title: A unification of models for meta-analysis of diagnostic accuracy studies without a gold standard.
abstract: Several statistical methods for meta-analysis of diagnostic accuracy studies have been discussed in the presence of a gold standard. However, in practice, the selected reference test may be imperfect due to measurement error, non-existence, invasive nature, or expensive cost of a gold standard. It has been suggested that treating an imperfect reference test as a gold standard can lead to substantial bias in the estimation of diagnostic test accuracy. Recently, two models have been proposed to account for imperfect reference test, namely, a multivariate generalized linear mixed model (MGLMM) and a hierarchical summary receiver operating characteristic (HSROC) model. Both models are very flexible in accounting for heterogeneity in accuracies of tests across studies as well as the dependence between tests. In this article, we show that these two models, although with different formulations, are closely related and are equivalent in the absence of study-level covariates. Furthermore, we provide the exact relations between the parameters of these two models and assumptions under which two models can be reduced to equivalent submodels. On the other hand, we show that some submodels of the MGLMM do not have corresponding equivalent submodels of the HSROC model, and vice versa. With three real examples, we illustrate the cases when fitting the MGLMM and HSROC models leads to equivalent submodels and hence identical inference, and the cases when the inferences from two models are slightly different. Our results generalize the important relations between the bivariate generalized linear mixed model and HSROC model when the reference test is a gold standard.
authors.affiliation: Division of Biostatistics, The University of Texas School of Public Health, Houston, Texas 77030, U.S.A.
authors.forename: Yulun
authors.initials: Y
authors.lastname: Liu
authors.affiliation: Division of Biostatistics, The University of Texas School of Public Health, Houston, Texas 77030, U.S.A.
authors.forename: Yong
authors.initials: Y
authors.lastname: Chen
authors.affiliation: Division of Biostatistics, University of Minnesota School of Public Health, Minneapolis, Minnesota 55455, U.S.A.
authors.forename: Haitao
authors.initials: H
authors.lastname: Chu
mesh_terms: D001172:Arthritis, Rheumatoid / Q000175:diagnosis; D001699:Biometry; D017023:Coronary Angiography / Q000592:standards / Q000706:statistics & numerical data; D003324:Coronary Artery Disease / Q000175:diagnosis / Q000000981:diagnostic imaging; D003955:Diagnostic Tests, Routine / Q000592:standards / Q000706:statistics & numerical data*; D019317:Evidence-Based Medicine / Q000592:standards / Q000706:statistics & numerical data; D005260:Female; D006801:Humans; D016014:Linear Models; D015201:Meta-Analysis as Topic; D015233:Models, Statistical; D015999:Multivariate Analysis; D065006:Papanicolaou Test / Q000592:standards / Q000706:statistics & numerical data; D012372:ROC Curve; D012015:Reference Standards; D012217:Rheumatoid Factor / Q000032:analysis; D014057:Tomography, X-Ray Computed / Q000592:standards / Q000706:statistics & numerical data; D002583:Uterine Cervical Neoplasms / Q000175:diagnosis
chemical_list: D012217:Rheumatoid Factor
keywords: Diagnostic test; Generalized linear mixed model; Hierarchical model; Imperfect reference test; Meta-analysis