uncertainty measurement on quantitative examination ... · pdf fileuncertainty measurement on...

2006/9/15 1/40

Uncertainty Measurement on Quantitative Examination Derived by PetrifilmTM EC Plate Method on Escherichia coli in Minced Meat

Kok Cheong Pat, Ip Kok Chao, Chan Ian Hoi, Vong Weng Man, Lei Sio Iong and Chio Hang I

IACM Laboratory, Macau S.A.R. People’s Republic of China

Abstract Modeling the level of fecal contamination by Escherichia coli on minced meats has both production hygiene and public health significance. The numeric model, using PetrifimTM EC (PEC) plate as a quantitative instrument, together with the main sources of the combined relative uncertainty are discussed in detail. The main components of the combined uncertainty affecting the model are classified into three categories: Sample Oriented Uncertainty (SMPOU), Procedure Oriented Uncertainty (PRCOU), and System Oriented Uncertainty (SYMOU). The main components of each category are discussed in detail, not only in the deriving of numeric models but also in the practical approach to optimizing laboratory techniques so as to obtain lower uncertainty in analytical results. Keywords: Uncertainty, microbiology, Escherichia coli, minced meats

Introduction Minced meat is one of the most popular foodstuffs in the Pearl River Delta area. Evidence increasingly indicates that minced meats have a higher probability of being contaminated by a fatal enteric pathogen—toxin-producing Escherichia coli O157:H7 [1]. E. coli is often used to assess hygiene practices at the meat production line [2-4]. This is particularly useful when processes are to be controlled according to Hazard Analysis Critical Control Point (HACCP) concepts, because the origin of the contamination, the contents of the gastrointestinal tract, is similar. When meat contamination from this source can be controlled, this is beneficial to the control of toxin-producing E. coli O157:H7 as well [5]. Modeling the level of fecal contamination by E. coli on minced meats has both meat production hygiene and public health significance. Numeric modeling of uncertainty in microbiology nowadays, especially in pathogenic microorganism analysis, is not just for the interpretation of analytical results or for the meeting of ISO-17025 requirements in laboratory accreditation. More importantly, quantitative variability or uncertainty has become an indispensable component of parameter inputs to the Modular Process Risk Model (MPRM) in quantitative microbiological risk assessment (QMRA).

Note: IACM: Instituto paa os Assuntos Civicos e Municipais; PetrifimTM EC plate (PEC) is a product of 3M™; BioBall is a product of BTF™

2006/9/15 2/40

Fig.Int.1 The main components of uncertainty/variability are shown in the fishbone chart.

Total Variability/Uncertainty

SYMOU

Sample Homogenization

Incubation Fault

Dilution FactionInoculation

Weighting MeasuringAccuracy

Volume

MeasuringAccuracy

IndividualReading

Temp. Time Humidity

IndividualReading

MeasuringAccuracy

Autoclave Weighting

Confirmation ErrorSystem Personnel Yield**

Overlap Colony

Media Effect

Adjusted Dilution Factor

Sample Stability

Bacteria Distrubution

Matrix Effect

Poisson Scatter

Counting Error **

** Exclusive items

PRCOU

SMPOU

SMPOU—Sample Oriented Uncertainty: More accurately, this should be termed variability, which is caused by

Distribution of microbes in sample; Matrix effect; Stability of sample – in terms of variability in growth of the microbes in sample.

Variability represents the true heterogeneity of the population that is a consequence of the physical, biochemical and micro-ecological system of the sample. Having the characteristic of variability dominating uncertainty, it is irreducible by further measurements but may change following the changing of external or internal condition of the system. Temperature shifting is a typical example of external condition change, while increasing/decreasing of potential gradient of oxidation/reduction is an example of an internal condition change. In traditional microbiology, the stability of sample is considered as variability, but in MPRM, both variability and uncertainty in growth after a fixed time period should be taken into account. Important note: sampling error or uncertainty caused by sampling procedure is not discussed in this document. PRCOU—Procedure Oriented Uncertainty: Includes uncertainties generated from the random errors of • Volume measuring, weighting;

Colony counting; Dilution making; Sample homogenizing.

