Bayesian bootstrap inference for the receiver operating characteristic surface

Abstract

Accurate diagnosis of disease is of great importance in clinical practice and medical research. The receiver operating characteristic (ROC) surface is a popular tool for evaluating the discriminatory ability of continuous diagnostic test outcomes when there exist three‐ordered disease classes (e.g., no disease, mild disease, and advanced disease). We propose the Bayesian bootstrap, a fully nonparametric method, for conducting inference about the ROC surface and its functionals, such as the volume under the ROC surface (VUS). The proposed method is based on a simple, yet interesting, representation of the ROC surface in terms of placement variables and has the appealing feature of producing point and interval estimates for the ROC surface and its corresponding VUS in a single integrated framework. Results from a simulation study demonstrate the ability of our method to successfully recover the true ROC surface and to produce valid inferences in a variety of complex scenarios. An application to data from the Trail Making Test to assess cognitive impairment in Parkinson's disease patients is provided.

Bayesian nonparametric estimation of ROC surface under verification bias

“…However, then the sampling process will be very close to the BB process, which is much easier to sample from with only a fixed number of independent exponential random variables (see Section 4.7 of Ghosal and van der Vaart 15 ). After writing this paper, we learned that this method was also recently proposed by de Carvalho, 7 which is an extension of the BB method of estimation of ROC curve proposed by Gu and Ghosal 17 for two categories.…”

“…A Bayesian nonparametric estimator has been proposed by Inácio et al 6 based on the mixtures of finite Pólya trees priors. Another Bayesian nonparametric method using the Bayesian bootstrap (BB) technique has been proposed by de Carvalho et al 7 who extend the method proposed by Gu et al, 8 from two dimensions to three.…”

Statistical methods for detecting outlying and influential studies in meta-analysis of diagnostic test accuracy studies

“…Our methods can be used as a sensitivity analysis tool concurrently with the current bivariate random-effects model or as a preliminary analysis tool for robust models that accommodate outlying and/or influential studies. Although the proposed methods are solely based on the usual binary (no disease, disease) diagnostic test assumption, a future work would aim to study the performance of the methods in the context of the three-way (e.g., no disease, mild disease, advanced disease) diagnostic design as in, for example, Ina´cio de Carvalho et al 30 More future work might investigate ways to quantify uncertainty by assigning the probability of actually being outlying to each study instead of dichotomizing the state of the studies. One of the potential approaches this could be achieved is to use the Bayesian approach of modeling as in Zhang et al 31 or to fit a mixture model from a Frequentist approach as in, for example, Beath.…”