Quantitative microbial risk assessment exemplified by Staphylococcus aureus in unripened cheese ...

16 Pages·2002·0.23 MB·English

InternationalJournalofFoodMicrobiology78(2002)155–170
www.elsevier.com/locate/ijfoodmicro
Quantitative microbial risk assessment exemplified by
Staphylococcus aureus in unripened cheese made from raw milk
Roland Lindqvista,*, Susanne Sylve´na, Ivar Va˚gsholmb
aNationalFoodAdministration,P.O.Box622,SE-75126Uppsala,Sweden
bTheNationalVeterinaryInstitute,SVA,SE-75189Uppsala,Sweden
Accepted26May2002
Abstract
This paper discusses some of the developments and problems in the field of quantitative microbial risk assessment,
especially exposure assessment and probabilistic risk assessment models. To illustrate some of the topics, an initial risk
assessment was presented, in which predictive microbiology and survey data were combined with probabilistic modelling to
simulatethelevelofStaphylococcusaureusinunripenedcheesemadefromrawmilkatthetimeofconsumption.Duetolimited
dataandabsenceofdose–responsemodels,acompleteriskassessmentwasnotpossible.Instead,thefinallevelofbacteriawas
usedasaproxyforthepotentialenterotoxinlevel,andthusthepotentialforcausingillness.Theassessmentendpointselected
for evaluation was the probability that a cheese contained at least 6 log cfu S. aureus g(cid:1)1 at the time of consumption; the
probability of an unsatisfactory cheese, P . The initial level of S. aureus, followed by storage temperature had the largest
uc
influenceonP atthetwopH-valuesinvestigated.P decreasedwithdecreasingpHandwasuptoafactorof30lowerinlow
uc uc
pHcheesesduetoaslowergrowthrate.Ofthemodelassumptionsexamined,i.e.theproportionofenterotoxigenicstrains,the
level of S. aureus in non-detect cheeses, the temperature limit for toxin production, andthe magnitude andvariability of the
thresholdforanunsatisfactorycheese,itwasthelatterthathadthegreatestimpactonP .Theuncertaintyintroducedbythis
uc
assumption was in most cases less than a factor of 36, the same order of magnitude as the maximum variability due to pH.
Severaldatagapswereidentifiedandsuggestionsweremadetoimprovetheinitialriskassessment,whichisvalidonlytothe
extent that the limited data reflected the true conditions andthat the assumptions madewere valid. Despitethe limitations, a
quantitativeapproachwasusefultogaininsightsandtoevaluateseveral factorsthatinfluence thepotentialriskandtomake
some inferences with relevance to risk management. For instance, the possible effect of using starter cultures in the cheese
making processto improvethe safety of these products.
D2002Elsevier ScienceB.V.All rights reserved.
Keywords:Microbialriskassessment;Staphylococcusaureus;Cheese
1. Introduction
Risk analysis within the field of food safety is a
strongly evolving activity and during recent years
* Correspondingauthor.Tel.:[phone];fax:+46-18-10-
several meetings have addressed the details of risk
5848.
E-mailaddress:[email protected](R.Lindqvist). management (FAO/WHO, 1997), risk assessment
0168-1605/02/$-seefrontmatterD2002ElsevierScienceB.V.Allrightsreserved.
PII:S0168-1605(02)00237-4
156 R.Lindqvistetal./InternationalJournalofFoodMicrobiology78(2002)155–170
(CAC, 1999) and risk communication (FAO/WHO, more infrequent consequences such as gastroenteritis
1998). Since the latest Food Micro meeting 1999 in related mortality (310 DALY) and Guillain–Barre
Veldhoven, which hosted a session devoted to risk syndrome (340 DALY), contributed as much as fre-
assessment the WHO/FAO and CODEX have quent acute gastroenteritis (440 DALY) to the total
launched several risk assessments for different patho- health burden of Campylobacter associated illness in
gen–food combinations, which have been discussed the Dutch population per year (1440 DALY).
in a series of expert consultations (e.g. FAO/WHO, Risk analysis consists of three partly overlapping
2000, in press). The purpose of developing these components; risk management, risk assessment, and
assessmentshasbeentoaddressspecificriskmanage- riskcommunication,andcanbedescribedasaframe-
ment questions and to improve and disseminate the work to analyse and manage any activity that may
methodology for risk assessment. Another important have negative consequences. In the context of food
objectiveoftheseactivitieswastodevelopguidelines safety, it is a tool, which in a formalised, systematic
and good practices for the conduct of the different and transparent way, enables responsible authorities
steps involved in a quantitative risk assessment, e.g. and international organisations to understand and if
hazard characterisation and dose–response (FAO/ necessary evaluate options to reduce a health risk.