Uncertainty represents the lack of perfect knowledge of the parameter under investigation. Having the characteristic of uncertainty dominating variability, it can be reduced by further measurements.

2006/9/15 3/40

SYMOU—System Oriented Uncertainty: Includes Uncertainties from culture media; Confirmation error representing the uncertainty generated from the testing method; System personal yield, the error of colony counting with laboratory-specific mean as reference; System adjustment of dilution factor, representing the extra uncertainty from the effect of the

lost of media during autoclaving and during the dispensing process; Incubation fault, representing the deviation caused by incubation conditions.

Most of the cases have the characteristic of combining variability and uncertainty. Separation of variability and uncertainty is possible in most cases even thought it is daunting. The components of variability are irreducible but can be reduced by system correction while the components of uncertainty can be reduced by further measurements but no response to system correction. Note: The rest of this study is presented in three parts corresponding to SMPOU, PRCOU and SYMOU, followed by a Summary. .....................................................................................................................................end of Introduction

2006/9/15 4/40

Part I Sample Oriented Uncertainties—SMPOU Estimating the variability caused by the distribution of microbes in sample choosing a probability distribution To estimate the variability caused by the distribution of microbes, choosing the ‘best’ probability distribution of the target microorganism is essential. Throughout this study, goodness of fit tests for distribution functions are based on the following methods:

Chi-square goodness of fit test [6,7]

__1

2__

__2

)(

x

xx

x

SS

n

ii∑

=

−==χ with n-1 degree of freedom (v) (I.1)

2)(05.0

2vχχ > P < 0.05 investigated distribution was not fitted to ECDF

2)(05.0

2vχχ < P > 0.05 investigated distribution was fitted to ECDF

EDCF (Empirical Cumulative Distribution Function)

Kolmogorov-Smirnov goodness of fit test:

This test is particularly suitable for assessing goodness of fit between an observed and an expected cumulative frequency distribution.

n : total experiment observations

if : observed frequency Xi from ECDF

∧

if : expected frequency P(X=xi) n‧ (I.2)

∑=

=k

iii XF

1 : the cumulative observed frequency (I.3)

( ) nxXPFk

ii •==∑

=

∧

1 : the cumulative expected frequency (I.4)

∧

−= iii FFd dmax = maximum id (I.5)

dma x> (dmax)0.05,k,n P < 0.05 investigated -- distribution was not fitted to ECDF

dma x< (dmax)0.05,k,n P > 0.05 investigated -- distribution was fitted to ECDF.

2006/9/15 5/40

Comparing two counts

If 20...._

2

_

1 >xandx 21

21

xx

xxZ+

−= (I.6)

If 20....5_

2

_

1 << xandx 21

21 1

xx

xxZ

+

−−= (I.7)

Z < 1.96 - no statistical significance between two counts with 95% confidence

The Monte Carlo (MC) simulation This is a method for iteratively evaluating a deterministic model by simulating the model using sets of random numbers as inputs. A simulation can typically involve over 10,000 evaluations of the model. It is very useful to obtain precise p values with cases of small datasets (small samples) or those with rare occurrences (few counts in huge datasets). MC simulation is often used for uncertainty analysis in the same way as for risk analysis.

Graphic plot with ECDF vs. tested distribution function

The Kolmogorov-Smirnov (K-S) test is based on the empirical cumulative distribution function. Given N ordered data points Y1, Y2 …YN, the ECDF is defined as:

NinEN)(= (I.8)

Where n(i) is the number of points less than Yi and the Yi are ordered from smallest to largest value. This is a step function that increases by 1/N at the value of each ordered data point.

Overviews of different probability distributions that can be used are widely available [8,9]. In this study only some frequently used distributions for Escherichia coli in meat products are being discussed.

