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

Stat Med. 1990 Mar;9(3):325-37. doi: 10.1002/sim.4780090315.


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.

Publication types

  • Comparative Study

MeSH terms

  • Acid Phosphatase / blood
  • Clinical Enzyme Tests*
  • Data Interpretation, Statistical*
  • Humans
  • Male
  • Normal Distribution
  • Prostatic Neoplasms / diagnosis*
  • Prostatic Neoplasms / enzymology
  • ROC Curve*
  • Reagent Kits, Diagnostic*


  • Reagent Kits, Diagnostic
  • Acid Phosphatase