WHO, in preparation(a)), and exposure assessment Risk assessment is a science-based process in which
(FAO/WHO, in preparation(b)). It can be envisaged questions that have been formulated during the risk
that when these documents have been finalised most evaluation step of the risk management process are
food safety issues will be addressed by development addressedtodevelopanunderstandingoftheproblem
of quantitative risk assessment models at the interna- and to come up with risk estimates. Reviews of the
tional level. The models will have to be adopted to four steps in a formal risk assessment were presented
reflect the conditions at the national level. In this at the latest Food Micro meeting in Veldhoven 1999;
respectitmaybeanticipatedthattheexposureassess- hazard identification and exposure assessment (Lam-
ment will be of particular importance due to national merding and Fazil, 2000) and hazard characterisation
differences in how food is produced and distributed, and risk characterisation (Buchanan et al., 2000),
in the occurrence of specific microorganisms, and in respectively. In short, in the exposure assessment,
the way food is prepared and consumed. the likelihood that an individual or a population will
Risk is defined as the probability and the conse- be exposed to a microbial hazard and the likely
quences of a hazard to occur. A risk in the context of numbers ingested are estimated (Lammerding and
foodsafetyistheprobabilityandtheconsequencesof Fazil, 2000). In the hazard identification step, the
adversehealtheffectsfollowingtheingestionoffood. relevant hazards, i.e. microorganisms and/or their
The separation of risk into two components is useful, toxin(s), and their main sources together with the
since risk may be managed both by actions to reduce relevant context are described. The likelihood of a
the probability and the consequences of the adverse response of any individual to an exposure to a
event. The second component is often overlooked in foodborne pathogen is dependent on the integration
microbialriskassessments,althoughitmayimplicitly of host, pathogen and food matrix effects which are
be considered in the selection of the biological end- described in the hazard characterisation step
point in the dose–response relationship, e.g. diar- (Buchanan et al., 2000). In the final risk character-
rhoea, morbidity, mortality. However, to be able to isation step, the exposure assessment serves as the
compare the public health risk and benefits of differ- input to the dose–response model selected from the
ent management options, it would be desirable to be hazardcharacterisation,inordertoevaluatetheriskin
able to integrate different biological endpoints in one relation to the risk management question. An impor-
publichealthmeasure.OnesuchmeasureisDisability tant part of this step is to estimate the uncertainty of
Adjusted Life Years (DALY), which is the sum of the estimates and the impact of critical assumptions
years of life lost by premature mortality and years made in the assessment (Buchanan et al., 2000).
livedwithdisability,weightedwithafactorbetween0 Thepurposeofthepresentworkistodiscusssome
and 1 for the severity of illness (Murray, 1996). For of the developments and problems in the field of
instance, Havelaar et al. (2000a,b) reported that the quantitative microbial risk assessment, especially as
R.Lindqvistetal./InternationalJournalofFoodMicrobiology78(2002)155–170 157
regards exposure assessment and probabilistic risk from the probability distribution defined for the
assessment models. As an illustration of some of the parameters, and represent, in principle, a scenario or
topics, an initial risk assessment of Staphylococcus event that may occur. The input distributions are
aureus in unripened cheese made from raw milk is sampled at random using the Monte Carlo or more
presented. often the Latin Hypercube, LHS, sampling methods.