Poisson distribution with fixed λ The Poisson(λ) distribution describes the probability of x ‘rare’ events when the expected number of events isλ. The Poisson distribution is related to the binomial by λ

= np. The binomial distribution is approximated by Poisson when n is large (say n>50) and p is small (say np<5) Parameter: λ

Mean(μ)=λ(mean = variance, that is μ=σ2) (I.9) Variance (σ2)=λ (I.10)

Gamma distribution A Gamma(α,β) distribution is one with a lower limit of 0 and no upper limit. It can be used to describe the probability distribution of the amount of time that lapses beforeα

rare events happen, given a mean time between eventsβ. If a = 1 (the time until a single event is of interest) the Gamma distribution is equal to the exponential distribution with λ=1/β. If a = n/2 and β=2 then the Gamma distribution is equal to the Chi-square distribution with degree of freedom df = n.

2006/9/15 6/40

An attractive characteristic of the Gamma distribution is that the sum of k random variables with a Gamma(a, β) distribution is Gamma(ka, β). Parameters: a and β

αβ=mean (I.11) 2αβ=SD (I.12)

Binomial distribution The binomial Bin(n,p) distribution describes the probability of x success in n trials, when the probability of success is known to be p. It can be considered as the ‘mother of all probability distributions’. To be used when n is relatively small, and neither p nor 1-p close to zero. Parameters: n, p

npXmean == (I.13) ( )pnpSD −= 1 (I.14)

Negative binomial distribution The probability of observing exactly x = 0,1,2,3….colonies is calculated from the successive terms in the series

⎭⎬⎫

⎩⎨⎧

+++

++

+⋅⎟

⎠⎞

⎜⎝⎛

+= L,

)1(!3)2)(1(,

)1(!2)1(,

1,1

1)( 32 c

kkkckk

ck

ccxp

k

(I.15)

The parameters of the formula (c,k) are estimates based on the observed count (z) and the combined relative uncertainty excluding distribution uncertainty wm as following:

.......22222 ++++= ATFVm wwwww then

2

1

mzwc = ; 2

1

mwk =

The negative binomial model is generally applicable to colony counts whenever the procedural uncertainty is not negligible [10].

Lognormal distribution

In the lognormal distribution, parameters considered have a normal distribution. Parameters: μ and σ. μ is estimated by calculating the mean of the data after transformation to the natural logarithm. σ is estimated by calculating the standard deviation of the data after transformation to the natural logarithm.

Normal distribution The normal distribution is a continuous distribution characterized by the mean μ and σ. The normal distribution is related to the binomial by np=μ and )1( pnp −=σ The binomial distribution is approximated by normal when n is large, say

)1(3 pnpnp −= .

2006/9/15 7/40

Bacteria distribution in minced meat: It is generally assumed that bacteria in meat are lognormally distributed [11]. In the lognormal distribution the logarithms of the parameter considered have a normal distribution. It has a lower limit zero, and a long tail. It is a convenient distribution because log transformation allows one to treat multiplications as sums. It is important in microbiology because microorganisms usually grow and die exponentially, and their numbers can therefore be considered as lognormally distributed. In general, many things in biology follow a lognormal distribution [12]. Though lacking statistical evidence, it is widely used in evaluation of the contamination at different stages of meat production [2-4, 13, 14]. But with distribution functions applied to measurement of uncertainty in microbiological analysis, especially those applied to Quantitative Microbiological Risk Analysis (QMRA), evidence based on quantitative statistics is essential. In practice, the distribution model of microorganisms in minced meat can be changed in accordance with the environmental and micro-ecological conditions. Reinders et al reported that in fresh products (minced beef) a Poisson distribution may be assumed, but after storage a more lognormal one is appropriate, at least for aerobic plate count (APC) [5]. During prolonged cold storage, the distribution of aerobic mesophilic microflora (APC) in minced beef shifts from a more homogeneously to a more clustered distribution [15]. This may be dependent on the temperature during storage. The shift from random distribution as observed with APC is explained by bacterial growth [5]. This may be different from the distribution of E. coli. The reason may be because the microflora in meat may include psychrophilic microflora which can multiply in low temperature, say 4-8℃, while E. coli remains stable at low temperature. In this study, through experiments, we try to verify the random distribution of E. coli in minced meats fresh and after cold storage (1 day at 4±2℃). Following the procedure by Simpson, Roe, and Lewontin [16], Steel and Torrie [6], and 張照寰, 詹紹康 et al [7], random distribution can be verified. In Experiment-1A and Experiment-1B of this study, samples of fresh minced pork and beef were collected from local retailers. The beef or pork was fresh from the slaughterhouse. Time elapsed from slaughtering to sampling was about 3 hours. No particular care of temperature control was observed in the retailing points. It could be assumed that the surface of the carcass was heavily contaminated. Within 20 minutes the samples were transported to the laboratory. Half of the samples were tested immediately, the other half were stored in cold storage (4±2℃) for 1 day then tested.

