Comparing tumour staging and grading systems: a case study and a review of the issues, using thymoma as a model

We consider the problem of comparing alternative cancer staging and grading systems. Statistical comparisons are on the basis of the ability to predict survival, but more qualitative criteria, such as parsimony, and distinctive prognostic separability of the categories are relevant also. Furthermore, some staging systems are clearly ordinal, while others are not. Three candidate statistical measures are studied and compared: explained variation; area under the ROC curve; and the probability of concordance of stage and survival. Each of these has individual strengths and weaknesses. A data set involving the staging of thymoma is analysed in detail to motivate the problem and illustrate the results.