Bayesian meta-analysis for test accuracy

Lyle D Broemeling
Broemeling & Associates Inc, Medical Lake, WA, USA

Abstract: Determining the accuracy of a medical test is quite difficult because accuracy is an elusive parameter to estimate. A common scenario is estimating the true and false positive fractions from different studies and arriving at a common value of the accuracy of the test. The accuracy is expressed with an estimate similar to the area under the receiver operating characteristic (ROC) curve. Under the assumption that the ROC area is the same across all tests, the true and false positive fractions can be plotted on the same graph to obtain an experimental ROC curve, called the summary ROC curve (SROC) curve. The estimate of the accuracy of the curve is the ordinate of the point of intersection, where the SROC curve intersects the line with equation true positive rate + false positive rate = 1. Using a Bayesian approach, the presentation begins with summarizing information about test accuracy for tests with ordinal and continuous scores, where it is assumed the tests share a common ROC curve, but the tests may differ in the threshold used to declare a positive test. The true and false positive rates are transformed so that one may use bilogistic regression to determine the accuracy of the combined tests where the posterior distribution of the parameters of the model are determined. Bayesian inferences are based on the posterior distribution of the SROC curve and the computations are executed with the WinBUGS software package, and several examples from various areas of medicine illustrate the methodology.

Keywords: Bayesian inferences, meta-analysis, SROC curve