LHS is a form of stratified sampling method often
regarded superior to the Monte Carlo method since it
2. Selected topics in probabilistic exposure reproduces the input distributions in fewer iterations
assessment (Vose,2000).However,LHSmayplacelessemphasis
on sampling from the tails of the input distributions
The Veldhoven reviews (Buchanan et al., 2000; and may be hard to implement in hierarchical model
Lammerding and Fazil, 2000) discussed the advan- structures consisting of several sub-models (Jordan et
tages of probabilistic modelling for addressing varia- al., 1999). The simulation result is a frequency dis-
bility and uncertainty of parameters in a risk tribution of the output of interest which provide not
assessment model. The majority of risk assessments only extreme values but also the most likely outcome
use a probabilistic approach but it may be considered basedonthecombinationsofinputprobabilityvalues
good practice to begin with a more simple determin- that could occur. The utility of probabilistic techni-
istic model to explore if probabilistic models are quesisdependentontheavailabilityofadequatedata,
necessary (EPA, 1997; Zwietering and van Gerwen, credible assumptions, and application of good scien-
2000). Probabilistic techniques, such as Monte Carlo tific practices in terms of clarity, transparency, repro-
analysis (Vose, 2000), have been demonstrated to be ducibility, and sound use of methods (EPA, 1997). In
useful tools for analysing the variability and uncer- thefieldofquantitativemicrobialriskassessment,the
tainty associated with model parameters in quantita- approaches to these issues and sound use of methods
tive risk assessments. Uncertainty, which refers to a are currently being developed. In this section, some
lack of knowledge, can be reduced by further study considerations related to the scope and development
and includes (EPA, 1997): (1) Scenario uncertainty of exposure assessments of food-borne microbial
(descriptive errors, aggregation errors, errors in pro- hazards will be addressed. The present description is
fessional judgement, incomplete analysis); (2) model by necessity sequential and ordered linearly along a
uncertainty (uncertainty due to necessary simplifica- time axis, in reality though the risk assessment proc-
tion of real-world processes, mis-specification of the essisdynamicanditerativeinnatureandmanyofthe
model structure, model misuse, use of inappropriate steps may be iterated and/or carried out in parallel
surrogate variables); and (3) parameter uncertainty (Anonymous, 2000).
(measurement errors, sampling errors, systematic
errors). Variability refers to the natural variation in 2.1. The purpose of the risk assessment
thesystemunderstudy,andfurtherstudiescanleadto
abettercharacterisationofvariability,butachangeof Thepurposeandobjectiveofanassessmentshould
thesystem,e.g.changingthefoodproductionsystem, guideitsconduct(MorganandHenrion,1990)and,in
is needed to reduce it. order to clearly and concisely define these, a close
In a probabilistic model, each uncertain model interaction between managers and assessors is neces-
input parameter is described by probability distribu- saryduringtheinitialphases.Insomeinstancesitmay
tions rather than by point estimates. There are a be necessary to limit the scope to be able to address
number of techniques to calculate the outcome dis- the questions by making them more specific or,
tribution such as the method of moments, exact alternatively, to develop more than one assessment.
algebraicsolutionsandMonteCarlosimulation(Vose, Theexposureassessmentshouldbemadeassimpleas
2000).UsingtheMonteCarloapproach,themodel is possiblewhilestillincluding theimportantsourcesof
calculateda number oftimestosimulate theoutcome risk.
distribution. Each time (iteration) the model is calcu- Based on the outcome of this initial phase deci-
lated values for the model parameters are sampled sions regarding the approaches to modelling, e.g.
158 R.Lindqvistetal./InternationalJournalofFoodMicrobiology78(2002)155–170
probabilistic or deterministic, dynamic or static, variability distribution may incorrectly be used as
empirical or mechanistic, and the structure of the if it were an uncertainty distribution (Vose, 2000).
assessmentmodel(whichpathways,singleormultiple The explicit separation of these two allows decision-
models) can be made. Dynamic models describe a makers to understand how model outputs might
processovertime(orspace)andareoftenconstructed improve if uncertainty is reduced. There are essen-
in terms of differential or difference equations, which tially two methods for producing second-order mod-
describe the rate of change. In contrast, static models els; the first calculates variability and simulates the
considertheprobabilityofaneventhappeningduring uncertainty, and the second method simulates the
agiventimeperiodoratapointintime (orlocation). variability, selecting for each simulation a random
Most QMRA’s have been driven by static risk man- sample from distributions for uncertain parameters
agement questions and the estimation of risk can (Vose, 2000).
