A probit latent class model with general correlation structures for evaluating accuracy of diagnostic tests

Traditional latent class modeling has been widely applied to assess the accuracy of dichotomous diagnostic tests. These models, however, assume that the tests are independent conditional on the true disease status, which is rarely valid in practice. Alternative models using probit analysis have been proposed to incorporate dependence among tests, but these models consider restricted correlation structures. In this article, we propose a probit latent class model that allows a general correlation structure. When combined with some helpful diagnostics, this model provides a more flexible framework from which to evaluate the correlation structure and model fit. Our model encompasses several other PLC models but uses a parameter-expanded Monte Carlo EM algorithm to obtain the maximum-likelihood estimates. The parameter-expanded EM algorithm was designed to accelerate the convergence rate of the EM algorithm by expanding the complete-data model to include a larger set of parameters and it ensures a simple solution in fitting the PLC model. We demonstrate our estimation and model selection methods using a simulation study and two published medical studies.