When the results of a reference (or gold standard) test are missing or not error-free, the accuracy of diagnostic tests is often assessed through latent class models with two latent classes, representing diseased or nondiseased status. Such models, however, require that conditional on the true disease status, the tests are statistically independent, an assumption often violated in practice. Consequently, the model generally fits the data poorly. In this paper, we develop a general latent class model with random effects to model the conditional dependence among multiple diagnostic tests (or readers). We also develop a graphical method for checking whether or not the conditional dependence is of concern and for identifying the pattern of the correlation. Using the random-effects model and the graphical method, a simple adequate model that is easy to interpret can be obtained. The methods are illustrated with three examples from the biometric literature. The proposed methodology is also applicable when the true disease status is indeed known and conditional dependence could well be present.