LINEAR-COMBINATIONS OF MULTIPLE DIAGNOSTIC MARKERS

The receiver operating characteristic (ROC) curve is a simple and meaningful measure to assess the usefulness of diagnostic markers. To use the information carried by multiple markers, we note that Fisher's linear discriminant function provides a linear combination of markers to maximize the sensitivity over the entire specificity range uniformly under the multivariate normal distribution model with proportional covariance matrices. With no restriction on covariance matrices, we also provide a solution of the best linear combination of markers in the sense that the area under the ROC curve of this combination is maximized among all possible linear combinations. We illustrate both situations discussed in the article with a cancer clinical trial data.