Download Model-based source estimation during foodborne disease outbreaks

Model-based source estimation during
foodborne disease outbreaks
Juliane Manitz1 , Thomas Kneib1
1
Department of Statistics and Econometrics, University of Göttingen, Göttingen,
Germany
E-mail for correspondence: [email protected]
Abstract: The 2011 E. coli outbreak in Germany exposed the lack of timely
and efficient source detection as an integral part of mitigation strategies during
foodborne disease outbreaks. Conventional public health source detection procedures use case-control studies and tracings along the food shipping chain. Such
methods are typically very time-consuming and suffer from problems associated
with data collected from patient interviews, such as bias. We introduce a new
network theoretic method to estimate the spatial source of food-borne disease
outbreaks and similar dynamical contagion phenomena. Our method requires
only infection reports regularly collected by public health institutes and knowledge of the underlying food shipment network topology. We fit a hierarchical
Bayesian spatio-temporal model to the infection counts, which uses the shortest
path tree of the contaminated food shipping network as neighbourhood definition. Using Bayesian model comparison criteria, our method assignes an epicenter
plausibility to each outbreak source candidate. We test our method in a spatial
dynamic simulation model for foodborne diseases and specifically validate our
approach for the German E. coli outbreak in 2011.
Keywords: Complex network; Spatio-temporal model; foodborne disease.
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Statement of the problem
Recently observed frequent foodborne disease outbreaks acutely demonstrated the need for timely and efficient source detection in the case of a
foodborne disease outbreak to public health bodies, risk assessment authorities, food industry, and society. Only efficient epidemic source detection
and timely removal of the contaminated product can prevent further disease
spread and impact on the population and economy.
Only in 66% of observed outbreaks, public health investigations were able to
find an evidence for the infection source (O’Brien et al., 2006). One reason is
the uncertain association between aetiology and food vehicle. Furthermore,
the multi-disciplinary nature of a foodborne disease outbreak investigation
task passes another major difficulty. It usually requires information from
many sources including interview-based data from case-control and cohort
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Model-based source detection
studies as well as tracings along the food shipping chain. We eliminate this
source of bias by basing our new source estimation method only on the
topology of the underlying food shipping network and infection reports.
Our methodological developments were motivated during the 2011 EHEC/HUS outbreak in Germany, which has been the largest worldwide reported
E. coli outbreak regarding the number of severe HUS cases. The vast majority of the infections occurred in northern Germany, while other cases
were travel related (see Figure 1). The source in the Lower Saxonian district Uelzen as well as outbreak trend and sprouts as transmission vehicle
were hard to predict, because the outbreak was caused by a rare serotype
O104:H4 (Frank et al., 2011).
EHEC incidence in Germany week 21, 2011
EHEC incidence in Germany week 22 2011
(27,30]
(27,30]
(24,27]
(24,27]
(21,24]
(21,24]
(18,21]
(18,21]
(15,18]
(15,18]
(12,15]
(12,15]
(9,12]
(9,12]
(6,9]
(6,9]
(3,6]
(3,6]
(0,3]
(0,3]
FIGURE 1. EHEC incidence in Germany in 21st and 22nd calendar week, 2011
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Deterministic source detection
First, we introduce the deterministic groundwork method for source detection during foodborne disease outbreaks. On the basis of these ideas, we
will develop the model-based source detection method in the next section.
We define a food shipping network G = (K, L) as a collection of nodes k ∈ K
connected by links L, where K 6= ∅ and L is a set of unordered pairs of
elements of K. In our context, nodes represent German districts while links
refer to their trade connections. Thus, the network by definition includes
all districts suspected to be the source of the outbreak, i.e. k0 ∈ K0 ⊆ K.
For simplicity, we construct the network using the gravity law of trade
(Anderson, 1979). Then, link weights are proportional to the connected
node population and inversely proportional to their Euclidian distance.
J. Manitz and T. Kneib
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For outbreak source tracing, we define the effective distance, which combines the deterministic distance, measured as shortest path length, and
the corresponding path probability. In this way, we are able to reorganize
the spatial pattern of infection counts to a circular tree representation for
all source candidates k0 ∈ K0 as root. We minimize the effective network
distance of all potential sources to the median centre of reported epidemic
mass. Looking at the circular tree representation with the true source as
root node, it is easy to spot a circle-like pattern of infected nodes (see
Figure 2).
FIGURE 2. Deterministic source detection with application to EHEC/HUS data.
(A) German map with shortest path tree. (B) Circular shortest path tree representation with root in Uelzen. Color-coding corresponds to the aggregated EHEC
incidence during the first three outbreak weeks (19th-22nd calendar week 2011)
In extensive simulation studies, we used a novel spatial dynamic model
for foodborne diseases and showed high detection probabilities in a variety of scenarios. These simulated scenarios were also used to assess the
uncertainty of the estimated outbreak source through prediction with a
generalized linear model (McCullagh and Nelder, 1989).
