OHEJP-RaDAR-D-JRP3-6.1 Integration of information by Bayesian evidence synthesis

In work package 6 of the EJP RaDAR project, we applied the Bayesian Evidence Synthesis
(BES) approach to estimate human carriage of ESBL-producing E coli (ESBL E. coli) in the Netherlands that is attributable to pork. BSE is a statistical modelling approach that can make use of all available information, by combining all relevant data with a priori knowledge regarding model parameters, and is suitable for estimation of parameters such as prevalence or incidence for which no direct measurements exist, but which may be indirectly informed by other data sources [1,2]. This approach importantly recognises all sources of uncertainty in the data sources contributing to the uncertainty of parameters of interest. As in meta-analysis, multiple sources of data informing the same parameter are naturally weighted by their accuracy; as a corollary, all data sources contributing information to a given parameter are also essentially weighted by precision. BES (under various names) has previously been applied to QMRA analyses [3] and in studies combining contamination risks in food processing with epidemiological data on infection risks [4].

The ultimate aim of implementing a full BSE network would be to eventually integrate information from all exposure pathways and all health effects and in multiple countries, but under the lights of the pilot project that RaDAR conforms, to make the initial problem tractable we focused only on ESBL E. coli in humans attributable to pork consumption in the Netherlands.

The main parameter of interest, annual carriage of ESBL E. coli in humans attributable to eating pork, is informed by two broad networks of information: (i) ‘bottom-up’ approach (quantitative microbial risk assessment, here on QMRA): infection in the entire chain of pork production, processing, distribution, and consumption and (ii) ‘top-down’ approach (here on EPI): epidemiological studies of carriage in humans. These two networks when combined in a single ‘joint’ analysis may lead to inconsistent estimates. In the BES framework, various aspects of model criticism (i.e., assessment of chain convergence, comparison of model variants in terms of deviance criteria) can help formally diagnosis the presence of inconsistencies, and also allow identification of potentially incorrect (model) assumptions and/or possibly biased data sources [5]. Thus, the full (integrated) model may help in finding conflicting evidence, and consequently provide a means for correcting the model. In the presence of substantial conflict, posterior distributions obtained from the full (joint) model may be at best inaccurate and at worst incorrect. Integration of two sub-models into a single model has involved technical challenges, but fortunately methods are now available to assist in such analyses [6,7].

We built up the full BES network for the pork chain as a multi-level Bayesian model, where parameters have initial prior distributions whose parameters in turn have prior distributions. This allows to manage the level of desired uncertainty and also to find the most representatives values for some priors, e.g., uncertainty in the estimated average values on top of the spread around that estimated value. The code for carrying out the calculations is written in R for JAGS.

The full QMRA pig processing model consists of a primary production farm model (WP2), and a slaughter process model, a consumption phase model, and a dose-response model (WP3), which are described more in detail in their corresponding work package reports. In here we will briefly explain how they are interlaced in the network and then joined together with the EPI model. The purpose from this report is to highlight the most prominent findings after successfully managed to implement the full BSE network. A manuscript describing this study in detail is currently being written (Bonacic Marinovic et al., in preparation) and will be submitted for publication during 2021, together with a manuscript resulting from the task from WP3.2, where the slaughter model and the consumer behaviour model, both part of the QMRA submodel, are also described in detail (Swart et al., in preparation).