usually be termed static, although they may contain
elements of dynamic modelling as well, e.g. model- 2.3. Thepathwaysandsteps includedinthe exposure
ling of microbial growth. assessment
2.2. Monte Carlo simulation and the separation of The relevant stages of the farm-to-fork chain, the
uncertainty and variability key processes and the level of detail necessary to
estimate the probability and the likely levels of
The basic goal of a Monte Carlo analysis is to exposures are determined with reference to the
quantitatively characterise the uncertainty and varia- assessment end point as defined by the risk manage-
bility in terms of risk, and to identify and understand ment question. It may not be possible or even
the relative contribution of the key sources of this necessary to model the whole farm-to-fork pathway
uncertainty and variability. There may be instances oreveryconceivable eventinasystemthatmay have
whereaprobabilisticMonteCarloanalysisforvarious animpactontheexposure.Dependingontheempha-
reasons is not an option. For instance, when it is not sis and the perspective of the risk assessment, differ-
expected to improve a risk assessment, when the risk ent approaches have been used in developing the
is well below concern, when neither time nor resour- overall model. For instance, the Event Tree describes
ces are available, when the problem can be managed a scenario from the initiating event to a defined
atalowcostanyway,orwhenrareeventshavealarge endpoint of the assessment (Roberts et al., 1995).
impact on the risk (EPA, 1997). In many other This approach serves to describe the high-risk path-
situations, probabilistic Monte Carlo analysis may ways that lead to contamination and subsequent dis-
be useful, e.g. when conservative point estimates fall easeandmayidentifyriskvariablesinneedoffurther
above levels of concern, in order to rank exposure data or modelling. In contrast to the Event Tree, the
sources,exposurepathwaysorcontaminants,orwhen FaultTreebeginswiththeoccurrenceofahazardand
costs are high or the consequences of not managing from there describes the events that must have
the problem are unacceptable. In practice, a tiered occurred for the hazard to be present (Roberts et al.,
approach beginning with a simple screening model 1995). This approach can provide a framework to
and progressing to more sophisticated and realistic analyse the likelihood of an event by determining the
models may often be the preferred approach (EPA, complete set of underlying conditions or events that
1997). allow the given event to occur (Jaykus, 1996). Addi-
The separation of variability and uncertainty of tional approaches to modelling used in assessments
parameters in QMRA models, second-order models, of microbial food hazards include a Dynamic Flow
have up to now rarely been made, a reflection of the Tree model (Marks et al., 1998) and a Process Risk
fact that this can be a daunting task. However, Model (Cassin et al., 1998). The former emphasises
neglecting the difference between them may lead to the dynamic nature of bacterial growth and incorpo-
improper risk estimates (Nauta, 2000) and/or incom- rates predictive microbiology using statistical analy-
plete understanding of the results (Vose, 2000). Also, sis of data, whereas the latter focuses on the integra-
if the distinction is not clear to the analyst, a tion of predictive microbiology and scenario analysis
R.Lindqvistetal./InternationalJournalofFoodMicrobiology78(2002)155–170 159
to provide an assessment of the hygienic character- may be biased due to differences in the methodology
istics of a manufacturing process. Variations on these used, e.g. in terms of sensitivity and specificity. If
themes exist. More elaborate and sophisticated clas- data on these are collected or can be calculated based
sifications and distinctions between approaches and on the survey results, apparent estimates can be
types of models than in the present work have been adjusted to come up with true prevalence estimates
proposed (see e.g. Hurd and Kaneene, 1993). The (Ebel and Schlosser, 2000).
broad types of models described here operate in only If the primary goal is to estimate the risk to a
one direction, which does not make the inclusion of population from a food–pathogen combination, it
feedback mechanisms possible. This may be a limit- may suffice to structure the model as to use data
ing factor when modelling complex biological sys- and information as close to the consumption point as
tems. Alternative models may include dynamic possible (e.g. Lindqvist and Westo¨o¨, 2000). This
models based on differential equations, or Markov approach could be useful for risk ranking as well
chain, and random-walk models or so-called neural (e.g. US-FDA/FSIS, 2000). In contrast, this approach
networks (Skjerve, 1999). The use of alternative hasamorelimitedapplicationingaininginsightsinto
structural and mathematical models, together with thefactorsmagnifyingtheriskorforconsiderationof
various types of model errors can represent important options to reduce the risk.
