Nonparametric predictive inference with parametric copulas for combining bivariate diagnostic tests

Abstract

Measuring the accuracy of diagnostic tests is crucial in many application areas including medicine, machine learning and credit scoring. The receiver operating characteristic (ROC) curve is a useful tool to assess the ability of a diagnostic test to discriminate among two classes or groups. In practice, multiple diagnostic tests or biomarkers may be combined to improve diagnostic accuracy, e.g. by maximizing the area under the ROC curve. In this paper we present Nonparametric Predictive Inference (NPI) for best linear combination of two biomarkers, where the dependence of the two biomarkers is modelled using parametric copulas. NPI is a frequentist statistical method that is explicitly aimed at using few modelling assumptions, enabled through the use of lower and upper probabilities to quantify uncertainty. The combination of NPI for the individual biomarkers, combined with a basic parametric copula to take dependence into account, has good robustness properties and leads to quite straightforward computation. We briefly comment on the results of a simulation study to investigate the performance of the proposed method in comparison to the empirical method. An example with data from the literature is provided to illustrate the proposed method, and related research problems are briefly discussed.