Maximizing an ROC-type measure via linear combinations of biomarkers

摘要

The receiver operating characteristic curve is a popular tool to describe and compare the diagnostic accuracy of biomarkers when the binary-scale gold standard is available. There are, however, many examples of diagnostic tests whose gold standards are continuous. Hence, several extensions are proposed to evaluate the diagnostic potential of biomarkers when the gold standard is continuous-scale. In practice, there may exist more than one biomarkers and diagnostic accuracy can be improved by combining multiple biomarkers. In this paper, an explicit form of diagnostic accuracy index and the corresponding linear combination that maximizes the diagnostic accuracy are derived under elliptical distribution assumption. Simulations are conducted to evaluate the performance of the diagnostic accuracy and the optimal linear combination under different distribution assumptions. The methodology is applied to a behavioral intervention study for families of youth with type 1 diabetes.