Semiparametric transformation models for multiple continuous biomarkers in ROC analysis

Recent technological advances continue to provide noninvasive and more accurate biomarkers for evaluating disease status. One standard tool for assessing the accuracy of diagnostic tests is the receiver operating characteristic (ROC) curve. Few statistical methods exist to accommodate multiple continuous-scale biomarkers in the framework of ROC analysis. In this paper, we propose a method to integrate continuous-scale biomarkers to optimize classification accuracy. Specifically, we develop semiparametric transformation models for multiple biomarkers. We assume that unknown and marker-specific transformations of biomarkers follow a multivariate normal distribution. Our models accommodate biomarkers subject to limits of detection and account for the dependence among biomarkers by including a subject-specific random effect. We also propose a diagnostic measure using an optimal linear combination of the transformed biomarkers. Our diagnostic rule does not depend on any monotone transformation of biomarkers and is not sensitive to extreme biomarker values. Nonparametric maximum likelihood estimation (NPMLE) is used for inference. We show that the parameter estimators are asymptotically normal and efficient. We illustrate our semiparametric approach using data from the Endometriosis, Natural History, Diagnosis, and Outcomes (ENDO) study.