Experiment-1A. In fresh minced pork, χ2=7.21 < χ2(0.05,4)=9.49 and after cold storage at 4℃ 24

hours, χ2=0.53 < χ2(0.05,4)=9.49. In comparison test, Z = 0.15 < 1.96

Experiment-1B. In fresh minced beef, χ2=5.07 < χ2

(0.5,9)=16.92 and after cold storage at 4℃ 24 hours, χ2=13.48 < χ2

(0.05,9)=16.92. In comparison test, Z = 1.08 < 1.96 Results of the statistical analysis above imply that E. coli is randomly distributed in minced meats both fresh and after cold storage, and could be modeled by Poisson distribution. The quantitative difference between E. coli in fresh minced meats and in minced meats which have been in cold storage has no statistical significance.

2006/9/15 8/40

From one-sample K-S tests with Monte Carlo simulation tests of SPSS (a statistic software package), the goodness of fit to Poisson distribution in minced pork and beef, both in fresh and chilled condition, was confirmed. Table I.1 SPSS statistic results for fresh minced pork

Table I.2 SPSS statistical results for minced pork after 24 hours in 4±2℃ storage

One-Sample Kolmogorov-Smirnov Test d

532.40000

.347

.347-.252.775.585.424c

.412

.437

NMeanPoisson Parameter a,b

AbsolutePositiveNegative

Most Extreme Differences

Kolmogorov-Smirnov ZAsymp. Sig. (2-tailed)

Sig.Lower BoundUpper Bound

99% ConfidenceInterval

Monte Carlo Sig.(2-tailed)

count

Test distribution is Poisson.a.

Calculated from data.b.

Based on 10000 sampled tables with starting seed 2000000.c.

type = chilledd.

One-Sample Kolmogorov-Smirnov Test d

531.20000

.277

.277-.230.620.837.602c

.590

.615








count




type = freshd.

2006/9/15 9/40

Table I.3 SPSS statistical results for fresh minced beef

One-Sample Kolmogorov-Smirnov Test c

1021.700000

.218

.218

-.152

.690

.728



Most ExtremeDifferences


count



type = freshc.

Table I.4 SPSS statistical results for minced beef after 24 hours in 4±2℃ storage

One-Sample Kolmogorov-Smirnov Test c

1029.400000

.163

.163

-.089

.517

.952





count



type = chilledc.

Experiment-1C was carried out to explore the distribution evolution of E. coli in minced meat at room temperature. Sampling procedure and the condition of samples were same as those of Experiment-1A and B. Ten sub samples were prepared and inoculated to duplicate PEC plates then incubated according to the standard operating procedure (SOP) of the test. The remaining sub samples were kept aseptically but under room temperature (18±2℃). The tests were repeated 2, 4, and 6 hours thereafter. The following is a summary of the results of the tests. In readings from the 0 hour and 2 hours groups, in ten sub samples, all 20 PEC plates of each group in 10-1 dilution had valid counts ranging from 21 to 50 cfu/plate (cfu means colony forming unit) in the 0 hour group and 28 to 94 cfu/plate in the 2 hours group. Due to interference by background bacteria, the results from the 4 and 6 hours groups were not used in this study. Applying the one-sample Kolmogorov-Smirnov test with Monte Carlo simulation test of SPSS, it was verified that the 0 hour counts were fitted to Poisson distribution. (P=0.588) but the 2 hours counts were not (P=0.001). Statistical results are shown in the following tables:

