Biomarker Selection in Medical Diagnosis

A biomarker is usually used as a diagnostic or assessment tool in medical research. Finding a single ideal biomarker of a high level of both sensitivity and specificity is not an easy task; especially when a high specificity is required for a population screening tool. Combining multiple biomarkers is a promising alternative and can provide a better overall performance than the use of a single biomarker. It is known that the area under the receiver operating characteristic (ROC) curve is most popular for evaluation of a diagnostic tool. In this study, we consider the criterion of the partial area under the ROC curve (pAUC) for the purpose of population screening. Under the binormality assumption, we obtain the optimal linear combination of biomarkers in the sense of maximizing the pAUC with a pre-specified specificity level. Furthermore, statistical testing procedures based on the optimal linear combination are developed to assess the discriminatory power of a biomarker set and an individual biomarker, respectively. Stepwise biomarker selections, by embedding the proposed tests, are introduced to identify those biomarkers of statistical significance among a biomarker set. Rather than for an exploratory study, our methods, providing computationally intensive statistical evidence, are more appropriate for a confirmatory analysis, where the data has been adequately filtered. The applicability of the proposed methods are shown via several real data sets with a moderate number of biomarkers.