Bivariate Random Effects Meta-Analysis Models for Diagnostic Test Accuracy Studies Using Arcsine-Based Transformations

Abstract

A diagnostic test identifies patients according to their disease status. Different meta-analytic models for diagnostic test accuracy studies have been developed to synthesize the sensitivity and specificity of the test. Because of the likely correlation between the sensitivity and specificity of a test, modeling the two parameters using a bivariate model is desirable. Historically, the logit transformation has been used to model sensitivity and specificity pairs from multiple studies as a bivariate normal. In this thesis, we propose two transformations, the arcsine square root and the Freeman-Tukey double arcsine transformation, in the context of a bivariate random-effects model to meta-analyze diagnostic test accuracy studies. We evaluated the performance of the three transformations (the commonly used logit and the proposed transformations) using an extensive simulation study in terms of bias, root mean square error and coverage probability. We illustrate the methods using three real data sets. The simulation study results showed that, for smaller sample size and higher values of sensitivity and specificity, the proposed transformations are less biased, have smaller root mean square error and better coverage probability than the standard logit transformation regardless of the number of studies. On the other hand, for large sample sizes, the usual logit transformation is less biased and has better coverage probability regardless of the true values of sensitivity, specificity and number of studies. However, when the sample size is large, the logit transformation has better root mean square error for moderate and large number of studies. The point estimates of the two parameters, sensitivity & specificity, from the methods using the three real data sets follow patterns similar to those reported by our simulation.