# Receiver operator characteristic

## Assess and compare the sensitivity and specificity of diagnostic tests using ROC curves

Receiver Operator Characteristic (ROC) curves assess the sensitivity and specificity of diagnostic tests scored with a

The ROC curve is a plot of the "true-positives" against the "false-positives." As the curve approaches the

There is a statistical measure yielded by the receiver operator characteristic curve that tests the diagnostic efficacy of a test. It is called the

Receiver operator characteristic curves can also be used to test the sensitivity and specificity of different diagnostic tests against each other. The diagnostic test with the

**continuous value or as a categorical "positive" or "negative."**Sensitivity and specificity of a diagnostic test with a continuous outcome depends upon what the**cut-off value**is for a "positive" test result. Increasing or decreasing the cut-off value will yield different levels of sensitivity and specificity along all points of the numerical continuum.The ROC curve is a plot of the "true-positives" against the "false-positives." As the curve approaches the

**upper left hand**corner of the graph, the test becomes more accurate. This is because the "true-positive" rate would be approaching 1 or 100% and the "false-positive" rate would be approaching 0 or 0%. The diagonal line represents the chance that a test will be positive or negative by chance.There is a statistical measure yielded by the receiver operator characteristic curve that tests the diagnostic efficacy of a test. It is called the

**area under the curve**(**AUC**) or**c-statistic**. Higher values of AUC or c-statistics means that the diagnostic test is performing well.Receiver operator characteristic curves can also be used to test the sensitivity and specificity of different diagnostic tests against each other. The diagnostic test with the

**highest AUC**or**c-statistic**is considered the best test.### The steps for conducting Receiver Operator Characteristic analysis in SPSS

1. The data is entered in a between-subjects fashion.

2. Click

3. Drag the cursor all the way to the bottom of the drop-down menu and click

4. Click on the continuous outcome variable to highlight it.

5. Click on the

6. Click on the "gold standard" continuous outcome variable to highlight it.

7. Click on the

8. In the

9. In the Display table, click on the

10. Click

2. Click

**.**__A__nalyze3. Drag the cursor all the way to the bottom of the drop-down menu and click

**ROC Cur**.__v__e4. Click on the continuous outcome variable to highlight it.

5. Click on the

**arrow**to move the variable into the**box.**__T__est Variable:6. Click on the "gold standard" continuous outcome variable to highlight it.

7. Click on the

**arrow**to move the variable into the**box.**__S__tate Variable:8. In the

**box, enter the**__V__alue of State Variable:**cut-off value**for a positive test for the "gold standard."9. In the Display table, click on the

**,**__W__ith diagonal reference line**Standard**, and__e__rror and confidence interval**boxes to select them.**__C__oordinate points of the ROC Curve10. Click

**OK**.### The steps for interpreting the output for Receiver Operator Characteristic in SPSS

Here is how to interpret the SPSS output:

1. Look at the

2. Look in the

If the

If the

If significant, look under the

3. Look in the

1. Look at the

**ROC curve**. The curve should be entirely above the diagonal line. If it falls below the line, the test is not interpretable.2. Look in the

**Area Under the Curve**table, under the**Aysmptotic Sig.**column. This is the*p*-value that is interpreted.If the

*p*-value is**LESS THAN .05**, then the test diagnoses the disease state at a statistically significant level.If the

*p*-value is**MORE THAN .05**, then the test does not do a significant job diagnostic disease states.If significant, look under the

**Area**column for the total AUC.3. Look in the

**Coordinates of the Curve**table, under the**Positive if Greater Than or Equal To**column. Whichever value in this column that coincides with the two highest values in the**Sensitivity**and**1-Specificity**columns is the best cut-off point for the diagnostic test. One can see how different values of the continuous scale will affect sensitivity and specificity.### The steps for comparing the sensitivity and specificity of several diagnostic tests in SPSS

1. The data is entered in a between-subjects fashion.

2. Click

3. Drag the cursor all the way to the bottom of the drop-down menu and click

4. Click on the first continuous outcome variable to highlight it.

5. Click on the

6. Repeat Steps 4 and 5 until all of the diagnostic test variables are in the

7. Click on the "gold standard" continuous outcome variable to highlight it.

8. Click on the

9. In the

10. In the Display table, click on the

11. Click

2. Click

**.**__A__nalyze3. Drag the cursor all the way to the bottom of the drop-down menu and click

**ROC Cur**.__v__e4. Click on the first continuous outcome variable to highlight it.

5. Click on the

**arrow**to move the variable into the**box.**__T__est Variable:6. Repeat Steps 4 and 5 until all of the diagnostic test variables are in the

**box.**__T__est Variable:7. Click on the "gold standard" continuous outcome variable to highlight it.

8. Click on the

**arrow**to move the variable into the**box.**__S__tate Variable:9. In the

**box, enter the**__V__alue of State Variable:**cut-off value**for a positive test for the "gold standard."10. In the Display table, click on the

**,**__W__ith diagonal reference line**Standard**, and__e__rror and confidence interval**boxes to select them.**__C__oordinate points of the ROC Curve11. Click

**OK**.### The steps for interpreting the SPSS ouput of an ROC comparing diagnostic tests

1. Look at the

2. Look in the

If a

If a

If significant, look under the

3. Look in the

**ROC curve**. The curves should be entirely above the diagonal line. If any curve falls below the line, then the test is not interpreted.2. Look in the

**Area Under the Curve**table, under the**Aysmptotic Sig.**column. These are the*p*-values that are interpreted.If a

*p*-value is**LESS THAN .05**, then the test does a significant job at diagnosing disease states.If a

*p*-value is**MORE THAN .05**, then the test does NOT do a significant job diagnosing disease states.If significant, look under the

**Area**column for the total AUC.3. Look in the

**Coordinates of the Curve**table, under the**Positive if Greater Than or Equal To**column. Whichever value in this column that coincides with the two highest values in the**Sensitivity**and**1-Specificity**columns is the best cut-off point for each diagnostic test. One can see how different values of each continuous scale will affect their respective sensitivity and specificity.Click on the

**Positive Predictive Value**button to continue.## Statistician Services for Professionals

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