6
Bayesian inference for quantifying Listeria monocytogenes prevalence and concentration in minced pork meat from presence/absence microbiological testing Nikolaos D. Andritsos, Marios Mataragas * , Spiros Paramithiotis, Panagiotis N. Skandamis, Eleftherios H. Drosinos Laboratory of Food Quality Control and Hygiene, Department of Food Science and Technology, Agricultural University of Athens, Iera Odos 75, GR-118 55 Athens, Greece article info Article history: Received 28 August 2011 Received in revised form 24 February 2012 Accepted 27 February 2012 Available online 13 March 2012 Keywords: Bayesian inference Listeria monocytogenes Pork meat Presence/absence testing Prevalence Uncertainty abstract The purpose of this work was to estimate the prevalence and concentration of Listeria monocytogenes in minced pork meat by the application of a Bayesian modeling approach. Samples (n ¼ 100) collected from local markets were tested for L. monocytogenes using in parallel the PALCAM, ALOA and RAPIDL.mono selective media. Presence of the pathogen was conrmed through biochemical and molecular tests. Independent experiments (n ¼ 10) for validation purposes were performed. No L. monocytogenes was enumerated by direct-plating (<10 CFU/g), though the pathogen was detected in 22% of the samples. Sensitivity and specicity varied depending on the culture method. L. monocytogenes concentration was estimated at 14e17 CFU/kg. Validation showed good agreement between observed and predicted prevalence (error ¼2.17%). The use of at least two culture media in parallel enhanced the efciency of L. monocytogenes detection. Bayesian modeling may reduce the time needed to draw conclusions regarding L. monocytogenes presence and the uncertainty of the results obtained. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Minced meat supports the growth of a wide variety of micro- organisms including Listeria monocytogenes, the causative agent of listeriosis (Lianou and Sofos, 2007; Sofos et al., 1995). Despite the low incidence of the disease in humans, listeriosis is characterized by high hospitalization and case fatality rates (i.e., 20e30%), espe- cially among Young, Old, Pregnant and Immune-compromised (YOPI) people (Mead et al., 1999). During the past three decades, the recorded cases of L. monocytogenes infections have been grown signicantly due to several outbreaks of foodborne related listeri- osis. The contamination levels in foods associated with L. monocytogenes infection were between 10 2 and 10 6 CFU/g or CFU/ ml in the majority of cases (Dawson et al., 2006). Predictive or quantitative microbiology describes microbial responses to a given set of conditions (e.g., temperature, pH and a w ) by mathematical equations (models). The models can be used to make predictions regarding pathogenic or spoilage microorgan- ismsbehavior under specied environmental conditions (McDonald and Sun, 1999; Vadasz and Vadasz, 2008). The majority of published models adopt a deterministic approach to the prediction of microorganismsbehavior, without taking account of possible variability and/or uncertainty in the output data, thus limiting their usefulness, for risk assessment and other purposes (Nauta, 2002; Pouillot and Lubran, 2011). Consequently, a more stochastic approach is needed; particularly as it is well known that routine culture methods are imperfect diagnostic tests with sensitivities and specicities less than 100% (Habib et al., 2008; Rosenquist et al., 2007). Estimation of pathogen prevalence from survey or screening test data can be erroneous. However, the true rather than the apparent prevalence can easily be calculated if the sensitivity and specicity of the test(s) used in surveys or for screening are known (Thruseld, 2007). In this way, undesirable under- or overestimation of prevalence can be avoided, thus enhancing understanding of the extent to which pathogens are in control at each stage in a food production chain. Recently, Bayesian methods have been introduced for predicting microbial growth parameters, with improvement of the accuracies of probabilistic models (Crepet et al., 2009; Delignette-Muller et al., 2006; Jaloustre et al., 2011; Pouillot et al., 2003). Bayesian analysis combines prior knowledge, described by probability distributions, with the avail- able data to produce updated posterior distributions (Lesaffre et al., 2007). * Corresponding author. Tel.: þ30 210 529 4683/4704; fax: þ30 210 529 4683. E-mail address: [email protected] (M. Mataragas). Contents lists available at SciVerse ScienceDirect Food Microbiology journal homepage: www.elsevier.com/locate/fm 0740-0020/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.fm.2012.02.016 Food Microbiology 31 (2012) 148e153

Bayesian inference for quantifying Listeria monocytogenes prevalence and concentration in minced pork meat from presence/absence microbiological testing

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Food Microbiology 31 (2012) 148e153

Contents lists available

Food Microbiology

journal homepage: www.elsevier .com/locate/ fm

Bayesian inference for quantifying Listeria monocytogenes prevalence andconcentration in minced pork meat from presence/absence microbiologicaltesting

Nikolaos D. Andritsos, Marios Mataragas*, Spiros Paramithiotis, Panagiotis N. Skandamis,Eleftherios H. DrosinosLaboratory of Food Quality Control and Hygiene, Department of Food Science and Technology, Agricultural University of Athens, Iera Odos 75, GR-118 55 Athens, Greece

a r t i c l e i n f o

Article history:Received 28 August 2011Received in revised form24 February 2012Accepted 27 February 2012Available online 13 March 2012

Keywords:Bayesian inferenceListeria monocytogenesPork meatPresence/absence testingPrevalenceUncertainty

* Corresponding author. Tel.: þ30 210 529 4683/47E-mail address: [email protected] (M. Mataragas).

