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
