When evaluating a diagnostic test, it is common that a gold standard is absent. One example is the diagnosis of SARS-CoV-2 infection using saliva sampling or nasopharyngeal swab. Without a gold standard, a pragmatic approach is to postulate a “reference standard”, defined as positive if either test is positive, or negative if both are negative. However, this pragmatic approach may overestimate sensitivities because subjects infected with SARS-CoV-2 may still have double-negative test results even when both tests exhibit perfect specificity. To address this limitation, we propose a Bayesian hierarchical model for simultaneously estimating the sensitivities, specificities, and disease prevalence in the absence of a gold standard. The proposed model allows adjusting for study-level covariates. We evaluate the model performance using a worked example based on a recently published meta-analysis on the diagnosis of SARS-CoV-2 infection and extensive simulations. Compared with the pragmatic reference standard approach, we demonstrate that the proposed Bayesian method provides a more accurate evaluation of prevalence, specificities, and sensitivities in a meta-analytic framework.