StatEL : ROC (Receiver Operating Characteristic) Curve

1 - Principles of ROC curve :

What is difficult to establich a proper diagnostic test is to find the correct threshold value that will differenciate a positive and a negative.

Indeed, if threshold is too low, we will consider too many people in the "disease" category, and sensitivity of the test is excellent. However, la specificity of this test is very bad because a lot of these subjects are "False Positive" and will be wrongly included in series of medical treatment.

On the contrary, a too high threshold gives the test a good specificity (few healthy people are included in the "disease" category), but sensitivity is very bad because test leaves many subjects that have trully the disease and that will not be included in series of medical treatment whereas they need them.

The best threshold for a medical test is the value for which sensitivity and specificity are the highest at the same time, that is a test able to detect the maximum number of patients that have the disease and to leave the maximum number of healthy patients.

ROC (Receiving Operator Characteristics) curve allows to find this threshold value by displaying sensitivity (Se) on the Y-axis and 1 minus specificity (1-Sp) on the X-axis :

statel ROC curve excel

You have choice between 3 different procedures :

statel ROC curve excel

According to your first choice, you are free to work on binary or numeric diagnostic test, and with different or dependent samples in case of 2 ROC curves comparison :

statel ROC curve excel

2 - Launch of ROC curve :

You have to specify how are identified subjects that have the studied disease and healthy subjects, then you have to select the cells range relative to the "Disease" variable as well as the cells range relative to the "Diagnosis" or "Medical Test" variable.

Nota bene : every selection must contain the same number of cells, otherwise a warning message will pop up.

statel ROC curve excel

By default, in case of numeric "Diagnosis" or "Medical Test", it is considered "Positive" when measure is higher than threshold value, you can specify that a test is considered as "Positif" when measure is lower than threshold value.

Click on "Calculate and draw the curve".

3 - Results of ROC curve :

Results are displayed on a new Excel sheet.

On the left part of the sheet, you can see table of selected data, as well as results of sensitivity/Specificity calculations according to every threshold value.

It is also reminded if test is "Positive" when measure is higher or lower than threshold, as well as the area under the curve, which is a measure of discriminant ability of the medical test.

statel ROC curve excel

The table is completed by calculation of 3 coefficients, measured for each threshold and which allow to evaluate advantage of each threshold value (cf. comments of each Excel column).

statel ROC curve excel

Beneath ROC curve you can see a table with informations related to red point on the curve (its threshold, values of Se/Sp and coefficients).

You can move this point thanks to "Up/Down" arrows on the left of this table. Informations of the table are automatically updated. Thus, you can vusually find the position on the curve that represents the best Se/Sp value and look at the table to find which threshold value it refers.

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