Abstract

Receiver Operating Characteristic (ROC) curves are widely used to evaluate the diagnostic accuracy of biomarkers in predicting binary disease outcomes. However, their utility diminishes when dealing with more than two outcome groups, as they cannot simultaneously differentiate between multiple outcomes. In such cases, ROC surfaces (for three outcome groups) or ROC manifolds (for more than three groups) are more appropriate alternatives.

Moreover, biomarker performance is often affected by various covariates. Incorporating these covariates into the analysis can improve the diagnostic accuracy model and offer deeper insights into how biomarker performance varies across different covariate levels. Traditional approaches to ROC surface regression involve modeling biomarkers for each outcome group regarding covariates or employing ordinal or multinomial logistic regression. While these methods can be informative, they may not fully capture covariates' complex, nonlinear effects.

In this project, we propose a novel approach to ROC surface regression using placement value (PV) to address the nonlinear influence of covariates. PV standardizes biomarker values for diseased groups relative to the healthy group, offering a more intuitive framework for modeling nonlinear covariate effects. This method redefines the ROC surface as a function of two placement values, enabling us to directly account for nonlinear covariate impacts.

Additionally, our approach allows for the determination of covariate-specific optimal thresholds, enhancing the discrimination of outcomes based on different covariate levels. We plan to apply this method to data from the NICHD Fetal Growth Studies to evaluate biomarker performance in predicting abnormal birthweight outcomes, such as small-for-gestational-age and large-for-gestational-age infants, across varying stages of gestation.