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Model-based source detection
A statistical method for source detection should be able to deal with different types of uncertainty. The shipping network is defined under uncertainty,
because its structures are highly adaptive to varying demand. During the
outbreak, public health institute investigations gain knowledge from riskoriented sampling. Moreover, the infectious disease counts show trend and
seasonality and suffer from under-reporting and reporting delay.
We assess this problem by a hierarchical Bayesian spatio-temporal model,
which distinguishes the regular background trend of sporadic cases and the
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Model-based source detection
epidemic part given a specific source candidate using the network structure as neighbourhood definition. We fit this model for all potential source
candidates and derive a posterior plausibility for being the source causing
the given outbreak pattern.
We assume the number of infected ykt in district k at time t to be negative
Binomial distributed, i.e.
ykt |µkt , ν
log(µkt ) = ηkt
∼ NB(µkt , ν),
=
log(Ek ) + βt + sk|k0 + xk ,
t = 1, . . . , T, k ∈ K,
where θ kt = (β1 , . . . , βT , s1|k0 , . . . , sK|k0 , x1 , . . . , xK , ν). Thereby, βt describes the epidemic time trend, sk|k0 the dispersal of the contaminated
infection vehicle alog the food shipping chain, and xk the local dispersal
of sproradic cases. Furthermore, the model is rescaled by offset Ek , the
population in district k.
The typical epidemic curve can be adapted by a time trend prior, which
follows a random walk of order one, i.e.
βt |βt−1 , τβ ∼ N(βt−1 , τβ−1 )
Furthermore, we model the dispersal of the contaminated food item on a
shortest path tree with source candidate k0 ∈ K0 by
!
X wkl
1
sl ,
,
sk|k0 |sl , k 6= l, w, k0 , τs ∼ N
wk+
wk+ τs
k∼l
P
where wk+ = k wkl . The weights wkl represent the link weights in the
shortest path tree with root k0 .
For the regular background trend of sporadic cases, we assume local spatial
dispersal. Thus, we define a standard Besag model prior for xk
!
1
1 X
xl ,
,
xk |xl , k 6= l, τx ∼ N
nk
nk τx
k∼l
where k ∼ l represent links in the local neighborhood structure.
On another level, we plan to incorporate uncertainty about the food shipping network structure by assigning priors to the shortest path tree weights
wkl
wkl ∼ Ga(ν/2, ν/2).
The estimation of the model becomes very complex, but can be solved
elegantly using a strategy suggested by Brezger et al. (2007).
We fit this Bayesian model with epidemic dispersal along differing shortest
path trees. They represent the efficient food shipping network of a contaminated infection vehicle with root in a potential source candidates k0 ∈ K0 .
Comparing these model fits for different sources, we can assign a plausibility to each tested potential source candidate for being the true source of
the observed outbreak.
J. Manitz and T. Kneib
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Conclusion
Altogether, the introduced model-based source detection method for foodborne disease outbreaks uses minimal data basis and introduces a networktheoretic approach for detection. Alternative approaches are time-consuming
and usually based on potentially biased patient interview data. The method
is designed to work for various indirectly transmitted infectious diseases,
but has as well the potential to detect the origin of various other propagtion patterns, such as the spread of technical innovations in agriculture or
delays in a railway system.
Acknowledgments: This research has been financially supported by grants
from the German Science Foundation (DFG), Research Training Group
1644 ’Scaling problems in Statistics’.
References
Anderson, J. (1979). A Theoretical Foundation for the Gravity Equation.
American Economic Review, 69, 106 – 116.
Brezger, A., Fahrmeir, L. and Hennerfeind, A. (2007). Adaptive Gaussian
Markov random fields with applications in human brain mapping.
Journal of the Royal Statistical Society: Series C (Applied Statistics),
56, 327 – 345.
Frank, C., et al. (2011). Epidemic Profile of Shiga-Toxin Producing Escherichia coli O104:H4 Outbreak in Germany. New England Journal
of Medicine, 365(19), 1771 – 1780.
Manitz, J., Kneib, T., Schlather, M., and Brockmann, D. (2013). Networkbased Source Detection for Foodborne Disease Epidemics Applied to
the German 2011 E. coli outbreak. Working paper.
McCullagh, P. and Nelder, J.A. (1989). Generalized linear models. London:
Chapman & Hall.
O’Brien, S.J., Gillespie, I.A., Sivanesan, M.A., Elson, R., Hughes, C., and
Adak, G.K. (2006). Publication bias in foodborne outbreaks of infectious intestinal disease and its implications for evidence-based food
policy. England and Wales 19922003. Epidemiology and Infection,
134, 667 – 674.