title: Prediction-based structured variable selection through the receiver operating characteristic curves.
abstract: In many clinical settings, a commonly encountered problem is to assess accuracy of a screening test for early detection of a disease. In these applications, predictive performance of the test is of interest. Variable selection may be useful in designing a medical test. An example is a research study conducted to design a new screening test by selecting variables from an existing screener with a hierarchical structure among variables: there are several root questions followed by their stem questions. The stem questions will only be asked after a subject has answered the root question. It is therefore unreasonable to select a model that only contains stem variables but not its root variable. In this work, we propose methods to perform variable selection with structured variables when predictive accuracy of a diagnostic test is the main concern of the analysis. We take a linear combination of individual variables to form a combined test. We then maximize a direct summary measure of the predictive performance of the test, the area under a receiver operating characteristic curve (AUC of an ROC), subject to a penalty function to control for overfitting. Since maximizing empirical AUC of the ROC of a combined test is a complicated nonconvex problem (Pepe, Cai, and Longton, 2006, Biometrics62, 221-229), we explore the connection between the empirical AUC and a support vector machine (SVM). We cast the problem of maximizing predictive performance of a combined test as a penalized SVM problem and apply a reparametrization to impose the hierarchical structure among variables. We also describe a penalized logistic regression variable selection procedure for structured variables and compare it with the ROC-based approaches. We use simulation studies based on real data to examine performance of the proposed methods. Finally we apply developed methods to design a structured screener to be used in primary care clinics to refer potentially psychotic patients for further specialty diagnostics and treatment.
authors.affiliation: Department of Biostatistics, Mailman School of Public Health, Columbia University, New York, New York 10032, USA. yuanjia.wang@columbia.edu
authors.forename: Yuanjia
authors.initials: Y
authors.lastname: Wang
authors.forename: Huaihou
authors.initials: H
authors.lastname: Chen
authors.forename: Runze
authors.initials: R
authors.lastname: Li
authors.forename: Naihua
authors.initials: N
authors.lastname: Duan
authors.forename: Roberto
authors.initials: R
authors.lastname: Lewis-Fernández
mesh_terms: D000341:Affective Disorders, Psychotic; D003198:Computer Simulation; D006801:Humans; D008722:Methods; D012372:ROC Curve