Statistical Inference for Box-Cox based Receiver Operating Characteristic Curves

Abstract

Receiver operating characteristic (ROC) curve analysis is widely used in evaluating the effectiveness of a diagnostic test/biomarker or classifier score. A parametric approach for statistical inference on ROC curves based on a Box-Cox transformation to normality has frequently been discussed in the literature. Many investigators have highlighted the difficulty of taking into account the variability of the estimated transformation parameter when carrying out such an analysis. This variability is often ignored and inferences are made by considering the estimated transformation parameter as fixed and known. In this paper, we will review the literature discussing the use of the Box-Cox transformation for ROC curves and the methodology for accounting for the estimation of the Box-Cox transformation parameter in the context of ROC analysis, and detail its application to a number of problems. We present a general framework for inference on any functional of interest, including common measures such as the AUC, the Youden index, and the sensitivity at a given specificity (and vice versa). We further developed a new R package (named 'rocbc') that carries out all discussed approaches and is available in CRAN.

Keywords: Box–Cox; ROC; correlated biomarkers; delta method; sensitivity; smooth ROC; specificity.