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

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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.