sources of uncertainty. It should be noticed that Given the complexity of many interrelated pro-
methods for dealing with uncertainty associated with cesses in any selected food pathway, it is often
the choice of the structure of risk models are lacking necessary to separate the overall pathway into a
(Morgan and Henrion, 1990). Preliminary analysis number of distinct modules each representing a par-
using alternative structural models may be examined ticular stage from production to consumption (Lam-
to determine if structural differences have important merding and Fazil, 2000). Common processes and
effects on the outputs of the model. However, the stages to be modelledin the exposure assessment can
scenario or event being modelled must be kept in be identified. These include production, distribution,
mind to ensure that the model provide answers to the storage, processing, preparation and handling. This
questions posed, that an event that could physically commonality opens up the possibility to develop
occurinrealityisdescribed,andthatcomparabledata common approaches for performing exposure assess-
which can be combined in the model are used (Vose, ments.Inthefuture,librariesorclearinghousescanbe
2000). envisioned which contains common exposure assess-
Since the exposure model itself is a tool to ment sub-modules that may be modified to the spe-
understand the problem under study and to identify cific problem by the potential end-user.
knowledge gaps, it is desirable that it is developed A general framework for quantitative exposure
independently from the consideration of the avail- assessment modelling, the Modular Process Risk
ability of data. This may be difficult in practice, Model (MPRM), was recently proposed (Nauta,
since the choice of model may be very dependent on 2001). In this framework, the consumption stage
the data that is available (Nauta, 2001). The data to was not addressed and processes in the primary
feed into probabilistic risk assessment models need productionwerenotexplicitlyconsidered.Theframe-
to be compiled and critically evaluated in terms of work resembles the approach of the Process Risk
sampling and analytical errors. The lack of repre- Model (Cassin et al., 1998), but at the heart of the
sentative data is a major threat to the accuracy of a proposal is the suggestion that each of the process
variability analysis. For instance, data from a survey steps in the exposure assessment can be identified as
may have to be weighted to correct for biases in the one of six basic processes; growth, inactivation,
sampling, e.g. based on the annual production in partitioning, mixing, removal and cross-contamina-
different regions (e.g. Ebel and Schlosser, 2000). tion. In each step, the number of microorganisms
Further, data from different sources that were col- per unit, e.g. carcass, bottle of milk, a package of
lected over different temporal or spatial scales may ground beef, is estimated. The size of the unit may
be the only data available and the direct combination change in the food pathway being described, for
of these may be difficult. In addition, the estimates instance as a result of mixing, i.e. several units are
160 R.Lindqvistetal./InternationalJournalofFoodMicrobiology78(2002)155–170
blendedintoalargerunit,orpartitioning,i.e.aunitis 3.2. Hazard characterisation
separated into smaller units. Removal is the process
when some units are selected and removed from the The acute effects follow after ingestion of pre-
process. Each of the six basic processes describes a formed Staphylococcal enterotoxins (SET) after a
specific sub-module in the model, and for each basic shortincubationperiod(1to7h)andincludenausea,
process a variety of models can be applied. While vomiting, abdominal pain, and diarrhoea (ICMSF,
theoretically possible to allocate a basic process to 1996). Not all strains are capable of producing SET,
each processing step, this may, in some cases, be but among the enterotoxigenic strains seven types of
unnecessaryortoocomplexinrelationtothepurpose toxins have been distinguished based on their anti-
of the exposure assessment. In those cases, it was genicproperties.TypesAandDarethemostcommon
proposed that consecutive processes could be consid- SET’s involved in food poisoning. These SET’s are
ered together, aggregated, and described by a ‘‘black formedduring theexponentialgrowth ofthebacteria,
box’’ model. In general, a model should be broken whereas the other types are predominately formed
down into smaller components, disaggregated, as when the bacteria enter the stationary phase (ICMSF,
much as necessary but not more for an efficient but 1996). The existence of long-term effects following a
accurate modelling in relation to the purpose of the S. aureus food poisoning is to our knowledge not
assessment (Vose, 2000). established. In animal studies a certain degree of
A beneficial consequence of the development of immunity have been shown after repeated exposure
the risk analysis framework may be the increased use to the same type of SET (ICMSF, 1996).
