Improving interpretation of latent class models for diagnostic tests: distinguishing target condition from measurands using directed acyclic graphs

In the absence of a perfect diagnostic test for a target condition, one or more imperfect tests may be used to arrive at a clinical diagnosis. Latent class analysis can be used to model data from imperfect tests with the objective of estimating test accuracy and target condition prevalence. Such models typically assume there are 2 latent classes underlying the observed data-target condition positive and target condition negative. However, as we illustrate, this would be an oversimplification when any of the observed tests has a measurand that is different from the target condition. We show how a directed acyclic graph can be used to illustrate the relationships between the relevant variables-the observed imperfect test results, their latent measurands, the latent target condition, covariates affecting observed or latent variables, and sources of conditional dependence. We then show how to determine the underlying latent classes and their labels. Finally, we examine how consideration of the measurand of each test impacts the likelihood and identifiability of the latent class model. Using simulation studies, we show how ignoring measurands, which are distinct from the target condition, can lead to mislabeling of the latent classes. We illustrate the value of the proposed approach by re-analyzing 2 datasets used in previously published latent class analyses of tests for pediatric tuberculosis and leptospirosis.