Combining Biomarkers by Maximizing the True Positive Rate for a Fixed False Positive Rate

Biomarkers abound in many areas of clinical research, and often investigators are interested in combining them for diagnosis, prognosis, or screening. In many applications, the true positive rate for a biomarker combination at a prespecified, clinically acceptable false positive rate is the most relevant measure of predictive capacity. We propose a distribution-free method for constructing biomarker combinations by maximizing the true positive rate while constraining the false positive rate. Theoretical results demonstrate desirable properties of biomarker combinations produced by the new method. In simulations, the biomarker combination provided by our method demonstrated improved operating characteristics in a variety of scenarios when compared with alternative methods for constructing biomarker combinations.