of quantitative approaches to address food safety No dose–response relationships were found in the
problems also at the national level. Such an example literature. Another limitation is that only data on the
is presented below. numberofS.aureusbacteria,nottheamountoftoxin
pergramofcheese,wasavailableforthisstudy.SET’s
havebeendetected infoodcontainingaround 106cfu
3. Example: initial risk assessment of S. aureus in g(cid:1)1 (Anunciacao et al., 1995), but there are reports
unripened cheese made from raw milk when both lower (Ro¨rvik and Granum, 1996) and
substantiallyhigherlevels(Gockleretal.,1988;Otero
3.1. Purpose of assessment/hazard identification et al., 1988) have been required for SET detection.
Thus, there are no simple relationships available
Since December 1998, the sale of dairy products betweenthenumberofbacteriaandtheconcentration
produced from raw milk is allowed by derogation in of the toxins. This taken together represents substan-
Sweden,ifproducedandsoldonthespotfromsmall- tial knowledge gaps.
scale facilities. To get a better basis for a review of
this derogation regulation an assessment of the risk 3.3. Exposure assessment
and the evaluation of some of the factors that influ-
ence its magnitude were requested. The biological 3.3.1. Prevalence and level of S. aureus in unripened
endpoint to be assessed was acute illness due to cheese at the time of sale
consumption of unripened cheese made from raw AsurveyofenterotoxigenicS.aureusinunripened
milk containing toxinogenic S. aureus. The presence cheese (n=37) produced in small-scale facilities in
ofS.aureusincheesemadefromrawmilkisaknown Sweden between August and September 1997 (Syl-
health hazard (Tham et al., 1990), and outbreaks due ve´n, 1998) indicated that about 30% of the samples
toconsumptionofcheesemadefrombothpasteurised contained S. aureus above the theoretical detection
and raw milk have been reported (Bone et al., 1989; limit of the analytical method, 100 cfu g(cid:1)1 (Table 1).
de Buyser et al., 2001). The risk was assessed based Considering the purpose of the assessment and the
on data on the prevalence and levels of S. aureus limited data available, it was decided to treat unrip-
detected in these products at the time of sale, and the ened cheeses made from raw milk as one group. This
predicted change in numbers during storage in the was a simplification since these types of cheeses
homes of the consumers (Fig. 1). include cheeses produced from goats or cows milk,
R.Lindqvistetal./InternationalJournalofFoodMicrobiology78(2002)155–170 161
Fig.1.Schematicdiagramofmodelsimulatingtheprobabilityofanunsatisfactorycheese,P .Theinputparametersofthemodelaredescribed
uc
inTable2.Onesimulationconsistedof10,000iterationsandZisthenumberofiterations(cheeses)abovethethreshold.
andrepresentdifferentgeographicalregionsandman- the results of the survey (Table 2). Seven of the
ufacturingprocesses.Whenmoredatabecomesavail- isolated strains were characterised and found to be
able this part of the analysis should be refined. able to produce SET, although toxin could not be
Further, it was assumed that cheeses can be grouped detected in any of the cheese samples analysed.
intolowlevel(<100cfug(cid:1)1),orhighlevel(>100cfu
g(cid:1)1) cheeses. The distribution of S. aureus in low 3.3.2. Prevalence and level of S. aureus in unripened
level cheese was assumed to vary uniformly between cheese at the time of consumption
(cid:1)1 and 2 log cfu g(cid:1)1, and in high level cheese In the absence of data on the level of S. aureus in
according to a cumulative distribution as defined by cheese at the time of consumption, these were simu-
162 R.Lindqvistetal./InternationalJournalofFoodMicrobiology78(2002)155–170
Table1 on display at the producers, and the survey was
SurveyoftheprevalenceandlevelsofS.aureusinunripenedcheese expected to reflect the levels found at the time of
producedfromrawmilkinSweden1997(Sylve´n,1998)
sale. Changes in the levels of bacteria between sale
Level(logcfug(cid:1)1) No.ofsamples andconsumptionareafunctionofinactivation(death)
Nd(<2) 26 and growth during storage in the refrigerators of the
2.8 1 consumers. The storage scenario investigated (Table
3.0 1
2)was based onexpert opinions oftheproducersand
3.3 1
the authorities. The predicted rate of inactivation was
3.6 1
>4.5 3 sloweveninthemostacidcheeses(pH4.9),24to55
4.6 1 days for a one-log reduction, compared to the max-
4.7 1 imum storage time (7 days), and inactivation was
5.1 1
therefore not considered.
