Zoonotic diseases are a major source of human morbidity world wide. In 2010, there were an estimated 600 million cases globally [1], of which 96 million were Campylobacter spp. resulting in 21,000 deaths [2]. Attributing cases of food-borne disease to putative sources of infection is crucial for identifying and prioritising food safety interventions, prompting routine national recording of human cases and surveillance of high-risk sources in many countries—for example FoodNet in the US [3], the Danish Zoonosis Centre (food.dtu.dk), and the Ministry for Primary Industries in New Zealand (foodsafety.govt.nz).

Traditional approaches to source attribution include observational risk assessment, extrapolation of surveillance or outbreak data, and epidemiological field studies [4]. The results of such direct observational methods may be highly uncertain due to long and variable disease incubation times, and many exposures of an individual to multiple sources of infection. Nevertheless, statistical modelling of human case count data, incorporating molecular strain typing of pathogen isolates from national surveillance programmes, has shown promise for identifying important sources of food-borne illness [5, 6].

The aim of this paper is to extend current approaches to statistical source attribution, and to provide a standard software package, sourceR, providing an intuitive interface to source attribution models for epidemiological domain specialists. Our principle innovation is a novel class of Bayesian non-parametric source attribution model which classifies strain types by differential epidemiological behaviour and accurately quantifies uncertainty. Furthermore, we allow for spatial and temporal heterogeneity in case and source data with the aim of detecting differential exposures to infection sources across space and time. sourceR represents the first standard software for source attribution, and is designed for use by epidemiologists and public health decision makers. It is written as an add-on package to R, the open-source lingua-franca for modern epidemiological analysis, and incorporates an object-orientated style to facilitate further model development and future maintainability.

The paper is structured as follows. We first introduce a motivating example and review existing source attribution models. The new model is described in the Design and Implementation section followed by a demonstration of model fitting using sourceR in the Materials and Methods section. Results and Discussion sections follow, and it concludes with details of Availability and Future directions.

Our approach addresses the deficiencies inherent in both the Hald and Modified Hald models by fitting a joint model for both source and human case sampling with non-parametric clustering of the type effects. This allows integration over uncertainty in the source sampling process without resorting to an approximate marginal probability distribution on p. The overdispersion is solved by non-parametrically clustering the pathogen types using a Dirichlet process (DP) on the type effect vector q. This is a data driven, automatic method which reduces the effective number of parameters in the model without requiring strong assumptions about τ² in Eq 4. Additionally, it quantifies the similarity between epidemiological characteristics (virulence, pathogenicity and survivability) of the subtypes forming the basis of future research on the genetic determinants of this behaviour. Often, human case data is associated with location such as urban/rural, or GPS coordinates whilst food samples are likely to be less spatially constrained (due to distances between production and sale locations). Both human and source data may exist for multiple time-periods. Therefore, we allow for spatial and temporal heterogeneity in the data.

The case study below illustrates how the sourceR package is used in practice. We compare the results of our approach with results from the Modified Hald, Asymmetric Island (see S2 Appendix and [16, 17]), and the “Dutch” model (see S3 Appendix and [18]). The priors for our model were selected to be minimally informative. The prevalence k_j is calculated by dividing the number of positive samples by the total number of samples for each source. In the data below, we note that for several samples the MLST typing failed, with the number of positive samples exceeding the apparent total number of MLST-typed isolates. Assuming MLST typing fails independently of pathogen type, this does not bias our results.

The model fitting process begins by formatting the data, constructing the HaldDP model and setting the McMC parameters before running the algorithm using the update() method.

## Format data

y <- Y(data = campy$cases, # Cases

 y = “Human”, type = “Type”, time = “Time”, location = “Location”)

x <- X(data = campy$sources, # Sources

 x = “Count”, type = “Type”, time = “Time”, source = “Source”)

k <- Prev(data = campy$prev, # Prevalences

 prev = “Value”, time = “Time”, source = “Source”)

## Set priors

priors = list(a_theta = 0.01, b_theta = 0.00001, a_alpha = 1, a_r = 0.1)

## Construct model

my_model <- HaldDP(y = y, x = x, k = k, priors = priors, a_q = 0.1)

## Set mcmc parameters

my_model$mcmc_params(n_iter = 1000, burn_in = 10000, thin = 500)

## Run model

my_model$update()

The sourceR package provides methods to extract and subset the complex posterior, calculate medians and credible intervals (with three possible methods percentile, SPIn [19], or Chen-Shao [20]) and plot a heatmap with a dendrogram showing the clustering of the type effects.

my_model$extract()

my_model$summary(alpha = 0.05, CI_type = “percentiles”)

my_model$plot_heatmap()

Fig 1 shows the the proportion of cases attributed to each source. The HaldDP model identified the highest proportion of human campylobacteriosis cases as coming from chicken produced by supplier A (a median of 67 percent of cases attributed). A further 11 percent were attributed to Chicken from poultry supplier B and 17 percent to Ovine. The median values for the proportion of cases attributed to each source are qualitatively similar between all models except the Dutch method.

To visualise how the DP has clustered the type effects, Gower’s distance [21] is used to compute a dissimilarity matrix between all pairs of types. Fig 2 shows that the DP identified four main type clusters (from 91 types). The violin plots of the marginal posterior distributions for each type effect (Fig 3) show the largest group of types has very small type effects and wide credible intervals compared to the other groups.

