mROC: A computer program for combining tumour markers in predicting disease states

Receiver operating characteristic (ROC) curves are limited when several diagnostic tests are available, mainly due to the problems of multiplicity and inter-relationships between the different tests. The program presented in this paper uses the generalised ROC criteria, as well as its confidence interval, obtained from the non-central F distribution, as a possible solution to this problem. This criterion corresponds to the best linear combination of the test for which the area under the ROC curve is maximal. Quantified marker values are assumed to follow a multivariate normal distribution but not necessarily with equal variances for two populations. Other options include Box-Cox variable transformations, QQ-plots, interactive graphics associated with changes in sensitivity and specificity as a function of the cut-off. We provide an example to illustrate the usefulness of data transformation and of how linear combination of markers can significantly improve discriminative power. This finding highlights potential difficulties with methods that reject individual markers based on univariate analyses.