A Procedure for Determining Whether a Simple Combination of Diagnostic Tests May Be Noninferior to the Theoretical Optimum Combination

Diagnosis accuracy can be improved by combining several complementary diagnostic tests. The likelihood ratio (LR) function is the optimal combination because it achieves the largest area under the receiver operating characteristic (ROC) curve. Derivation and interpretation of the LR function, however, can be complicated. Linear discriminant/logistic functions are simple but may not be optimal. In this article, the authors propose a statistical framework to determine when such linear combinations are noninferior alternatives to the LR function. They propose a nonparametric procedure to calculate LR functions and estimate the optimal area under the curve (AUC). The authors then define noninferiority of a simpler combination to the LR function with regard to the AUC of ROC curves. A bootstrap procedure is proposed to test the noninferiority. Monte Carlo simulation experiments are used to evaluate the performance of the proposed methods. Data from the Study of Osteoporotic Fractures are used to demonstrate the procedure.