Multiple diagnostic tests and risk factors for a disease are commonly available to clinicians. Their combinations can often improve diagnostic utility. The Neyman-Pearson theorem proves the likelihood ratio (LR) score as the uniformly most powerful combination that achieves the maximum area under (AUC) the receiver operating characteristic (ROC) curve (McIntosh and Pepe, 2002). When we are unwilling to make parametric assumptions about the joint distribution of the testing results, derivation of LR score and its interpretation can be complicated. On the other hand, the linear combinations, such as linear discriminant (LD) function and logistic regression equations, are often used to combine these results in clinical applications. Such simple linear combinations may not be optimal for non-normal variables or normal variables with different covariance matrices between patients and controls. In this talk, I will present a statistical framework to determine when such linear combinations can be used as non-inferior alternatives to the optimum LR score. I first propose a non-parametric procedure to calculate LR scores and estimate the optimal AUC of ROC based on the Mann-Whitney statistic. I will then define the non-inferiority of a simpler combination to the optimal LR score with regards to the AUC of ROC curves. A bootstrap test procedure has been proposed to test the non-inferiority of a linear combination to the optimum LR score. Monte Carlo simulation experiments were conducted to evaluate the performance of the proposed estimates of the optimal AUC and the bootstrap test statistics. The procedure is illustrated using data from a study of osteoporotic fractures. If time allows, I will also discuss work about tree-based nonlinear combinations of risk factors as well as a statistical test to compare the utility of two diagnostic tests in the presence of linear combinations of other covariates.

This is a joint work with Dr. Hua Jin, Department of Mathematics, South China Normal University. The work is supported by NIH 5R01EB004079 and NIH R03 AR47104.



Seminar Date:
April 5, 2007