### Introduction

### Sensitivity, specificity, false positive, and false negative

### What is the ROC curve?

### Types of ROC curves

### How is a ROC curve drawn?

### The area under the curve (AUC)

_{1}vs. AUC

_{2}), the test can be tested using the following Z-statistics. To determine whether an AUC (A

_{1}) is significant under the null hypothesis, Z can be calculated by substituting A

_{2}= 0.5.

### Partial AUC (pAUC)

_{1}=

*e*and FPR

_{1}_{2}=

*e*), which can be expressed as A (

_{2}*e*≤ FPR ≤

_{1}*e*). For the entire ROC curve to be designated,

_{2}*e*= 0,

_{1}*e*= 1, and

_{2}*e*=

_{1}*e*=

_{2}*e*is the sensitivity at the point where FPR =

*e*. However, a potential problem with the pAUC is that the minimum possible value of the pAUC depends on the region along the ROC curve that is selected.

_{1}=

*e*and FPR

_{1}_{2}=

*e*is equal to

_{2}*e*–

_{2}*e*, which is the width of the region when sensitivity = 1.0. By using the pAUC, it is possible to focus on the region of the ROC curve appropriate to a specific clinical situation. Therefore, the performance of the diagnostic test can be evaluated in a specific FPR interval that is appropriate to the purpose of the study.

_{1}### The sample size for the ROC curve analysis

_{1}and AUC

_{2}, where AUC

_{2}= 0.5 for the null hypothesis), the significance level (α), power (1 – β), and the ratio of negative/positive results should be considered [16]. For example, if there are twice as many negative results as positive results, the ratio = 2, and if there is the same number of negative and positive results, the ratio = 1. If two tests are performed on the same group to evaluate test performance, the two ROC curves are not independent of each other. Therefore, two correlation coefficients are additionally needed between the two diagnostic methods both for cases showing negative results and those showing positive results [21]. The correlation coefficient required here is Pearson’s correlation coefficient when the test result is measured as a continuous variable and Kendalls’ tau (τ) when measured as an ordinal variable [21].

### Determining the optimal cut-off value

#### Youden’s J statistic

#### Euclidean distance

#### Accuracy

#### Index of union (IU)

#### Cost approach

*f*

_{m}) [29]. These are calculated as follows:

##### (6)

_{FP}, C

_{TN}, C

_{FN}, and C

_{TP}refer to the costs of FPs, TNs, FNs, and TPs, respectively. These four costs should be expressed as a common unit. When the cost index (

*f*

_{m}) is maximized, the average cost is minimized, and this point is considered the optimal cut-off value.

_{FP}, and the C

_{FN}, the point at which the MCT is minimized is determined as the optimal cut-off value [29] and expressed as follows:

#### Positive likelihood ratio (LR^{+}) and negative likelihood ratio (LR^{–})

^{+}is the ratio of true positives to false positives, and LR

^{–}is the ratio of false negatives to true negatives.

^{+}or minimizes LR

^{–}.