The model itself is a descendant of the so-called Hald model, a Bayesian approach first developed in 2004 that uses microbial subtyping data to infer the sources of foodborne illness. In this implementation, Salmonella isolates from humans and from four animal sources—broilers, laying hens, pigs, and turkeys—are subtyped by serovar and, for the two dominant serovars Enteritidis and Typhimurium, additionally by phage type. The model considers more than thirty serovars in total, ranging from Salmonella Agama to Salmonella Virchow, along with rough strains and unspecified serotypes. Based on the distribution of these subtypes across sources and among human cases, the model estimates how many human salmonellosis cases can be attributed to each source, including an unknown category that captures infections the four animal reservoirs cannot explain.

Two datasets from Germany parameterize the model. The first, called baseline data, comes from four baseline studies conducted between 2004 and 2007 under European harmonized monitoring programs. The second, called monitoring data, was compiled from national Salmonella control programs during 2010 and 2011. Because national monitoring of Salmonella prevalence in pigs was carried out only in 2011, the pig data from that year were combined with the poultry data from 2010, under the assumption that serotype distributions in the animals were equal in both years. Human case data came from the Robert Koch Institute, with serotype distributions obtained from the SurvStat@RKI database and phage type information for Enteritidis and Typhimurium provided by the institute’s national Salmonella reference laboratory. Since only a subset of human isolates had been phage typed, the researchers assumed that the phage type distribution among typed strains was representative of the untyped ones.

Mathematically, the model assumes that the number of observed human cases for each Salmonella subtype is Poisson distributed, with the expected number of cases caused by subtype i in source j defined as the product of four factors: the amount of source j consumed, the prevalence of subtype i in source j, a subtype-dependent factor describing the ability of that subtype to cause illness, and a source-dependent factor describing the ability of that source to serve as a vector for Salmonella. Consumption is measured in tons of meat for broilers, pigs, and turkeys, and in number of eggs for laying hens. The subtype-dependent and source-dependent factors are unknown parameters estimated from the data, with uniform distributions assumed as priors.

The specific variant used here incorporates a reparameterization introduced by David and colleagues in 2013, which exploits so-called unique types—Salmonella subtypes found exclusively in one food source and in no other source under consideration. When unique types exist for a source, the corresponding subtype-dependent parameters are fixed according to a data-based formula, which improves the robustness of the source attribution estimates and addresses convergence difficulties reported with the original Hald model. For sources without unique types, the source-dependent parameter is instead defined directly from the total number of observed cases divided by the amount consumed. This reparameterization can only be applied when all serotypes are phage typed, which is why the two dominant serovars, Enteritidis and Typhimurium, were excluded from it in the original application.

Running the model requires the programming language R together with the open-source software OpenBUGS, linked through the R package R2OpenBUGS. The FSKX-compliant version bundles the model script, visualization script, simulation settings, and harmonized metadata annotated with controlled vocabulary, so that the model can be executed, modified, and adapted to new data. Two simulation scenarios are provided: a default scenario based on the baseline data and a second scenario based on the monitoring data. The transformation into the FSKX format took about one day of work for a person already familiar with the format, and the packaged model predicts the same source attribution as the original version because the R and OpenBUGS code is nearly identical to the code used in the original publication.

But packaging a Bayesian model is only half the story. The researchers also documented three technical pitfalls that can silently corrupt results when running Bayesian models based on Markov chain Monte Carlo (MCMC) calculations. The first concerns the completeness of posterior distributions. The limits of the uniform prior distributions have a strong influence on whether the posterior distributions are complete or trimmed. With the chosen limits—an upper bound of 0.2 for the source-dependent parameters and 1 for the subtype-dependent parameters—complete posteriors were obtained for both datasets. Reducing the upper limit of the subtype-dependent prior to 0.2 produced incomplete, trimmed posteriors, a problem that might affect only some but not all model parameters, making it easy to overlook.

The second pitfall involves the choice of initial values for the Markov chains. The model runs with five chains, and the researchers demonstrated three parameter scenarios using the baseline data. When the starting points were evenly spaced in the lower fifth of the plane of possible starting values, the chains converged successfully and the error bars on the source attribution results were small. When the starting points clustered near two distant points, convergence slowed for some parameters and the error bars grew much larger. When the starting points clustered near two other points, some chains failed to converge at all within 30,000 iterations, and the error bars became larger still. Because the error bars represent a 90 percent equal-tailed interval of the posterior distribution of the number of human cases, poor convergence directly inflates the apparent uncertainty of the source attribution estimates, potentially misleading anyone who reads the results without checking the diagnostics.

The third pitfall concerns the consumption data. Some authors have argued that the consumption parameter serves merely as a scaling factor and could be set to 1 or omitted altogether. For this model, that simplification caused serious problems. With all consumption parameters set to 1 and the original priors, OpenBUGS failed to execute the model, reporting a conjugate gamma updater error for one of the subtype-dependent parameters. Enlarging the subtype-dependent prior removed the numerical error, but the results remained inconsistent—the predicted number of human cases for certain subtypes was not in the same order of magnitude as the observed cases, with observed numbers up to a factor of 2000 larger than the model estimates. Only when the prior for the source-dependent parameters was enlarged to a uniform distribution between 0 and 30,000 did the model produce consistent results for both datasets. One interpretation is that when consumption data are simplified, the subtype-dependent and source-dependent parameters must compensate, effectively becoming complex prior distributions that combine the potential of each Salmonella subtype and each source to cause salmonellosis.

The source attribution results themselves are revealing. For the baseline period 2004 to 2007, laying hens caused the majority of salmonellosis cases among the considered sources, while turkeys caused the smallest burden. For the monitoring period 2010 to 2011, the majority of cases resulted from unknown sources, closely followed by laying hens and pigs, with a relatively low burden from turkeys. Although the two datasets were compiled in a comparable way and no significant difference was expected, the packaged model provides the basis for such comparisons. Beyond the specific findings, the researchers argue that the reproducibility challenge in computational science is real: models are often re-invented and re-implemented in time-consuming and error-prone processes because of limited documentation, versioning, and scope information. By providing an annotated, ready-to-use source attribution model in an open exchange format, the team hopes to facilitate model exchange, adjustment, and reuse by the international and multi-sectoral One Health community, saving future researchers much of the painstaking work that would otherwise be needed to rebuild such models from scratch.

Subject of Research: Epidemiology

Article Title: An FSKX compliant source attribution model for salmonellosis and a look at its major hidden pitfalls

Article References: Sundermann, E. M., Correia Carreira, G., & Käsbohrer, A. (2021). An FSKX compliant source attribution model for salmonellosis and a look at its major hidden pitfalls. Food Modelling Journal, 2, Article e70008. https://doi.org/10.3897/fmj.2.70008

Image Credits: AI Generated

DOI: 10.3897/fmj.2.70008

Keywords: Salmonella, source attribution, Bayesian model, food safety, FSKX, Markov chain Monte Carlo, zoonoses, One Health, microbial subtyping, Germany, OpenBUGS, reproducibility