2006/9/15 10/40

Table I.5 SPSS statistical results for Goodness fit test of Poisson Distribution at 0 hour

Experiment 1C Goodness fit test of Poisson Distribution at 0 hour by One-Sample Kolmogorov-Smirnov Test with Monte Carlo Test

2034.45000

.145

.145-.097.649.793.588c

.576

.601

NMeanPoisson Parametera,b


Most Extreme Difference





count




Table 1.6 SPSS statistical results for Goodness fit test of Poisson Distribution at 2 hour

Experiment 1C Goodness of fit test of Poisson Distribution at 2 hours by One-Sample Kolmogorov-Smirnov Test with Monte Carlo test

2051.90000

.412

.412-.2501.841

.002

.001c

.000

.001

NMeanPoisson Parametera,b


Most Extreme Differenc





count




ECDF was constructed and plotted against the Poisson distribution function which was generated by SPSS computer function (Figs. I.1 and I.2)

2006/9/15 11/40

Fig. I.1 Graphic plot with ECDF vs. Poisson distribution function at 0 hour

Distribution Function Goodness of Fit Test

Ecdf vs Poisson at 0 hour

count

42.00000

37.00000

36.00000

34.00000

28.00000

28.00000

21.00000

Com

ulat

ive

prob

abili

ty

1.2

1.0

.8

.6

.4

.2

0.0

ECDF

POISSON

Fig. I.2 Graphic plot with ECDF vs. Poisson distribution function at 0 hour


ECDF vs POISSON at 2 hours

COUNT

81.00000

50.00000

45.00000

43.00000

40.00000

36.00000

28.00000

Cum

ulat

ive

prob

abili

ty

1.2

1.0

.8

.6

.4

.2

0.0

ECDF

POISSON

Applying two-samples Kolmogorov-Smirnov goodness of fit test of SPSS (V.10.1), and comparing the difference between ECDF and lognormal distribution functions based on the test results, we found that the difference is of no statistical significance. (P = 0.153). Plotting of the functions revealed that lognormal was closer to the ECDF (Fig. I.3) Table I.7 SPSS statistical results for Goodness fit test of Lognormal at 2 hour

Test Statistics ECDF vs Lognormal a

.429

.429-.4291.134.153




VALUE

Grouping Variable: ITEMa.

2006/9/15 12/40

Fig. I.3 Graphic plot with ECDF vs. Lognormal distribution function at 2 hour

Furthermore,

different distribution models were applied in comparison tests. At 0 hour, we could not find significant difference except for a negative binomial distribution. This may be due to an unsuitable set-up of the model (especially the threshold value), but in the 2 hours results, it appears that lognormal has the best fit (Figs. 1.4-1.6). Fig. I.4 Graphic plot with ECDF vs. Poisson vs. binominal vs. Neg. binominal at 0 hour


Ecdf vs Poisson vs Binominal vs Neg. Binominal at 0 hour

COUNT

42.00000

37.00000

36.00000

34.00000

28.00000

28.00000

21.00000

Com

ulat

tive

prob

abili

ty

1.2

1.0

.8

.6

.4

.2

0.0

ECDF

POISSON

BINOMIN

NEGBINOM


ECDF vs POISSON vs LOGNORMAL

COUNT

81.00000

50.00000

45.00000

43.00000

40.00000

36.00000

28.00000

Val

ue

1.2

1.0

.8

.6

.4

.2

0.0

ECDF

POISSON

LOGNORM

2006/9/15 13/40

Fig. I.5 Graphic plot with ECDF vs. Poisson vs. Gamma at 0 hour


Ecdf vs Poisson vs Gamma at 0 hour

Count

42.00000

37.00000

36.00000

34.00000

28.00000

28.00000

21.00000

Com

ulat

ive

prob

abili

ty

1.2

1.0

.8

.6

.4

.2

0.0

ECDF

POISSON

GAMMA

Fig.I.6 Graphic plot with ECDF vs. Poisson vs. Binominal vs. Neg. binominal at 2 hour