0740-0020/$ e see front matter � 2012 Elsevier Ltd.doi:10.1016/j.fm.2012.02.016

a b s t r a c t

The purpose of this work was to estimate the prevalence and concentration of Listeria monocytogenes inminced pork meat by the application of a Bayesian modeling approach. Samples (n ¼ 100) collected fromlocal markets were tested for L. monocytogenes using in parallel the PALCAM, ALOA and RAPID’L.monoselective media. Presence of the pathogen was confirmed through biochemical and molecular tests.Independent experiments (n ¼ 10) for validation purposes were performed. No L. monocytogenes wasenumerated by direct-plating (<10 CFU/g), though the pathogen was detected in 22% of the samples.Sensitivity and specificity varied depending on the culture method. L. monocytogenes concentration wasestimated at 14e17 CFU/kg. Validation showed good agreement between observed and predictedprevalence (error ¼ �2.17%). The use of at least two culture media in parallel enhanced the efficiency ofL. monocytogenes detection. Bayesian modeling may reduce the time needed to draw conclusionsregarding L. monocytogenes presence and the uncertainty of the results obtained.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Minced meat supports the growth of a wide variety of micro-organisms including Listeria monocytogenes, the causative agent oflisteriosis (Lianou and Sofos, 2007; Sofos et al., 1995). Despite thelow incidence of the disease in humans, listeriosis is characterizedby high hospitalization and case fatality rates (i.e., 20e30%), espe-cially among Young, Old, Pregnant and Immune-compromised(YOPI) people (Mead et al., 1999). During the past three decades,the recorded cases of L. monocytogenes infections have been grownsignificantly due to several outbreaks of foodborne related listeri-osis. The contamination levels in foods associated withL. monocytogenes infectionwere between 102 and 106 CFU/g or CFU/ml in the majority of cases (Dawson et al., 2006).

Predictive or quantitative microbiology describes microbialresponses to a given set of conditions (e.g., temperature, pH and aw)by mathematical equations (models). The models can be used tomake predictions regarding pathogenic or spoilage microorgan-isms’ behavior under specified environmental conditions(McDonald and Sun, 1999; Vadasz and Vadasz, 2008). The majority

04; fax: þ30 210 529 4683.

All rights reserved.

of published models adopt a deterministic approach to theprediction of microorganisms’ behavior, without taking account ofpossible variability and/or uncertainty in the output data, thuslimiting their usefulness, for risk assessment and other purposes(Nauta, 2002; Pouillot and Lubran, 2011). Consequently, a morestochastic approach is needed; particularly as it is well known thatroutine culture methods are imperfect diagnostic tests withsensitivities and specificities less than 100% (Habib et al., 2008;Rosenquist et al., 2007). Estimation of pathogen prevalence fromsurvey or screening test data can be erroneous. However, the truerather than the apparent prevalence can easily be calculated if thesensitivity and specificity of the test(s) used in surveys or forscreening are known (Thrusfield, 2007). In this way, undesirableunder- or overestimation of prevalence can be avoided, thusenhancing understanding of the extent to which pathogens are incontrol at each stage in a food production chain. Recently, Bayesianmethods have been introduced for predicting microbial growthparameters, with improvement of the accuracies of probabilisticmodels (Crepet et al., 2009; Delignette-Muller et al., 2006; Jaloustreet al., 2011; Pouillot et al., 2003). Bayesian analysis combines priorknowledge, described by probability distributions, with the avail-able data to produce updated posterior distributions (Lesaffre et al.,2007).

Page 2: Bayesian inference for quantifying Listeria monocytogenes prevalence and concentration in minced pork meat from presence/absence microbiological testing

model{

detected~dbin(APr,total)APr<-CPr*SE+(1-CPr)*(1-SP)SE~dbeta(17,7)SP~dbeta(79,1)CPr~dbeta(1,1)

}

Datalist(detected=16, total=100)

Fig. 1. Model 1 used for estimating total confirmed prevalence (CPr) of Listeria mon-ocytogenes, sensitivity (SE) and specificity (SP) of each method with Markov chainMonte Carlo in WinBUGS. Data displayed in this model, i.e., for the ‘detected’parameter (APr, apparent prevalence) and uncertainty distributions of SE and SP, arederived from PALCAM. Data used for ALOA and RAPID’L.mono are described in the text.

N.D. Andritsos et al. / Food Microbiology 31 (2012) 148e153 149

The aim of this study was to accurately estimate the prevalenceand concentration of L. monocytogenes in minced pork meat frompresence/absence microbiological data by the application ofa Bayesian modeling approach. In addition, the sensitivities andspecificities of three culture media commonly used for the detec-tion of L. monocytogenes were compared.

