The receiver operating characteristic (ROC) curve is a well-accepted measure of accuracy for diagnostic tests. In many applications, test performance is affected by covariates. As a result, several regression methodologies have been developed to model the ROC as a function of covariate effects within the generalized linear model (GLM) framework. We present an alternative to two existing parametric and semi-parametric methods for estimating a covariate-adjusted ROC. These methods utilize GLMs for binary data with an expected value equal to the probability that the test result for a diseased subject exceeds that of a non-diseased subject with the same covariate values. This probability is referred to as the placement value. Given that the ROC is the cumulative distribution of the placement values, we propose a new method that directly models the placement values through beta regression. We compare the beta regression method to the existing parametric and semiparametric approaches with simulation and a clinical study. Bayesian extensions for the parametric and the beta methods are developed and the performance of these extensions is evaluated through simulation. We apply the proposed beta regression approach and its Bayesian extension to a simple network meta-analysis problem using a Bayesian indicator model selection method.