BAYESIAN SEMI-PARAMETRIC AND NON-PARAMETRIC ESTIMATION OF RECEIVER OPERATING CHARACTERISTIC (ROC) SURFACE

Abstract

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. Bayesian methods are robust as it allows computability and the distributions based on this are flexible. Therefore, inference based on parametric distributions can be either misleading or insufficient. 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 and Mixtures of Finite Polya Trees, which are robust models that can handle nonstandard features in data in modelling the diagnostic data, were used to model the test outcomes. The models proved to address difficulties in modelling continuous diagnostic data with skewness, multimodality, or other nonstandard features. Semiparametric and Nonparametric models for receiver operating characteristic surface estimation were fitted using Markov Chain Monte Carlo with simple Metropolis Hastings steps. The mixing parameters, means and variances were updated with random-walk type proposals centred at some definite values. The Semi-parametric and Nonparametric, parametric approaches were considered for estimating the receiver operating characteristic surface’svolume under the surface (VUS). 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. Similarly, the non-parametric methods lead substantially to the same conclusions. In summary, to overcome the strict assumptions of parametric models, Bayesian semi-parametric model involving Dirichlet process mixtures of normals as well as non-parametric model that involve mixtures of finite Polya trees can be applied for Receiver Operating Characteristics surface estimation as they both have desirable performance.