2. Materials and methods

2.1. Collection of minced pork meat samples

Samples (n ¼ 100) of naturally contaminated fresh minced porkmeat (weight of each sample equal to 500 g) were purchased fromretail outlets within the metropolitan area of Athens, Greece,during a survey between May 2009 and March 2010. Samples weretransported to the laboratory, under refrigeration in polystyreneboxes or isothermal bags, stored at chill temperature (4 � 2 �C) anddrawn separately in random sequence for analysis. The analysisstarted within 2 h of the arrival of samples at the laboratory.

2.2. Detection and enumeration of L. monocytogenes in mincedpork meat

Enrichment and direct-plating were performed according toInternational Organization for Standardization (ISO) standards11290-1:1996 and 11290-2:1998, respectively (ISO, 1996, 1998).Briefly, for pathogen detection a representative analytical unit of25 g, taken randomly from different parts of each sample, wastransferred aseptically into a sterile stomacher bag (SewardMedical, London, UK) and 225 ml of sterile half-strength Fraserbroth (Biolife, Milan, Italy) were added. The contents werehomogenized at room temperature in a Stomacher 400-laboratoryblender (Seward Medical), for 1 min at normal speed and for 30 s athigh speed, and then incubated at 30 �C for 24 h. Afterwards, a 10 mlportion of each broth was spread on each of the duplicate plates ofPALCAM (Biolife), ALOA (Biolife) and RAPID’L.mono (Bio-Rad Lab.,Paris, France) selective agars. The plates were incubated at 37 �C for48 h. Enumeration of L. monocytogenes in each broth was per-formed by spreading 1 ml on three plates, i.e., 0.33 ml of a 10�1

dilution of the broth on each duplicate plate of the same selectiveagars and incubating the plates at 37 �C for 48 h.

2.3. Confirmation of L. monocytogenes presence e biochemical andmolecular tests

From 10 to 15 typical L. monocytogenes colonies per samplewereisolated for further confirmation from most samples. When thenumber of colonies from each plate of the same medium was lessthan five, all colonies were isolated. A total of 296 isolates werecollected. Biochemical tests (motility, Gram stain, catalase andoxidase reactions for genus confirmation; haemolysis andfermentation of rhamnose, xylose, mannitol and methyl a-D-man-nopyranoside for specie confirmation) and specific polymerasechain reaction (PCR) were performed to confirm isolates asL. monocytogenes (D’Agostino et al., 2004; Gasanov et al., 2005;Prentice and Neaves, 1992).

2.4. Inputs of the Bayesian analysis

The objective was to set up a predictive model for L. mono-cytogenes prevalence estimations; and to give examples on howpathogen concentration, and the sensitivity and specificity of theculture-dependent methods used could be calculated from pres-ence/absence microbiological data by Bayesian modeling. There-fore, data obtained from the survey for L. monocytogenes presence

in samples were used as input for the Bayesian analysis. Adistinction was made between: a) the apparent prevalence (APr),i.e., the proportion of samples in the population positive forL. monocytogenes according to the test used, and b) the totalconfirmed prevalence (CPr), i.e., the prevalence determined bycombining the results from all methods after conductingbiochemical and molecular confirmatory tests.

The test methods were used in parallel. Parallel testing increasesthe sensitivity, i.e., the chance of identifying samples contaminatedwith L. monocytogenes is increased. Parallel testing also allowed theclassification of each sample into four categories, depending onwhether or not data obtained from presence/absence microbio-logical testing were in accordance with confirmatory results frombiochemical and molecular tests. The categories are: a)positiveepositive (PP), i.e., confirmed positive samples (CP), b)positiveenegative (PN), i.e., false positive samples (FP), c)negativeepositive (NP), i.e., false negative samples (FN) and d)negativeenegative (NN), i.e., confirmed negative samples (CN).From this classification the observed sensitivity (SE) and specificity(SP) were estimated:

SE ¼ PP=ðPPþ NPÞ (1)

SP ¼ NN=ðPNþ NNÞ (2)

2.5. Bayesian models

2.5.1. L. monocytogenes prevalence and tests characteristics(sensitivity and specificity)

Two Bayesian models were employed in the analysis based onVose (2008). The first (Model 1) was used to determine pathogenCPr as well as the SE and SP for eachmethod, separately (Fig. 1). Thesecond (Model 2) was used to determine the same set of parame-ters combining the results obtained from ALOA and RAPID’L.mono,simultaneously (Fig. 2). The latter was done to investigate thepossibility of determining prevalence of the pathogen directly fromtests results without the need for further biochemical and molec-ular tests. Sensitivity represents the probability that a randomlyselected contaminated sample will test positive, while specificity isthe probability of a randomly selected uncontaminated sampletesting negative (Thrusfield, 2007; Vose, 2008). Outputs of the twoBayesian models were the updated distributions for CPr, SE and SP.

