ROC Curves

ROC Curves is part of:
  • Life Survival analysis software

  • System configuration

    • Windows:
      • Versions: 9x/Me/NT/2000/XP/Vista/Win 7/Win 8
      • Excel: 97 and later
      • Processor: 32 or 64 bits
      • Hard disk: 150 Mb
    • Mac OS X:
      • OS: OS X
      • Excel: X, 2004 and 2011
      • Hard disk: 150Mb.

Benefits

  • Easy and user-friendly
    Easy and user-friendly XLSTAT is flawlessly integrated with Microsoft Excel which is the most popular spreadsheet worldwide. This integration makes it one of the simplest available tools to work with as it utilizes the same philosophy as Microsoft Excel. The program is accessible in a dedicated XLSTAT tab. The analyses are grouped into functional menus. The dialog boxes are user-friendly and setting up an analysis is straightforward.
  • Data and results shared seamlessly
    Data and results shared seamlessly One of the greatest advantages of XLSTAT is the way you can share data and results seamlessly. As the results are stored in Microsoft Excel, anyone can access them. There is no need for the receiver to have an XLSTAT license or any additional viewer which makes your team-work easier and more affordable. In addition, results are easily integrable into other Microsoft Office software such as PowerPoint, so that you can create striking presentation in minutes.
  • Modular
    Modular XLSTAT is a modular product. XLSTAT-Pro is a core statistical module of XLSTAT which includes all the mainstream functionalities in statistics and multivariate analysis. More advanced features contained in add-on modules can be added for specific applications. This way you can adapt the software to your needs making the software more cost-efficient.
  • Didactic
    Didactic The results of XLSTAT are organized by analysis and are easy to navigate. Moreover useful information is provided along with the results to assist you in your interpretation.
  • Affordable
    Affordable XLSTAT is a complete and modular analytical solution that can suit any analytical business needs. It is very reasonably priced so that the return of your investment is almost immediate. Any XLSTAT license comes with top level support and assistance.
  • Accessible - Available in many languages
    Accessible - Available in many languages We have ensured XLSTAT is accessible to everyone by making the program available in many languages, including Chinese, English, French, German, Italian, Japanese, Polish, Portuguese and Spanish.
  • Automatable and customizable
    Automatable and customizable Most of the statistical functions available in XLSTAT can be called directly from the Visual Basic window of Microsoft Excel. They can be modified and integrated to more code to fit to the specificity of your domain. Adding tables and plots as well as modifying existing outputs becomes easy. Furthermore, XLSTAT includes some special tools on the dialog boxes to generate automatically the VBA code in order to reproduce your analysis using the VBA editor or to simply load pre-set settings. This effortless automation of routine analysis will be a huge time saver on your part.

The ROC curve generated by XLSTAT-Life software allows to represent the evolution of the proportion of true positive cases (also called sensitivity) as a function of the proportion of false positives cases (corresponding to 1 minus specificity), and to evaluate a binary classifier such as a test to diagnose a disease, or to control the presence of defects on a manufactured product.

ROC curve definition

The ROC curve corresponds to the graphical representation of the couple (1 – specificity, sensitivity) for the various possible threshold values.

Here are some important definitions:

Area Under the Curve

The area under the curve (AUC) is a synthetic index calculated for ROC curves. The AUC is the probability that a positive event is classified as positive by the test given all possible values of the test. For an ideal model we have AUC = 1 (above in blue), where for a random pattern we have AUC = 0.5 (above in red). One usually considers that the model is good when the value of the AUC is higher than 0.7. A well discriminating model should have an AUC between 0.87 and 0.9. A model with an AUC above 0.9 is excellent.

Sen (1960), Bamber (1975) and Hanley and McNeil (1982) have proposed different methods to calculate the variance of the AUC. All are available in XLSTAT. XLSTAT offers as well a comparison test of the AUC to 0.5, the value 0.5 corresponding to a random classifier. This test is based on the difference between the AUC and 0.5 divided by the variance calculated according to one of the three proposed methods. The statistic obtained is supposed to follow a standard normal distribution, which allows the calculation of the p-value.

The AUC can also be used to compare different tests between them. If the different tests have been applied to different groups of individuals, samples are independent. In this case, XLSTAT uses a Student test to compare the AUCs (which requires assuming the normality of the AUC, which is acceptable if the samples are not too small). If different tests were applied to the same individuals, the samples are paired. In this case, XLSTAT calculates the covariance matrix of the AUCs as described by Delong and Delong (1988) on the basis of Sen’s work (1960), to then calculate the variance of the difference between two AUCs, and to calculate the p-value assuming the normality.

XLSTAT results for the ROC analysis

In addition to the ROC and AUC curve, other results are computed.

ROC analysis

The ROC analysis table displays for each possible threshold value of the test variable, the various indices presented in the description section. On the line below the table you'll find a reminder of the rule set out in the dialog box to identify positive cases compared to the threshold value. Below the table you will find a stacked bars chart showing the evolution of the TP, TN, FP, FN depending on the value of the threshold value. If the corresponding option was activated, the decision plot is then displayed (for example, changes in the cost depending on the threshold value).

Comparison of the AUC to 0.5

These results allow to compare the test to a random classifier. The confidence interval corresponds to the difference. Various statistics are then displayed including the p-value, followed by the interpretation of the comparison test.

Comparison of the AUCs

If you selected several test variables, once the above results are displayed for each variable, you will find the covariance matrix of the AUC, followed by the table of differences for each pair of AUCs with as comments the confidence interval, and then the table of the p-values. Values in bold correspond to significant differences. Last, a graph that compares the ROC curves displayed.

Tutorials

Screenshots