When evaluating a diagnostic test, it is common that a gold standard may not be available. One example is the diagnosis of SARS‐CoV‐2 infection using saliva sampling or nasopharyngeal swabs. 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 sensitivity, specificity, 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 an 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, specificity, and sensitivity in a meta‐analytic framework.