Page 3: Bayesian inference for quantifying Listeria monocytogenes prevalence and concentration in minced pork meat from presence/absence microbiological testing

model{

d[1:4]~dmulti(APr[1:4],100)APr[1]<-CPr*(1-SE1)*(1-SE2)+(1-CPr)*SP1*SP2APr[2]<-CPr*(1-SE1)*SE2+(1-CPr)*SP1*(1-SP2)APr[3]<-CPr*SE1*(1-SE2)+(1-CPr)*(1-SP1)*SP2APr[4]<-CPr*SE1*SE2+(1-CPr)*(1-SP1)*(1-SP2)

CPr~dbeta(1,1)SE1~dbeta(16,8)SE2~dbeta(18,6)SP1~dbeta(75,5)SP2~dbeta(70,10)

}

Data

list(d=c(66,15,8,11))

Fig. 2. Model 2 used for estimating total confirmed prevalence (CPr) of Listeria mon-ocytogenes, and the methods sensitivity (SE) and specificity (SP) with Markov chainMonte Carlo in WinBUGS, combining the results obtained from ALOA and RAP-ID’L.mono. SE1 and SP1 are related to ALOA whilst SE2 and SP2 are related to RAP-ID’L.mono. Each equation of the apparent prevalence (APr), i.e., APr [1], APr [2], APr [3]and APr [4], corresponds to the NN, NP, PN and PP sample categories, respectively,specified in the text.

N.D. Andritsos et al. / Food Microbiology 31 (2012) 148e153150

Uncertainty distributions for CPr, SE and SPwere all correlated withAPr according to the following equation (Lesaffre et al., 2007):

APr ¼ CPr� SEþ ð1� CPrÞ � ð1� SPÞ (3)

The analysis was performed with Markov Chain Monte CarlousingWinBUGS v1.4 (Spiegelhalter et al., 2003). The burn-in periodwas 1,00,000 iterations. Convergence of models was checked byreference to Gelman-Rubin convergence diagnostic graphs.

2.5.2. L. monocytogenes concentrationBased on Vose (2008), a Bayesian model was set up in Microsoft

Excel 2007 (Microsoft, Redmond, WA, USA) and simulated with@Risk v4.5 software (Palisade Corp., Ithaca, NY, USA) to constructthe posterior distributions, in an attempt to estimate pathogenconcentration from data for the number of samples of givingpositive results with the two chromogenic media ALOA and RAP-ID’L.mono. Briefly, four columns (A1, A2, A3 and A4) were con-structed. The A1 column contained the concentration (CFU/kg) from0.05 to 50.00, with a 0.05 step. The next column (A2) contained theprior, which was equal to one because no prior information wasknown regarding L. monocytogenes concentration (uniformedprior). The last two columns contained the likelihood function (A3)and the posterior (A4). For the likelihood, a binomial distributionwas used assuming that each sample is independent and has thesame probability of being contaminated. The syntax of the distri-bution was:

BINOMDISTðt;n; p; cÞ (4)

where t, number of successes in trials; n, number of independenttrials; p, probability of success on each trial; and c, a value whichdetermines the form of the function. If c is: a) equal to one, thenBINOMDIST returns the cumulative distribution function or b)equal to zero, then it returns the probability mass function(Microsoft Excel Help). In this case, the c parameter was equal to

zero so as to give the probability of having t contaminated samplesout of n. The posterior distribution (A4 column) was equal to:

Posterior ¼ RiskMean ðprior� likelihoodÞ (5)

The population of L. monocytogenes in a sample was assumed tofollow a Poisson (l � s) distribution, where l is the mean L. mono-cytogenes concentration in the sample (CFU/kg) and s is the samplesize analyzed (kg), i.e., 0.025 kg. The probability of at least oneL. monocytogenes cell being present in a sample of 0.025 kg is1 � EXP(�l) since the probability of having no L. monocytogenes ina sample of 0.025 kg is given by a Poisson probability mass functionfor x ¼ 0, i.e., p(0) ¼ EXP(�l) (Vose, 2008). Therefore, the pparameter of the binomial distribution was equal to:

p ¼ 1� EXP ð�l� s� SEÞ (6)

where l is the L. monocytogenes concentration equal to the corre-sponding cell of the A1 column; and SE is the sensitivity of eachmethod. SE was described by the beta distribution:

SE ¼ RiskBetaðconfirmed positive samples

þ 1; expected positive samples

� confirmed positive samplesþ 1Þ (7)

where confirmed positive samples are the samples found positive byALOA or RAPID’L.mono after conducting the confirmatory tests; andexpected positive samples are the total number of samplesconfirmed as positive by both biochemical and molecular tests, i.e.,the total confirmed prevalence.

2.6. Model validation

A model-independent experiment was performed in order tovalidate the capability of Model 2 to predict CPr of the pathogen inminced pork. Ten samples (n ¼ 10) of naturally contaminated freshminced pork of 500 g were purchased from butchers’ shops andsupermarkets inAthens,Greece. The sampleswereobtainedbetweenApril 2010 and May 2010. Sample transportation and preservationwere the sameasdescribed in subsection2.1.Microbiological analysisof samples, using in parallel only the ALOA and RAPID’L.mono agars,and confirmation of typical L. monocytogenes isolates by biochemicalandmolecular tests, were performed following the same proceduresas described in subsections 2.2 and 2.3.

