Two simple algorithms on linear combination of multiple biomarkers to maximize partial area under the ROC curve
In clinical practices, it is common that several biomakers are related to a specific disease and each single marker does not have enough diagnostic power. An effective way to improve the diagnostic accuracy is to combine multiple markers. It is known that the area under the receiver operating characteristic curve (AUC) is very popular for evaluation of a diagnostic tool. Su and Liu (1993) derived the best linear combination that maximizes AUC when the markers are multivariate normally distributed. However, there are many applications that do not operate in the entire range of the curve, but only in particular regions of it, for example, high specificity regions. In these cases, it is more practical to analyze the partial area under the curve (pAUC). In this paper, we propose two easy-implemented algorithms, to find the best linear combination of multiple biomarkers that optimizes the pAUC, for given range of specificity. Analysis of synthesized and real datasets shows that the proposed algorithms achieve larger predictive pAUC values on future observations than existing methods, such as Su and Lius method, logistic regression and others.
linear combination biomarkers diagnostic accuracy receive operating characteristic (roc) curve partial area under roc curve (pauc)