Mohamad reza Davoudi, could you indicate why you are not able to produce an ROC curve like those in the figure you've reproduced in your question, or what it is that you're trying to achieve, please? That might give some clues for people to start helping you.

Is the problem, for example, superimposing the curves, or is it something else?

Dear Mohamad reza Davoudi:

To depict several ROC curves, you only must introduce in the top square (contrast variable) the different index tests (quantitative variables) you want to obtain a ROC curve. However, you must use the same reference standard (dichotomous) for all of them (state variable).

The point in the curve that maximizes the length of vertical line from such point to the diagonal line is the better cut-off. However, SPSS do not give you the specific cut-off for such point, neither the values of sensitivity nor specificity.

There is a free temporal software (Medcalc®) that depicts beautiful and informative graphics and automatically calculate the best cut-off and the sensitivity and specificity in that point.

Another way to find the best cut-off point for a test is finding that point that maximizes the Youden index.

Youden index= Sensitivity + specificity -1

When you run a ROC curve in SPSS, this software gives you a table with three columns: “cutoff”, “sensitivity” and “1-specificity”.

With this information, you can easily build a Youden index for every cut-off. The only problem is that you need “specificity -1” for the Youden index, not “1-specificty”. Thus, you must change the sign of the column “1-specificity” given by SPSS.

-(1-specificity)=-1+specificity.

Thus:

1) Create the Youden index: create a new column by adding Sensitivity + -(specificity-1).

2) Arrange the table by ordering the created Youden index from higher to lower. The line with the highest Youden Index corresponds to the best cut-off for such a test.

Please, note that the best cut-off is that that globally maximizes sensitivity and specificity. For some reasons, you could move such point up or down to maximize sensitivity (eg. screening) or specificity (eg. confirmatory test).

Ángel Herráiz-Adillo

Dear Angel

Thanks for your help.

Dear Mohamad reza Davoudi,

How we can estimate various cut-of-point scores in the same time? seems to be a very interesting question, however I can not make nay contribution as I do not have any idea about of what it is all bout.

Best Regards

Desalegn Abraha

Desalegn Abraha Gebrekidan

Dear Dr. Gebrekidan

Thanks for your comment

Yes. for any problems, we have various scales and every clinician used a different scale. But which one is the best and sensitive!!!

Best Regards

Dear Dr Mohamad reza Davoudi,

Can you please help me to understand how we can estimate various cut-of-point scores in the sametime? With some basic knowledge it might be possible to understand te subject matter and to follow the discussion.

Best Regards

Desalegn Abraha

Ángel Herráiz-Adillo

we using SPSS software. Analayze>>>classify>>>Roccurve

in "Test variable " you can add various scales for assessing cut off the points.

With "coordinate the curve" table you can choose the best cut off point for every table.

About determining the best cut off points, you must consider sensitivity and specificity.

Below link is a good reference about determining these features.

Article Understanding and using sensitivity, specificity and predictive values

I am running the SPSS 20 version.

In such version, the route to create a ROC curve is "Analyze >>> ROC curve".

The route "Analyze >>> Clasify >>>" does not include ROC curves.

I think we just have a different version.

Best regards

Desalegn Abraha Gebrekidan

we using SPSS software. Analayze>>>classify>>>Roccurve

in "Test variable " you can add various scales for assessing cut off the points.

With "coordinate the curve" table you can choose the best cut off point for every table.

About determining the best cut off points, you must consider sensitivity and specificity.

Below link is a good reference about determining these features.

Article Understanding and using sensitivity, specificity and predictive values

Mohamad reza Davoudi, it's several years since I looked closely at ROC curves (I was considering writing an article about them because I thought it's easy to misunderstand them and I wanted to shed some light on them in case my attempt helped others), and my sense back then was that it's not simply a matter of deciding where a curve comes closest to the upper left-hand corner of the ROC space - i.e., where sensitivity and specificity are "equally maximized".

About 3 years ago, I wrote an article about sensitivity, specificity, and predictive values in which I considered some of the ins and outs concerning sensitivity and specificity that researchers, clinicians, students, and teachers seem to have problems with. Near the end of that article, I dealt with some important considerations that clinicians might take into account with regard to predictive values (which would flow back to sensitivity and specificity) - thus demonstrating that matching up sensitivity and specificity isn't always the best tack to take. Sometimes, it could be better to have one noticeably higher than the other.

In case you're interested, my article is in an open access journal, so freely available:

Trevethan, R. (2017). Sensitivity, specificity, and predictive values: Foundations, pliabilities, and pitfalls in research and practice. Frontiers in Public Health, 5:307. https://doi.org/10.3389/fpubh.2017.00307

I hope it might be helpful if you look at it.

All the best with your research.

Robert Trevethan

Dear Dr.Trevethan

thanks for your valuable reply.

Warm regards