3. Results and discussion

No L. monocytogenes was enumerated by direct-plating(<10 CFU/g), although the pathogen was detected in 16% (PAL-CAM), 19% (ALOA) and 26% (RAPID’L.mono) of the samples byenrichment without further confirmation, i.e., APr. Only oneenrichment step was included in the detection procedure becausestandard methods such as PALCAM have been shown to performbetter after 24 h of sample incubation in half-strength Fraser broth(primary enrichment) for various naturally contaminated products(Becker et al., 2006), while ALOA and RAPID’L.mono did not showany differences regarding L. monocytogenes detection whena second enrichment step was used (Becker et al., 2006). However,after confirmation by biochemical and molecular tests, 22 sampleswere identified as positive for L. monocytogenes (CPr ¼ 22%).Samples classified as PP, PN, NP and NN after applying thebiochemical and molecular tests are shown in Table 1. From thistable and Eqs. (1) and (2), the observed SE values were estimated tobe 72.7%, 68.2% and 77.3%, and the observed SP values were esti-mated to be 100.0%, 94.9% and 88.5%, for PALCAM, ALOA andRAPID’L.mono, respectively.

Page 4: Bayesian inference for quantifying Listeria monocytogenes prevalence and concentration in minced pork meat from presence/absence microbiological testing

Table 1Results obtained for each culture-dependentmethod after applying biochemical andmolecular confirmatory tests.

Test Result Confirmatory tests results

positive negative

PALCAM positive 16 0negative 6 78

ALOA positive 15 4negative 7 74

RAPID’L.mono positive 17 9negative 5 69

Table 3Distribution statistics for total confirmed prevalence (CPr), sensitivity (SE) andspecificity (SP) of each culture-dependent method.

Test Statistic Mean Standarddeviation

95% confidence intervalfor mean

Median

PALCAM CPr 0.230 0.068 0.119e0.384 0.223SE 0.695 0.094 0.495e0.861 0.701SP 0.987 0.013 0.954e1.000 0.991

ALOA CPr 0.232 0.090 0.075e0.434 0.224SE 0.650 0.098 0.448e0.827 0.654SP 0.937 0.027 0.875e0.979 0.940

RAPID’L.mono CPr 0.231 0.094 0.059e0.432 0.227SE 0.736 0.091 0.542e0.892 0.743SP 0.874 0.036 0.796e0.937 0.877

N.D. Andritsos et al. / Food Microbiology 31 (2012) 148e153 151

Initial uncertainty about SE and SP was described by a betadistribution. Prior CPr was equal to beta(1,1), i.e., a uniform distri-bution indicating no prior knowledge (Figs. 1 and 2). The preva-lence of L. monocytogenes found by confirmatory tests (22%) wasnot used as prior information. Prevalence is not constant because itvaries with the number of samples taken from the populationunder consideration. On the other hand, SE and SP tend to be quiterobust as their values change only a little between low and highprevalence populations (Thrusfield, 2007; SISA, 2011). In futuresurveys of minced pork meat, pathogen prevalence will be theunknown parameter that should be predicted by the model. Ingeneral, it should be described by a distribution which shows noprior knowledge about the parameter, such as beta(1,1).

The parameters of the beta distribution for SE and SP werecalculated as follows: results of confirmatory tests showed that 22samples were contaminated with L. monocytogenes, with 16 (PAL-CAM), 15 (ALOA) and 17 (RAPID’L.mono) samples confirmed aspositive, and 78 (PALCAM), 74 (ALOA) and 69 (RAPID’L.mono)samples confirmed as negative. That is, 22 positive samples wereexpected but 16, 15 and 17 positive samples were detected byPALCAM, ALOA and RAPID’L.mono, respectively. Similarly, for thenegative samples, 78 samples were expected to be negative but 78(PALCAM), 74 (ALOA) and 69 (RAPID’L.mono) negative sampleswere recorded. Therefore, SE ¼ beta(confirmed contaminatedsamples or CP þ 1, expected positive samples � confirmedcontaminated samples or CP þ 1) and SP ¼ beta(confirmed noncontaminated samples or CN þ 1, expected negativesamples� confirmed non contaminated samples or CNþ 1). Hence,the beta distribution for the SE and SP of PALCAM will be:SE ¼ beta(16 þ 1, 22 � 16 þ 1) ¼ beta(17,7) and SP ¼ beta(78 þ 1,78 � 78 þ 1) ¼ beta(79,1). In the same way, the beta distributionsfor the SE and SP of ALOA and RAPID’L.mono were calculated(Table 2).

The ‘detected’ parameter of Model 1 (Fig. 1) was the number ofpositive samples detected by each method, i.e., the sum of CP andFP samples (16 for PALCAM, 19 for ALOA and 26 for RAPID’L.mono).This parameter was initially described by a binomial distribution asthe probability of having x (equal to the APr) L. monocytogenes-contaminated samples out of the total samples tested, i.e., n ¼ 100assuming that each sample was independent and had the sameprobability of being contaminated. The APr parameter was then

Table 2Calculation of the initial uncertainties regarding sensitivity (SE) and specificity (SP).