>5.5 1
Meana:1.6logcfug(cid:1)1 Worstcase:6.0logcfug(cid:1)1 Predictive models describing growth of S. aureus
as a function of temperature and pH are available in
S.aureuswasdetectedin11outof37samples.
Nd=notdetected. both thePathogenModelingProgram(USDA, 1998),
a Mean of the logs. The level in non-detect cheeses was and in Food MicroModel, but these cannot be linked
assumedtobe0.5logcfug(cid:1)1,i.e.themeanoftheUniform((cid:1)1,2) directly in an iterative process, which is necessary to
distribution.
performtheMonteCarlosimulation. Therefore,Food
MicroModel was used to predict doubling times at
lated using a predictive growth model (Food Micro- storagetemperaturesbetween7.5and13.5jC,andat
Model ver. 3.02, Leatherhead, Surrey, UK). Cheeses twopH-values,5.2and6.5,respectively.Growthwas
analysedinthesurveyweresampledfromthecheeses assumedtobenegligiblebelow7.5jC. Thedata was
Table2
Descriptionofmodelinputs
Symbol Name Unit Assumption/distribution
Producer
P PrevalenceofS.aureusincheeses 0.3orBeta(11+1,37(cid:1)11+1)
p
1(cid:1)P Prevalenceofnon-detectcheeses
p
C Levelinpositivecheese Logcfug(cid:1)1 CumulativebasedondatainTable1RiskCumul(2;6;
pos
{2.8;3;3.3;3.6;4.5;4.6;4.7;5.1;5.5};
{0.083;0.167;0.25;0.333;0.583;0.667;0.75;0.833;0.917}
C Levelinnon-detectcheese Logcfug(cid:1)1 Uniform((cid:1)1,2),Uniform(0,2)orUniform((cid:1)2,2)
neg
N LevelofS.aureusincheese Logcfug(cid:1)1 Discrete(C :C ,P :(1(cid:1)P))
0 pos neg p p
atthetimeofsale
Consumer
T Storagetemperature jC Trigen(4,8,12,2.5%,99%)a
t Storagetime h Triang(1,72,168)a
s
t lagphaseatpH5.2 h lnt =(cid:1)3.82545(cid:2)lnT+13.18789(R2=0.997)
lag lag
t lagphaseatpH6.5 h lnt =(cid:1)3.43821(cid:2)lnT+11.53728(R2=0.999)
lag lag
DT DoublingtimeatpH5.2 h lnDT=(cid:1)2.66466(cid:2)lnT+9.15909(R2=0.998)
DT DoublingtimeatpH6.5 h lnDT=(cid:1)2.51334(cid:2)lnT+7.98642(R2=0.997)
t Timeforgrowth h t =t(cid:1)t
eff eff s lag
N LevelofS.aureusatthe Logcfug(cid:1)1 N=N+Log (2)(cid:2)(t /DT)
t t 0 10 eff
timeofconsumption,t
s
Unsatisfactorycheese,P
uc
Threshold Constant Logcfug(cid:1)1 106,105,107,or108
Variable Logcfug(cid:1)1 Triang(5,6,8)orUniform(5,8)
a Basedonexpertopinion.
R.Lindqvistetal./InternationalJournalofFoodMicrobiology78(2002)155–170 163
log–log transformed to obtain a simple, linear, rela- 10,000 iterations using Latin Hypercube sampling.
tionship between doubling time and temperature that The model is described schematically in Fig. 1. In
could be used in the simulation model (Table 2). The developing the risk assessment, several assumptions
doubling time was then used in combination with a were made and the influence of these assumptions on
simplegrowthmodeltopredictthelognumbersatthe the magnitude of P were also investigated (Fig. 1).
