eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2018-10-31 6 6 218 223 10.12691/ajams-6-6-1 AJAMS2018661 article Ben K. Koech benykip@gmail.com 1 Department of Mathematics and Computer Science, University of Eldoret, P O Box 9591-30100, Eldoret, Kenya Receiver operating characteristic curve analysis is widely used in biomedical research to assess the performance of diagnostic tests. Estimation of receiver operating characteristic curves based on parametric approach has been widely used over years. However, this is limited by the fact that distribution of almost all diseases in epidemiology cannot be established quite easily. Semi parametric methods are robust as it allows computability and the distributions based on this are flexible. Furthermore, there is need for generalization of the receiver operating characteristic curve (since, the analysis largely assumes that test results are dichotomous) to allow tests to have more than two outcomes. The receiver operating characteristic curve was generalized to constitute a surface, which uses volume under the surface (VUS) to measure the accuracy of a diagnostic test. Dirichlet process mixtures of normals, which is a robust model that can handle nonstandard features in data in modelling the diagnostic data, were used to model the test outcomes. Semiparametric Dirichlet process mixtures of normals for receiver operating characteristic surface estimation were fitted using Markov Chain Monte Carlo with simple Metropolis Hastings steps. The Semi-parametric simulation results indicate that even when the parametric assumption holds, these models give accurate results as the volume under the surface (VUS) for both methods were greater than 1/6, the value of a 'useless test'. Graphically, the semiparametric receiver operating characteristic surface has the appealing feature of being continuous and smooth, thus allowing for useful interpretation of the diagnostic performance at all thresholds. http://pubs.sciepub.com/ajams/6/6/1/ajams-6-6-1.pdf Bayesian Semiparametric Estimation Dirichlet process mixtures of normals Receiver operating characteristics Volume Under Surface