Diagnostic accuracy, a measure of diagnostic tests for correctly identifying patients with or without a target disease, plays an important role in evidence-based medicine. Diagnostic accuracy of a new test ideally should be evaluated by comparing to a gold standard; however, in many medical applications it may be invasive, costly, or even unethical to obtain a gold standard for particular diseases. When the accuracy of a new candidate test under evaluation is assessed by comparison to an imperfect reference test, bias is expected to occur and result in either overestimates or underestimates of its true accuracy. In addition, diagnostic test studies often involve repeated measurements of the same patient, such as the paired eyes or multiple teeth, and generally lead to correlated and clustered data. Using the conventional statistical methods to estimate diagnostic accuracy can be biased by ignoring the within-cluster correlations. Despite numerous statistical approaches have been proposed to tackle this problem, the methodology to deal with correlated and clustered data in the absence of a gold standard is limited. In this article, we propose a method based on the composite likelihood function to derive simple and intuitive closed-form solutions for estimates of diagnostic accuracy, in terms of sensitivity and specificity. Through simulation studies, we illustrate the relative advantages of the proposed method over the existing methods that simply treat an imperfect reference test as a gold standard in correlated and clustered data. Compared with the existing methods, the proposed method can reduce not only substantial bias, but also the computational burden. Moreover, to demonstrate the utility of this approach, we apply the proposed method to the study of National-Eye-Institute-funded Telemedicine Approaches to Evaluating of Acute-Phase Retinopathy of Prematurity (e-ROP), for estimating accuracies of both the ophthalmologist examination and the image evaluation., (© 2021 John Wiley & Sons Ltd.)