title: Evaluating the improvement in diagnostic utility from adding new predictors.
abstract: Multiple diagnostic tests and risk factors are commonly available for many diseases. This information can be either redundant or complimentary. Combining them may improve the diagnostic/predictive accuracy, but also unnecessarily increase complexity, risks, and/or costs. The improved accuracy gained by including additional variables can be evaluated by the increment of the area under (AUC) the receiver-operating characteristic curves with and without the new variable(s). In this study, we derive a new test statistic to accurately and efficiently determine the statistical significance of this incremental AUC under a multivariate normality assumption. Our test links AUC difference to a quadratic form of a standardized mean shift in a unit of the inverse covariance matrix through a properly linear transformation of all diagnostic variables. The distribution of the quadratic estimator is related to the multivariate Behrens-Fisher problem. We provide explicit mathematical solutions of the estimator and its approximate non-central F-distribution, type I error rate, and sample size formula. We use simulation studies to prove that our new test maintains prespecified type I error rates as well as reasonable statistical power under practical sample sizes. We use data from the Study of Osteoporotic Fractures as an application example to illustrate our method.
authors.affiliation: Department of Radiology and Biomedical Imaging, University of California, San Francisco, 94143-0946, USA.
authors.forename: Caixia
authors.initials: C
authors.lastname: Li
authors.forename: Ying
authors.initials: Y
authors.lastname: Lu
mesh_terms: D000368:Aged; D019540:Area Under Curve; D019644:Arthroplasty, Replacement, Hip; D003933:Diagnosis; D016002:Discriminant Analysis; D005260:Female; D006620:Hip Fractures / Q000150:complications / Q000175:diagnosis / Q000503:physiopathology / Q000601:surgery; D006801:Humans; D016014:Linear Models; D015233:Models, Statistical; D015999:Multivariate Analysis; D010024:Osteoporosis / Q000150:complications; D012372:ROC Curve; D012307:Risk Factors