Test CPa FNa Total confirmed positive FPa

PALCAM 16 6 22 0ALOA 15 7 22 4RAPID’L.mono 17 5 22 9

a CP, confirmed positive samples; FN, false negative samples; FP, false positive sampleb beta (CP þ 1, Total confirmed positive � CP þ 1).c beta (CN þ 1, Total confirmed negative � CN þ 1).

described as a function of CPr, SE and SP according to Eq. (3). InTable 3, distribution statistics obtained for CPr, SE and SP of eachmethod after running Model 1 with the WinBUGS program aredisplayed. The results showed the imperfect nature of culture-dependent methods. RAPID’L.mono showed the highest sensi-tivity but also the lowest specificity, which can be attributed to thehigh number of FP samples that occurred with this method. PAL-CAM displayed the highest specificity, as was expected, sincecolonies of all Listeria spp. can grow on the agar, so further confir-mation of the presence of L. monocytogenes is needed. Conse-quently, FP results are excluded with PALCAM, whereas the othertwo media allow immediate discrimination of the pathogen fromother Listeria species, which may yield FP results. In Table 3, meanas well as median values are given, because for data sets withextreme values in tails the median provides a better estimate of thelocation than the mean (Anonymous, 2011). The median is a loca-tion measure that tends to have robustness of validity, whichmeans that confidence intervals for the location of population havea 95% chance of covering the population location regardless of theunderlying distribution (Mosteller and Tukey, 1977). The fact thatALOA and RAPID’L.mono allow direct determination ofL. monocytogenes plus having an indication for their SE and SPvalues, were factors incorporated into a second model, to investi-gate the chances of predicting CPr of the pathogen in minced porkmeat by combining results from these two media without need forconfirmation of L. monocytogenes.

Model 2 was based on the multinomial distribution (Fig. 2).The hypothesis here was that two diagnostic tests, i.e., ALOA andRAPID’L.mono, were available for detecting product contami-nated with L. monocytogenes, and there was prior knowledge ofSE and SP for both tests but with some uncertainty about theirvalues. The aim was to estimate prevalence of the pathogen afterparallel testing of 100 samples with both tests. The results forALOA and RAPID’L.mono were recorded as positive or negative,respectively, resulting in 66 NN, 15 NP, 8 PN and 11 PP samples.These four categories were described as functions of CPr, SE andSP. The NN, NP, PN and PP categories correspond to APr[1], APr[2], APr[3] and APr[4] equations, respectively. SE1 and SP1 arerelated to the ALOA diagnostic test whilst SE2 and SP2 are related

CNa Total confirmed negative betaSEb betaSPc

78 78 (17,7) (79,1)74 78 (16,8) (75,5)69 78 (18,6) (70,10)

s; and CN, confirmed negative samples.

Page 5: Bayesian inference for quantifying Listeria monocytogenes prevalence and concentration in minced pork meat from presence/absence microbiological testing

Table 4Distribution statistics for total confirmed prevalence (CPr), sensitivity (SE) andspecificity (SP) after combining the ALOA and RAPID’L.mono results.

Statistic Mean Standarddeviation

95% confidenceinterval for mean

Median

CPr 0.227 0.065 0.111e0.365 0.222SE1a 0.658 0.087 0.485e0.822 0.660SP1a 0.938 0.023 0.887e0.977 0.940SE2a 0.744 0.079 0.581e0.887 0.748SP2a 0.875 0.031 0.810e0.931 0.876

a SE1 and SP2, sensitivity and specificity, respectively, for the ALOA; SE2 and SP2,sensitivity and specificity, respectively, for the RAPID’L.mono.

0

25

50

75

100

0 20 40 60

Fre

quen

cy (%

)

Population (cfu/kg)

Fig. 3. Distribution of Listeria monocytogenes concentration based on ALOA (black line)and RAPID’L.mono (grey line) through Bayesian analysis of the initial data (n ¼ 100).

N.D. Andritsos et al. / Food Microbiology 31 (2012) 148e153152

to the RAPID’L.mono diagnostic test. Data from Table 2, for theinitial uncertainty distributions of SE and SP, and the relevantNN, NP, PN and PP samples were used as inputs. CPr was esti-mated at 22.2%, the median value of the distribution, which wasclose to the observed value (22%). SE and SP were estimated at0.660 and 0.940, respectively, for the ALOA and at 0.748 and0.876, respectively, for the RAPID’L.mono (Table 4). These valueswere not substantially different from those estimated by Model 1(Table 3).

For the validation experiment, the number of samples found ineach of the four categories was: NN ¼ 7, NP ¼ 1, PN ¼ 0 and PP ¼ 2.Model 2 was used to predict the CPr of the pathogen. After runningthe model, it was found that CPr was equal to 29.4% whileL. monocytogenes was confirmed by biochemical and moleculartests in 3 of the 10 samples (30%). Furthermore, SE and SP of themethods applied were almost the same as the observed values(Table 5), which confirms SE and SP as robust indices that showlittle change with population prevalence (Thrusfield, 2007; SISA,2011). Thus, the CPr of L. monocytogenes in minced pork meatcould be predicted from presence/absence results alone using asprior information the SE and SP of ALOA and RAPID’L.monomethods.

L. monocytogenes concentration, utilizing the initial data, i.e.,n ¼ 100, was estimated at 14 CFU/kg (8e23 CFU/kg) based on ALOAand 17 CFU/kg (11e26 CFU/kg) based on RAPID’L.mono (Fig. 3). Theinput data for the binomial distribution were the following: onehundred samples (n ¼ 100) of 25 g (or 0.025 kg) were analyzed forL. monocytogenes. From these samples, 19 were found positiveaccording to ALOA (t ¼ 19) and 26 were found positive according toRAPID’L.mono (t ¼ 26).

