Latent variable modeling of diagnostic accuracy

Latent class analysis has been applied in medical research to assessing the sensitivity and specificity of diagnostic tests/diagnosticians. In these applications, a dichotomous latent variable corresponding to the unobserved true disease status of the patients is assumed. Associations among multiple diagnostic tests are attributed to the unobserved heterogeneity induced by the latent variable, and inferences for the sensitivities and specificities of the diagnostic tests are made possible even though the true disease status is unknown. However, a shortcoming of this approach to analyses of diagnostic tests is that the standard assumption of conditional independence among the diagnostic tests given a latent class is contraindicated by the data in some applications. In the present paper, models incorporating dependence among the diagnostic tests given a latent class are proposed. The models are parameterized so that the sensitivities and specificities of the diagnostic tests are simple functions of model parameters, and the usual latent class model obtains as a special case. Marginal models are used to account for the dependencies within each latent class. An accelerated EM gradient algorithm is demonstrated to obtain maximum likelihood estimates of the parameters of interest, as well as estimates of the precision of the estimates.