ROC curve analysis-什么是ROC分析

What is a ROC curve?

A ROC curve is a plot of the true positive rate (Sensitivity) in function of the false positive rate (100-Specificity) for different cut-off points of a parameter. Each point on the ROC curve represents a sensitivity/specificity pair corresponding to a particular decision threshold. The Area Under the ROC curve (AUC) is a measure of how well a parameter can distinguish between two diagnostic groups (diseased/normal).

MedCalc creates a complete sensitivity/specificity report.

The ROC curve is a fundamental tool for diagnostic test evaluation.

Theory summary

The diagnostic performance of a test, or the accuracy of a test to discriminate diseased cases from normal cases is evaluated using Receiver Operating Characteristic (ROC) curve analysis (Metz, 1978; Zweig & Campbell, 1993). ROC curves can also be used to compare the diagnostic performance of two or more laboratory or diagnostic tests (Griner et al., 1981).

When you consider the results of a particular test in two populations, one population with a disease, the other population without the disease, you will rarely observe a perfect separation between the two groups. Indeed, the distribution of the test results will overlap, as shown in the following figure.

ROC-curve-overlapping-distributions

For every possible cut-off point or criterion value you select to discriminate between the two populations, there will be some cases with the disease correctly classified as positive (TP = True Positive fraction), but some cases with the disease will be classified negative (FN = False Negative fraction). On the other hand, some cases without the disease will be correctly classified as negative (TN = True Negative fraction), but some cases without the disease will be classified as positive (FP = False Positive fraction).

Schematic outcomes of a test

The different fractions (TP, FP, TN, FN) are represented in the following table.

Disease
Test Present n Absent n Total
Positive True Positive (TP) a False Positive (FP) c a + c
Negative False Negative (FN) b True Negative (TN) d b + d
Total a + b c + d

The following statistics can be defined:

Sensitivity
a
a + b
Specificity
d
c + d
Positive
Likelihood
Ratio
Sensitivity
1 – Specificity
Negative
Likelihood
Ratio
1 – Sensitivity
Specificity
Positive
Predictive
Value
a
a + c
Negative
Predictive
Value
d
b + d
  • Sensitivity: probability that a test result will be positive when the disease is present (true positive rate, expressed as a percentage).
    Sensitivity=aa+b
  • Specificity: probability that a test result will be negative when the disease is not present (true negative rate, expressed as a percentage).
    Specificity=dc+d
  • Positive likelihood ratio: ratio between the probability of a positive test result given the presence of the disease and the probability of a positive test result given the absence of the disease, i.e.
    +LR=True positive rateFalse positive rate=Sensitivity1Specificity
  • Negative likelihood ratio: ratio between the probability of a negative test result given the presence of the disease and the probability of a negative test result given the absence of the disease, i.e.
    LR=False negative rateTrue negative rate=1SensitivitySpecificity
  • Positive predictive value: probability that the disease is present when the test is positive (expressed as a percentage).
    PPV=aa+c
  • Negative predictive value: probability that the disease is not present when the test is negative (expressed as a percentage).
    NPV=db+d

Sensitivity and specificity versus criterion value

When you select a higher criterion value, the false positive fraction will decrease with increased specificity but on the other hand the true positive fraction and sensitivity will decrease:

ROC-curve-sensitivity-specificity

When you select a lower threshold value, then the true positive fraction and sensitivity will increase. On the other hand the false positive fraction will also increase, and therefore the true negative fraction and specificity will decrease.

The ROC curve

In a Receiver Operating Characteristic (ROC) curve the true positive rate (Sensitivity) is plotted in function of the false positive rate (100-Specificity) for different cut-off points. Each point on the ROC curve represents a sensitivity/specificity pair corresponding to a particular decision threshold. A test with perfect discrimination (no overlap in the two distributions) has a ROC curve that passes through the upper left corner (100% sensitivity, 100% specificity). Therefore the closer the ROC curve is to the upper left corner, the higher the overall accuracy of the test (Zweig & Campbell, 1993).

ROC-curve-example

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