The models developed in this study are applicable within theexperimental limits only for ground pork, L. monocytogenes andthe media used. Different sensitivities and specificities can beexpected for L. monocytogenes detected in other food matricesusing other media (Aragon-Alegro et al., 2008; Stessl et al.,2009).

Table 5Validation of the predictive capability of model 2.

Statistic Observedvalue

Predicted value Error (%)a

Mean Standarddeviation

95% confidenceinterval for mean

Median

CPr 0.300 0.309 0.149 0.068e0.636 0.294 �2.17SE1b 0.682 0.671 0.091 0.482e0.836 0.675 �1.00SP1b 0.949 0.942 0.025 0.884e0.981 0.945 �0.38SE2b 0.773 0.764 0.082 0.586e0.904 0.770 �0.42SP2b 0.885 0.879 0.035 0.802e0.939 0.882 �0.38

a Error between median and observed value calculated as follows: Error(%) ¼ [(predicted � observed)/observed] � 100. The minus symbol indicates thatobserved value was higher than predicted.

b SE1 and SP2, sensitivity and specificity, respectively, for ALOA; SE2 and SP2,sensitivity and specificity, respectively, for RAPID’L.mono.

4. Conclusions

Nomethod alonewasperfect for detecting CProf L.monocytogenesinmincedpork. RAPID’L.monodisplayed thehighest SE amongothersbut also produced the highest number of FP samples. On the otherhand, PALCAM was the most specific method since no FP sampleswere observed. The latter resultwas expected since PALCAMdoes notdistinguish the pathogen from the other Listeria species and thereforetypical Listeria spp. coloniesmust becollected to confirmthepresenceof L. monocytogenes. In this way, FP samples were excluded. Incontrast, ALOA and RAPID’L.mono do allow differentiation ofL. monocytogenes from other Listeria species. Hence, only typicalL.monocytogenes colonies are isolated for further confirmation and FPsamples are likely to be obtained. However, the parallel use of thesetwo chromogenic media enhances the efficiency of L. monocytogenesdetection in minced pork meat. The Bayesian Model 2 might predictCPr for the pathogen with high accuracy using only the resultsacquired fromthetwomedia, i.e., positiveornegative,without furtherconfirmation of typical L. monocytogenes colonies. Finally, betterhandling of the uncertainty associated with parameters of interestsuch as CPr, SE and SP could be achieved through Bayesian analysis,and L. monocytogenes concentration could be estimated from pres-ence/absence test results. In general, Bayesian modeling may reducethe timeneeded todrawconclusionsaboutL.monocytogenespresenceand the uncertainty of results.

Acknowledgements

This study was supported by Alexander S. Onassis Public BenefitFoundation, through granting a PhD scholarship on Food QualityManagement & Hygiene Assurance Systems to the author N. D.Andritsos (Scholarship Code No.: G-ZC 003-2/2008-2009).

Appendix/Supplementary data

Supplementary data related to this article can be found online atdoi:10.1016/j.fm.2012.02.016.

References

Anonymous, 2011. Measures of location. In: Engineering Statistics Handbook. URL:http://www.itl.nist.gov/div898/handbook/eda/section3/eda351.htm (accessed22.07.11).

Aragon-Alegro, L.C., Aragon, D.C., Martinez, E.Z., Landgraf, M., de MeloFranco, B.D.G., Destro, M.T., 2008. Performance of a chromogenic medium forthe isolation of Listeria monocytogenes in food. Food Control 19, 483e486.

Becker, B., Schuler, S., Lohneis, M., Sabrowski, A., Curtis, G.D.W., Holzapfel, W.H.,2006. Comparison of two chromogenic media for the detection of Listeria

Page 6: Bayesian inference for quantifying Listeria monocytogenes prevalence and concentration in minced pork meat from presence/absence microbiological testing

N.D. Andritsos et al. / Food Microbiology 31 (2012) 148e153 153

monocytogenes with the plating media recommended by EN/DIN 11290-1. Int. J.Food Microbiol. 109, 127e131.

Crepet, A., Stahl, V., Carlin, F., 2009. Development of hierarchical Bayesian model toestimate the growth parameters of Listeria monocytogenes in minimally pro-cessed fresh leafy salads. Int. J. Food Microbiol. 131, 112e119.

D’Agostino, M., Wagner, M., Vazquez-Boland, J.A., Kuchta, T., Karpiskova, R.,Hoorfar, J., Novella, S., Scortti, M., Ellison, J., Murray, A., Fernandes, I., Kuhn, M.,Pazlarova, J., Heuvelink, A., Cook, N., 2004. A validated PCR-based method todetect Listeria monocytogenes using raw milk as a food model e Towards aninternational standard. J. Food Prot. 67, 1646e1655.

Dawson, S.J., Evans, M.R.W., Willby, D., Bardwell, J., Chamberlain, N., Lewis, D.A.,2006. Listeria outbreak associated with sandwich consumption from a hospitalretail shop, United Kingdom. Euro Surveill. 11, 89e90.

