Abstract
Evaluation of sensitivity and specificity of diagnostic tests in the absence of a gold standard typicallyrelies on latent structure models. For example, two extensions of latent class models in thebiostatistics literature, Gaussian random effects (Qu et al., 1996) and finite mixture (Albert andDodd, 2004), form the basis of several recent approaches to estimating sensitivity and specificityof diagnostic tests when no (or partial) gold standard evaluation is available. These models attemptto account for additional item dependencies that cannot be explained with traditional latent classmodels, where the classes typically correspond to healthy and diseased individuals.We propose an alternative latent structure model, namely, the extended mixture Grade of Membership(GoM) model, for evaluation of diagnostic tests without a gold standard. The extendedmixture GoM model allows for test results to be dependent on latent degree of disease severity,while also allowing for the presence of some individuals with deterministic response patterns suchas all-positive and all-negative test results. We formulate and estimate the model in a hierarchicalBayesian framework. We use a simulation study to compare recovery of true sensitivity and specificityparameters with the extended mixture GoM model, and the latent class, Gaussian randomeffects, and finite mixture models.Our findings indicate that when the true generating model contains deterministic mixture componentsand the sample size is large, all four models tend to underestimate sensitivity and overestimatespecificity parameters. These results emphasize the need for sensitivity analyses in real lifeapplications when the data generating model is unknown. Employing a number of latent structuremodels and examining how the assumptions on latent structure affect conclusions about accuracy ofdiagnostic tests is a crucial step in analyzing test performance without a gold standard. We illustratethe sensitivity analysis approach using data on screening for Chlamydia trachomatis. This exampledemonstrates that the extended mixture GoM model not only provides us with new latent structureand the corresponding interpretation to mechanisms that give rise to test results, but also providesnew insights for estimating test accuracy without a gold standard.