Estimation of Receiver Operating Characteristic Surface Using Mixtures of Finite Polya Trees (MFPT)

Abstract

Generalisation of Receiver operating characteristic (ROC) curve has become increasingly useful in evaluating the performance of diagnostic tests that have more than binary outcomes. While parametric approaches have been widely used over the years, the limitations associated with parametric assumptions often make it difficult to modelling the volume under surface for data that do not meet criteria under parametric distributions. As such, estimation of ROC surface using nonparametric approaches have been proposed to obtained insights on available data. One of the common approaches to non-parametric estimation is the use of Bayesian models where assumptions about priors can be made then posterior distributions obtained which can then be used to model the data. This study uses Polya tree priors where mixtures of Polya trees approach was used to model simulated three-way ROC data. The results of VUS estimation which is considered a suitable inference in evaluating performance of a diagnostic test, indicated that the mixtures of Polya trees model fitted well the ROC surface data. Further, the model performed relatively well compared to parametric and semiparametric models under similar assumptions. Keywords: non-parametric estimation, mixtures of finite polya trees, receiver operating characteristics, volume under surface