A Framework for the Joint Modeling of Longitudinal Diagnostic Outcome Data and Latent Infection Status: Application to Investigating the Temporal Relationship between Infection and Disease

Abstract

For many diseases the infection status of individuals cannot be observed directly, but can only be inferred from biomarkers that are subject to measurement error. Diagnosis of infection based on observed symptoms can itself be regarded as an imperfect test of infection status. The temporal relationship between infection and marker outcomes may be complex, especially for recurrent diseases where individuals can experience multiple bouts of infection. We propose an approach that first models the unobserved longitudinal infection status of individuals conditional on relevant covariates, and then jointly models the longitudinal sequence of biomarker outcomes conditional on infection status and covariate information through time, thus resulting in a joint model for longitudinal infection and biomarker sequences. This model can be used to investigate the temporal dynamics of infection, and to evaluate the usefulness of biomarkers for monitoring purposes. Our work is motivated and illustrated by a longitudinal study of bovine digital dermatitis (BDD) on commercial dairy farms in North West England and North Wales, in which the infection of interest is Treponeme spp., and the biomarkers of interest are a continuous enzyme-linked immunosorbent assay test outcome and a dichotomous outcome, foot lesion status. BDD is known to be one of the possible causes of foot lesions in cows.