Receiver operator characteristic (ROC) curves and non-normal data: an empirical study

This paper evaluates the performance of several diagnostic kits for assessing levels of serum prostatic acid phosphatase on patients at different stages of cancer of the prostate. Each patient was studied with several kits. We compare results obtained for receiver operator characteristic (ROC) curve methodology with data assumed to follow a normal distribution, with log-transformed data assumed to follow a normal distribution, and when neither of these assumptions holds. There were important differences between the results of the different approaches. For these data, the normal distribution assumption should be used with extreme caution. The log-transformed based results compared favourably with the non-parametric, but unconsidered application of the method should be avoided.