Receiver Operating Characteristic (ROC) curve analysis is useful for evaluating the performance of diagnostic tests that classify individuals into categories of those with and those without a condition (Zou et al. 2007; Metz et al. 1978). The data obtained from a diagnostic test will often exist on a scale (i.e. blood pressure, hormone concentration), and a decision will need to be made on whether a certain test value indicates that the condition is present (positive test) or not (negative test). Where this ‘line’ is drawn is termed the decision or positivity threshold. For example, a blood pressure cut-off value for hypertension is 135/80.
The choice of a decision threshold will have a large effect on the sensitivity and specificity of a test. While setting a low threshold will result in a large proportion of true positives being correctly identified as positive, it will also decrease the rate of true negatives. In other words, a lower threshold increases sensitivity but decreases specificity. The inverse is also true for high thresholds. As sensitivity and specificity depend on the selection of a decision threshold, ROC analysis is used to plot the sensitivity (y-axis) against 1-specificity (x-axis) as the threshold value changes (Macaskill et al. 2010). This gives a visual representation of the relationship between sensitivity and specificity of a diagnostic test as the threshold value changes. This can be measured quantitatively by assessing the area under the curve (AUC) (Hanley and McNeil. 1982). The AUC for a perfect test is 1.0, and a test with no differentiation between disorder and no disorder has an AUC of 0.5 (Lalkhen and McCluskey. 2008).
Figure 9.1 shows an ROC curve from Erol et al. 2014 with an AUC of 0.81 (95%CI 0.80 to 0.82).
The diagonal line shows the baseline result of a test with no differential power (AUC=0.5).
Figure 9.1: ROC graph for the use of prostate specific antigen free/total ratios for the diagnosis of prostate cancer