Delignette-Muller, M.L., Cornu, M., Pouillot, R., Denis, J.B., 2006. Use of Bayesianmodeling in risk assessment: application to growth of Listeria monocytogenesand food flora in cold-smoked salmon. Int. J. Food Microbiol. 106, 195e208.

Gasanov, U., Hughes, D., Hansbro, P.M., 2005. Methods for the isolation and iden-tification of Listeria spp. and Listeria monocytogenes: a review. FEMS Microbiol.Rev. 29, 851e875.

Habib, I., Sampers, I., Uyttendaele, M., De Zutter, L., Berkvens, D., 2008. A Bayesianmodeling framework to estimate Campylobacter prevalence and culturemethods sensitivity: application to a chicken meat survey in Belgium. J. Appl.Microbiol. 105, 2002e2008.

International Organization for Standardization (ISO), 1996. Microbiology of Food andAnimal Feeding StuffseHorizontalMethod for theDetection andEnumerationofListeria monocytogenes e Part 1: Detection Method. Geneva, Switzerland.

International Organization for Standardization (ISO), 1998. Microbiology of Foodand Animal Feeding Stuffs e Horizontal Method for the Detection andEnumeration of Listeria monocytogenes e Part 2: Enumeration Method. Geneva,Switzerland.

Jaloustre, S., Cornu, M., Morelli, E., Noel, V., Delignette-Muller, M.L., 2011. Bayesianmodeling of Clostridium perfringens growth in beef-in-sauce products. FoodMicrobiol. 28, 311e320.

Lianou, A., Sofos, J.N., 2007. A review of the incidence and transmission of Listeriamonocytogenes in ready-to-eat products in retail and food service environ-ments. J. Food Prot. 70, 2172e2198.

Lesaffre, E., Speybroeck, N., Berkvens, D., 2007. Bayes and diagnostic testing. Vet.Parasitol. 148, 58e61.

McDonald, K., Sun, D.W., 1999. Predictive food microbiology for the meet industry:a review. Int. J. Food Microbiol. 52, 1e27.

Mead, P.S., Slutsker, L., Dietz, V., McCaig, L.F., Bresee, J.S., Shapiro, C., Griffin, P.M.,Tauxe, R.V., 1999. Food-related illness and death in the United States. Emerg.Infect. Dis. 5, 607e625.

Mosteller, F., Tukey, J.W., 1977. Data analysis and regression: a second course instatistics. Addison-Wesley, Reading, MA.

Nauta, M.J., 2002. Modeling bacterial growth in quantitative microbiological riskassessment: is it possible? Int. J. Food Microbiol. 73, 297e304.

Pouillot, R., Albert, I., Cornu, M., Denis, J.B., 2003. Estimation of uncertainty andvariability in bacterial growth using Bayesian inference: application to Listeriamonocytogenes. Int. J. Food Microbiol. 81, 87e104.

Pouillot, R., Lubran, M.B., 2011. Predictive microbiology models vs. modelingmicrobial growth within Listeria monocytogenes risk assessment: whatparameters matter and why. Food Microbiol. 28, 720e726.

Prentice, G.A., Neaves, P., 1992. The identification of Listeria species. In: Board, R.G.,Jones, D., Skinner, F.A. (Eds.), Applied Bacterial Symposium. Blackwell ScienceLtd, Oxford, pp. 283e296.

Rosenquist, H., Bengtsson, A., Hansen, T.B., 2007. A collaborative study ona Nordic standard protocol for detection and enumeration of thermotolerantCampylobacter in food (NMKL 119, 3. Ed., 2007). Int. J. Food Microbiol. 118,201e213.

Simple Interactive Statistical Analysis (SISA), 2011. Diagnostic effectiveness. URL:http://www.quantitativeskills.com/sisa/statistics/diaghlp.htm (accessed22.07.11).

Sofos, J.N., Barbosa, W.B., Wederquist, H.J., Schmidt, G.R., Smith, G.C., 1995.Potential for growth and inhibition of Listeria monocytogenes in meat andpoultry products. In: Charalambous, G. (Ed.), Food flavors: Generation,Analysis and Process Influence. Elsevier Science B.V, Amsterdam,pp. 1243e1264.

Spiegelhalter, D.J., Thomas, A., Best, N.G., Lunn, D., 2003. WinBUGS Version 1.4 UserManual. MRC Biostatistics Unit, Cambridge.

Stessl, B., Luf, N., Wagner, M., Schoder, D., 2009. Performance testing of six chro-mogenic ALOA-type media for the detection of Listeria monocytogenes. J. Appl.Microbiol. 106, 651e659.

Thrusfield, M., 2007. Veterinary Epidemiology, third ed. Blackwell Science Ltd,Oxford.

Vadasz, P., Vadasz, A.S., 2008. Microbial models. In: Jorgensen, S.E., Fath, B.(Eds.), Encyclopedia of Ecology. Elsevier Science B.V, Amsterdam,pp. 2369e2389.

Vose, D., 2008. Risk Analysis: a Quantitative Guide, third ed.. John Wiley & Sons Ltd,Oxford.