We review methods for analysing the performance of several diagnostic tests when patients must be classified as having a disease or not, when no gold standard is available. For latent class analysis (LCA) to provide consistent estimates of sensitivity, specificity and prevalence, traditionally 'independent errors conditional on disease status' have been assumed. Recent approaches derive estimators under more flexible assumptions. However, all likelihood-based approaches suffer from the sparseness of tables generated by this type of data; an issue which is often ignored. In light of this, we examine the potential and limitations of LCAs of diagnostic tests. We are guided by a data set of visceral leishmaniasis tests. In the example, LCA estimates suggest that the traditional reference test, parasitology, has poor sensitivity and underestimates prevalence. From a technical standpoint, including more test results in one analysis yields increasing degrees of sparseness in the table which are seen to lead to discordant values of asymptotically equivalent test statistics and eventually lack of convergence of the LCA algorithm. We suggest some strategies to cope with this.