A modelling framework for the prediction of herd-level probability of infection from longitudinal data

The collective control programmes (CPs) that exist for many infectious diseases of farmanimals rely on the application of diagnostic testing at regular time intervals for theidentification of infected animals or herds. The diversity of these CPs complicates thetrade of animals between regions or countries because the definition of freedom frominfection differs from one CP to another. In this paper, we describe a statistical model forthe prediction of herd-level probabilities of infection from longitudinal data collected aspart of CPs against infectious diseases of cattle. The model was applied to data collectedas part of a CP against bovine viral diarrhoea virus (BVDV) infection in Loire-Atlantique,France. The model represents infection as a herd latent status with a monthly dynamics.This latent status determines test results through test sensitivity and test specificity. Theprobability of becoming status positive between consecutive months is modelled as afunction of risk factors (when available) using logistic regression. Modelling is performedin a Bayesian framework, using either Stan or JAGS. Prior distributions need to be providedfor the sensitivities and specificities of the different tests used, for the probability ofremaining status positive between months as well as for the probability of becomingpositive between months. When risk factors are available, prior distributions need to beprovided for the coefficients of the logistic regression, replacing the prior for the probabilityof becoming positive. From these prior distributions and from the longitudinal data, themodel returns posterior probability distributions for being status positive for all herds onthe current month. Data from the previous months are used for parameter estimation.The impact of using different prior distributions and model implementations on parameterestimation was evaluated. The main advantage of this model is its ability to predict aprobability of being status positive in a month from inputs that can vary in terms of natureof test, frequency of testing and risk factor availability/presence. The main challenge inapplying the model to the BVDV CP data was in identifying prior distributions, especiallyfor test characteristics, that corresponded to the latent status of interest, i.e. herds withat least one persistently infected (PI) animal. The model is available on Github as an Rpackage (https://github.com/AurMad/STOCfree) and can be used to carry out output-basedevaluation of disease CPs.