Comparing Estimation Methods for the Area Under the Bi-Weibull ROC Curve.

Abstract

In this paper, we carried out extensive simulation studies to compare the performances of partial and maximum likelihood based methods for estimating the area under the bi-Weibull ROC curve. Further, real data sets from HIV/AIDS research were analyzed for illustrative purposes. Simulation results suggest that both methods perform well and yield similar results for Weibull data. However, for non-Weibull data, both methods perform poorly. The bi-Weibull model yields smooth estimates of ROC curves and a closed-form expression for the area under the ROC curve. Moreover, by adjusting its shape parameter, the bi-Weibull model can represent a variety of distributions, such as exponential, Rayleigh, normal, and extreme value distributions. Its compatibility with Cox's proportional hazards model facilitates the derivation of covariate-adjusted ROC curves and supports analyses involving correlated and longitudinal biomarkers. These properties make the model very useful in the ROC curve analyses. Thus, the bi-Weibull model should be considered as an alternative when the restrictive distributional assumptions of the commonly used parametric models (e.g., binormal model) are not met.