Model fit and convergence was assessed visually using trace and autocorrelation plots (see Fig A and Fig B in S4 Appendix).

sourceR represents a significant advance in source attribution modelling, and translation of advanced statistical methods into mainstream epidemiological use. In particular, the DP clustering results in a large decrease in the effective number of parameters in the model and allows detection of unusually virulent subtypes (group 2 in Fig 3) by epidemiological behaviour. The subtypes in each cluster have similar epidemiological traits (such as virulence, pathogenicity and survivability) which forms the basis for future research on genetic determinants of those traits. Additionally, if a particular type moved into the high virulence group when repeating the analysis with further data from a later time period, it would flag that type as possibly evolving to become more risky for humans. The type effects for group 3 subtypes have very wide credible intervals due to the sparsity of source samples and human cases for those types.

The relatively large uncertainty for the disease origin (the credible intervals of ξ) is likely due to C. jejuni’s complex epidemiology [6] giving rise to a posteriori correlations between components of α and q. This is expected due to bias/variance trade-off: the Dutch and Island models both lack type effects risking biased results due to not all types being equally likely to infect humans. The Island model also possesses inherently strong and difficult to verify a priori assumptions (see [16] and S2 Appendix) which are not subject to uncertainty quantification. Moreover, by removing the approximation inherent in the Modified Hald model, we expect the HaldDP model to more accurately reflect inferential uncertainty—this is particularly important for decision making in food hygiene policy, especially when commercial interests must be supported by rigorous scientific advice.

Mixing and a posteriori correlations of the HaldDP model are significantly decreased in comparison to the Modified Hald model, if not entirely resolved. Although heterogeneity in X is required to fit the models, a sparse or highly unbalanced source matrix increases posterior correlations between some source and type effects. In our experience, the algorithm works best when the source matrix has a moderate amount of heterogeneity.

Whilst the HaldDP results for ξ are qualitatively similar to those from the other models (Fig 1, we note an interesting disagreement between the Island and Hald model derivatives when comparing the the number of cases attributed to Ovine and Bovine. We conjecture that this may be due to some non-identifiability between Bovine and Ovine sources as both sources have high contamination from the same types increasing the sensitivity of ξ to sampling error. It may also be due to lack of explicit source and type effects in the Island model. Resolving this disparity is the subject of ongoing research.

The stable release version of sourceR is available from the Comprehensive R Archive Network, released under a GPL-3 licence. The development version is available at http://fhm-chicas-code.lancs.ac.uk/millerp/sourceR. As this package develops, we intend sourceR to become a platform for new source attribution model development, providing a central analytic resource for public health professionals.

The main focus of extending sourceR will be on modelling spatiotemporal correlation in the time and location dependent parameters. A spatiotemporal correlation model on α_tl could be used to identify particular foci of source contamination, enabling targeted investigation of particular food supply regions. Implementation of time varying type effects may be appropriate as Campylobacter can evolve quickly and genetic variation conferring virulence may not be apparent from coarse-scale MLST typing [22]. Interaction terms between some sources and types would allow for the biologically plausible possibility that certain types are differentially likely to survive and cause disease, dependent on the food source they appear in. Additionally, water/ environmental samples could be attributed to the other sources of infection allowing estimation of the proportion of cases attributed to different paths of infection (direct infection from the source versus infection via the environment).

However, including interaction terms and additional paths of infection would significantly increase the number of parameters and the number and strength of posterior correlations. With higher posterior correlations, the current Metropolis-Hastings based fitting algorithm would suffer from a loss of efficiency. This could be addressed with gradient-based fitting algorithms such as Hamiltonian Monte Carlo (HMC) [23] which are designed to converge to high-dimensional, non-orthogonal target distributions much more quickly. In particular, the No U-Turn Sample (NUTS) presents an attractive method for tuning HMC adaptively, a quality which we consider necessary to minimise user intervention and maximise research productivity [24].

With increased interest in source attribution models for both food-borne pathogens, sourceR has been written with extensibility in mind. In particular, the DAG representation allows for rapid construction of modified and new models. The package routines are written in R (as opposed to C or C++) to aid readability, with the node class hierarchy and three stage workflow designed to aid the addition of new model classes. All internal classes and methods are documented to enable prospective developers to familiarise themselves with the source code quickly, and an extensive test suite is provided. We note that the DAG framework is not limited solely to source attribution models and may used for other Bayesian applications, particularly those for which a Dirichlet process is required.

We have presented a novel source attribution model which builds upon, and unites, the Hald and Modified Hald approaches. It is widely applicable, fully joint, and does not require approximations or a large number of assumptions. Mixing and a posteriori correlations are significantly decreased in comparison to the Modified Hald model. Furthermore, it allows the data to inform type effect clustering using a Bayesian non-parametric model which identifies groups of sub types with similar putative virulence, pathogenicity and survivability. This is a significant improvement over the previous attempts to improve model identifiability (fixing some source and type effects a priori, or modelling the type effects as random using a 2 stage model). Like the Modified Hald model, the new model incorporates uncertainty in the prevalence matrix into the model, however, it does this by fitting a fully joint model rather than a 2 step model. This has the advantage of allowing the human cases to influence the uncertainty in the source data and preserves the restriction on the sum of the prevalences for each source. The sourceR package implements this model to enable straightforward attribution of cases of zoonotic infection to putative sources of infection by epidemiologists and public health decision makers.