Estimating Optimum Linear Combination of Multiple Correlated Diagnostic Tests at a Fixed Specificity with Receiver Operating Characteristic Curves

Abstract

Receiver operating characteristic (ROC) methodology is widely used to evaluate diagnostic tests. It is not uncommon in medical practice that multiple diagnostic tests are applied to the same study sample. A variety of methods have been proposed to combine such potentially correlated tests to increase the diagnostic accuracy. Usually the optimum combination is searched based on the area under a ROC curve (AUC), an overall summary statistics that measures the distance between the distributions of diseased and non-diseased populations. For many clinical practitioners, however, a more relevant question of interest may be "what the sensitivity would be for a given specificity (say, 90%) or what the specificity would be for a given sensitivity?". Generally there is no unique linear combination superior to all others over the entire range of specificities or sensitivities. Under the framework of a ROC curve, in this paper we presented a method to estimate an optimum linear combination maximizing sensitivity at a fixed specificity while assuming a multivariate normal distribution in diagnostic tests. The method was applied to a real-world study where the accuracy of two biomarkers was evaluated in the diagnosis of pancreatic cancer. The performance of the method was also evaluated by simulation studies.