An application of Bayesian growth mixture modelling to estimate infection incidences from repeated serological tests

Abstract

Diagnoses of infectious diseases are often performed using antibody detection through enzyme-linked immunosorbent assay techniques. These data are usually dichotomized into positive and negative samples using a fixed cut-off and prevalences of infection are subsequently estimated assuming perfect correspondence between the dichotomized test results and infection status. In contrast to this approach, in this case study, we estimate the effect of distributing insecticide impregnated bednets to prevent Leishmania infection through mixture modelling of the original continuous data. We analyze the data from a cluster randomized intervention trial using a generalized latent variable model consisting of a longitudinal mixture model for the observed outcome and a Hidden Markov model for the underlying unobserved disease status to estimate the effect of an intervention. The response and structural models are jointly estimated in a Bayesian framework. This model has the advantage that it avoids the need to choose an arbitrary cut-off and allows for uncertainty in the infection status. In this paper, we describe the development of the model and selection of priors, the application to the motivating data, model checking and simulation results.