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.  
Highlights
Generalisation of Receiver operating characteristic (ROC) curve in assessing how diagnostic tests perform can be a challenging task (Koech, 2018) especially since the tests more than two outcomes leading to multiple true class rates and false class rates
Generalisation of Receiver operating characteristic (ROC) curve has become increasingly useful in evaluating the performance of diagnostic tests that have more than binary outcomes
The simulation study sought to examine whether the non-parametric estimator was efficient in modelling ROC and provide reasonable inference on performance of a three-way diagnostic test
Summary
Generalisation of Receiver operating characteristic (ROC) curve in assessing how diagnostic tests perform can be a challenging task (Koech, 2018) especially since the tests more than two outcomes leading to multiple true class rates and false class rates. Ferguson (1983), West (1990) and Escobar & West (1995) are some of the notable scholarly works that have underpinned the use of non-parametric methods in in estimating the accuracy of diagnostic test They have suggested that when observations on some random variable follow a distribution which is assumed to be is a random sample function of a non-parametric scholastic process (Dirichlet process), the random measure’s conditional distribution can be calculated. The assumption in this case are derived from Bayesian viewpoint Studies, such as Choi et al (2006) have proposed Bayesian parametric multivariate ROC methodology as alternative to Gaussian estimation of diagnostic tests owing to the limitations of normality assumptions in cases especially rare diseases that have not been well studied. Hanson et al (2008) estimated several ROC curves using the mixtures of Polya trees (MFPT) in estimation of multivariate serologic data
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