uc
selected storage conditions (Table 2). The lower pH- To investigate the influence of the arbitrarily selected
value may be representative for cheeses produced and constant threshold value we made a set of
using a starter culture, whereas the higher was the simulations using a constant threshold of 5, 7 and 8
average pH when 48 unripened cheeses of different log cfu g(cid:1)1, respectively, or a variable threshold with
typeswereanalysedbetween1988and1994(pH=4.9 distribution Triangular(5,6,8) and Uniform(5,8) log
to 7.3, Bjo¨rn Wallde´n, pers. comm.). It was assumed cfu g(cid:1)1, respectively (Table 2). In addition, the
thattherewasalag-phasebeforegrowthwasinitiated influence of a lower proportion, 40%, of enterotox-
andarelationship betweenlag-phase andtemperature inogenic strains was also tested. This proportion was
was calculated in the same way as for doubling time found in Norwegian cheeses made from raw milk
(Table 2). (Kruse, 1999). To investigate the influence of a
temperature limit for toxin production the model
3.3.3. Consumption was calculated under the condition that the storage
The absence of a dose–response model made it temperaturemustbeabove10jCfortoxinproduction
pointless to consider consumption in the exposure tooccur.Toinvestigatetheinfluenceoftheminimum
assessment. In order to evaluate risk at the consumer level of S. aureus in low level cheese, three simula-
level,preparation(includingcross-contamination)and tionswerecarriedoutwiththesamerandomgenerator
consumption steps need to be incorporated into the seed but using (cid:1)2, (cid:1)1, and 0 log cfu g(cid:1)1, respec-
exposure assessment. Since data on consumer behav- tively, as the minimum value in the uniform distribu-
iour is scarce simplifying assumptions often have to tion. The upper parameter was kept constant at 2 log
be made. This constitutes a serious data gap and cfu g(cid:1)1.
consequently a major source of uncertainty. Theuncertaintyintheestimationoftheprevalence
of S. aureus in cheese based on the survey can be
3.4. Risk characterisation described by a beta-function; Beta(n(cid:1)s+1, s+1),
where n is the total number of samples and s is the
Since consumption was not considered and a number of positive samples (Vose, 2000). This beta-
dose–response model was lacking the present study function describes the probability distribution of true
was not a complete risk assessment. Instead the level prevalences, which could have yielded 11 positive
of bacteria per gram was used as a proxy for the samples if a total of 37 samples were analysed. To
potential SETconcentration and hence, for the poten- demonstrate the influence of this uncertainty on the
tial risk to cause illness. The assessment endpoint simulated levels of S. aureus and P , variability and
uc
selected for evaluation purposes was the probability uncertainty was separated in a second-order model.
that an unripened cheese made from raw milk con- The model calculated variability, and the effect of
tained at least 6 log cfu S. aureus g(cid:1)1 at the time of uncertainty was investigated by simulating the model
consumption. This endpoint was termed P , the 10 times. Prior to each simulation, a value for the
uc
probability of an unsatisfactory cheese. The relation prevalence was sampled from the probability distri-
ofthisendpointtopublichealthwasnotdefinedandit bution described by Beta(27, 12).
should be emphasised that in order to fully assess the
impact of a hazard both to an individual and to 3.4.1. Results of risk characterisation
society, a dose–response model and a full exposure
assessment including consumption is necessary. 3.4.1.1. Simulated levels of S. aureus in cheese.
A spreadsheet model was developed in Excel, and Based on the mean or the median of the model
simulated using the @Risk software version 4.0 parameters,thesimulatedlevelofS.aureuswasalways
(Palisade, NY, USA). A simulation consisted of below the threshold, while it was always above the
164 R.Lindqvistetal./InternationalJournalofFoodMicrobiology78(2002)155–170
thresholdintheworstcase-scenario(datanotshown). consumption was 0.67 (high pH) and 0.74 (low pH),
Thus,pointestimateswasnotusefulinthisstudyanda respectively (Fig. 2b).
probabilisticapproachwasusedinthefollowing. The final level of bacteria at the time of consump-
The simulated level of bacteria in low pH cheese tion depends on the interplay between the model
was generally lower than in high pH cheese, due to parameters and it does not take exceedingly large
the slower growth in a more acid environment (Fig. values for unsatisfactory levels of bacteria to result
2a). For instance, the probability that a cheese con- (Table 3). In high pH cheese, the lowest storage
tains less than 1000 cfu S. aureus g(cid:1)1 at the time of temperature resulting in an unsatisfactory cheese
Fig.2.SimulatedlevelsofS.aureus,logN,atthetimeofconsumption.AcomparisonofthelevelsinhighandlowpHcheese,respectively,
t
presentedin(a)asaprobabilitydistributionplot,andin(b)asacumulativeprobabilitydistributionplot.Thetableinsertshowsthe5percentile,
95percentile,themean,andmedianofthesimulatedlevel(logcfug(cid:1)1).