Abstract

Both of the ROC analysis (Receiver Operating Characteristic Analysis) and the survival analysis can be used to analyze data from the diagnostic medicine. In the ROC analysis, data will be summarized according to the true condition status (D=0, D=1) and the test results (T=0, T=1) of the patients. An ROC curve is a plot of TPR(T=1, D=1) versus its FPR(T=1 , D=0) of the test. It is not affected by the prevalence of the condition.

The survival analysis can analyze the censoring data. Therefore, no information from each sample will be lost. That lets us get more matched results as the true condition.

Each of the two analyses has its merits. And there are several similar points between two analyses. For example, an ROC curve is a non-decreasing curve, and several functions in survival analysis are also non-decreasing functions. Both two analyses are accordance with the true condition status and the test results. Therefore, the transformed functions have their meanings.

The functions from survival analysis were used to transform the ROC data. In this way, the prevalence can be shown. When two ROC curves which come from different diseases with different prevalence are the same, the transformed functions can be used to distinguish which ROC curve which has a smaller error for T=1.


If the areas of the ROC curves are the same, but two curves are came form different bionormail distributions. The parameter b can be used to determine the ROC curves’ stability at linear areas of the ROC curves. When the ratio of b/Var (the variances of the tests) is smaller, the ROC curve is more stable.