# Comparison of ROC curves

Command: | Statistics ROC curves Comparison of ROC curves |

## Description

Use **Comparison of ROC curves** to test the statistical significance of the difference between the areas under 2 to 6 dependent ROC curves (derived from the same cases) with the method of DeLong et al. (1988) or Hanley & McNeil, 1983.

## Required input

In the dialog box you need to enter:

**Data**

**Variables**: select the variables of interest (at least 2, maximum 6).**Classification variable**: select a dichotomous variable indicating diagnosis (0=negative, 1=positive).If your data are coded differently, you can use the Define status tool to recode your data.**Filter**: (optionally) a filter in order to include only a selected subgroup of cases (e.g. AGE>21, SEX="Male").

**Methodology**:

**DeLong et al.**: use the method of Delong et al. (1988) for the calculation of the Standard Error of the Area Under the Curve (AUC) and of the difference between two AUCs (recommended).**Hanley & McNeil**: use the methods of Hanley & McNeil (1982, 1983) for the calculation of the Standard Error of the Area Under the Curve (AUC) and of the difference between two AUCs.**Binomial exact Confidence Interval for the AUC**: calculate exact Binomial Confidence Intervals for the Area Under the Curves (AUC) (recommended). If this option is not selected, the Confidence Intervals for the AUCs are calculated as AUC ± 1.96 SE (Standard Error). This option does not apply to the difference between two AUCs).

**Graph**

- Select
**Display ROC curves window**to obtain the ROC curves in a separate graph window. Option:- mark points corresponding to criterion values.

When you have completed the dialog box, click OK to proceed.

## Results

The results window shows the data for the different ROC curves followed by the result of pairwise comparison of all ROC curves: the difference between the areas, the standard error, the 95% confidence interval for the difference and P-value. If P is less than the conventional 5% (P<0.05), the conclusion is that the two compared areas are significantly different.

## Display Roc curves

When you have selected *Display ROC curves window *in the dialog box, the program will also open a graph window with the different ROC curves.

## Literature

- DeLong ER, DeLong DM, Clarke-Pearson DL (1988): Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. Biometrics 44:837-845.
- Hanley JA, Hajian-Tilaki KO (1997) Sampling variability of nonparametric estimates of the areas under receiver operating characteristic curves: an update. Academic Rediology 4:49-58.
- Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143:29-36.
- Hanley JA, McNeil BJ (1983) A method of comparing the areas under receiver operating characteristic curves derived from the same cases. Radiology 148:839-843.

## See also

## Recommended book

## The Statistical Evaluation of Medical Tests for Classification and Prediction

Margaret Sullivan Pepe

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