistical methods including k-means cluster analysis, and receiver operating characteristic curve. Results: In women younger than 35 years old with any BMI, cut-off points obtained for FAI hormone were in lower percentiles; however, in older women, the results of the two methods were almost the same. Cut-off points of DHEAS in under 35 years old women of normal and obese weight and women older than 35 years old with normal weight calculated by ROC curve method was in higher percentiles than that in the cluster analysis method. In >35 years obese women, obtained cut-off points for DHEAS ROC curve was in lower percentiles in comparison to cluster analysis Conclusion: Although our study depicts the differences among the cutoff values among two statistical methods; however, lacking a gold standard test to define hyperandrogenism, we need further studies to obtain more comprehensive results.

Background & Aim: In multivariate receiver operating characteristic (MROC) curve analysis, comparing two tests is usually done by means of area under the curve (AUC’s) and sensitivities. However, the existing procedures have not addressed the issue of comparing two MROC curves when they cross each other.Methods & Materials: A modified version of AUC (mAUC) under MROC setup is proposed to address the above-mentioned problem. It is also shown that mAUC performs better than AUC. The performance of mAUC in the aspect of crossover curves is supported by a real dataset and simulation studies at different sample sizes.Results: Two real datasets, namely, Intra Uterine Growth Restricted Fetal Doppler Study (IUGRFDS) and Indian liver patient (ILP) datasets are used and apart from these simulation studies are also carried out to observe the effect of sample size. These mAUC’s are then compared with each other to show that difference exists between two curves while comparing AUC’s cannot identify the true difference existing between them. With respect to IUGRFDS dataset, MROC curves of the diagnostic procedures middle cerebral artery and cerebroplacental ratio cross each other and are found to be similar when their AUC’s and mAUC’s are compared. In ILP dataset, the extent of correct classification achieved in the case of males is shown to be better than that of females when mAUC’s at 0.5 and 0.8 are compared.Conclusion: It is observed that the mAUC’s are competent in identifying the true difference between the crossover MROC curves when the sample size is adequate, and the l values are 0.5 and 0.8 but not 0.3.