Modelling variation in test sensitivity for monitoring leptospirosis in beef cattle

When Bayesian latent class analysis is used for diagnostic test data in the absence of a gold standard test, it is common to assume that any unknown test sensitivities and specificities are constant across different populations. Indeed this assumption is often necessary for model identifiability. However there are a number of practical situations, depending on the type of test and the nature of the disease, where this assumption may not be true. We present a case study of using a microscopic agglutination test to diagnose leptospiroris infection in beef cattle, which strongly suggests that sensitivity in particular varies among herds. We develop and fit an alternative model in which sensitivity is related to within-herd prevalence, and discuss the statistical and epidemiological implications.