Ecdf vs Poisson vs Binominal vs Neg. Binominal at 2 hours

COUNT

81.00000

50.00000

45.00000

43.00000

40.00000

36.00000

28.00000

Val

ue

1.2

1.0

.8

.6

.4

.2

0.0

ECDF

POISSON

BINOMIN

NEGBINOM

2006/9/15 14/40

The results of Experiment 1-C strongly support the assumption that E. coli was randomly distributed in minced beef initially, so counts of organism could be fitted to random distribution functions—Poisson, binomial, and Gamma distribution models. But after 2 hours at room temperature, lognormal was well fitted to describe the distribution situation. It may be that clustering of E. coli happened during the 2 hours period.

Based on the results of Experiments 1A, 1B, and 1C, if the sample is correctly handled during sampling, transporting, and reserving before analysis (here the temperature factor has to be doubly emphasized), we can apply the Poisson distribution model to evaluate the distribution variance in the examination of E. coli in minced meat by the PEC method, because of random distribution and because of the convenience of implementation since only one parameter—mean (λ)—is needed. The model We can apply the numeric model for the weighted average concentration of particles [17] in the final suspension, which is:

VZF

v

zFy n

ii

n

ii

==∑

∑

=

=

1

1 (I.16)

The uncertainty generated by the Poisson scatter It is generally acceptable to assume that the colony-forming particles (`germs`, `propagules`) from which the colonies of a plate potentially arise, originate in a perfectly mixed suspension. This is particularly true if the final suspension is a dilution of the original sample. The statistical distribution of the number of particles observed in a fixed volume can be predicted by the Poisson model. Poisson scatter is a general expression chosen to represent the variation in particle numbers observed in a series of faultlessly measured aliquots of fully mixed particle suspensions. The relative standard deviation squared, 2

zW , is the most appropriate expression of uncertainty in this connection:

Zz

W n

ii

z11

1

2 ==∑

=

(I.17)

z is the number, or average number, of colonies observed[18].

When a lot of minced beef is sampled for E. coli by quantitative tests using PEC method, the results of the tests show a probability distribution which is the sum of the actual uncertainties in the E. coli from sample to sample and the uncertainties due to the PEC method of enumeration. Many steps of the test procedure can cause uncertainty in the results (Fig. I.7).

2006/9/15 15/40

Fig. I.7 Source of uncertainties (random errors) in the results of the enumeration of E. coli in minced beef (adapted from Reinders et al. [5])

Uncertainties from PEC plate to PEC plate: Reinders et al. [5], through theoretical approach and verification with experimental data, concluded Poisson distribution is an acceptable function for the distribution of plate counts from 1 ml of a 10 ml suspension from minced beef sample, and a good alternative for the binomial distribution. Furthermore, they concluded while the means for single and duplicate plating are the same, the standard deviation is reduced by a factor of 2/1 (0.707), as expected. Experiment-2 of this study was undertaken to verify the same assumption, but for E. coli in minced beef using PEC plates. From 250 ml 10-1 suspension of fresh minced beef, 10 sets of duplicate PECs were inoculated. In the Poisson fitting test, χ2=2.63 < χ2

(0.05,9)=16.92, implying that Poisson distribution is fitted to describe the distribution of E. coli in the suspension. This was verified by the one-sample K-S test with Monte Carlo test (by SPSS) P=0.629.

2006/9/15 16/40

Table I.8 SPSS statistical results for Goodness fit test of Poisson distribution among PEC plates Experiment 2 Verification of E.coli among PEC plates

by One-Sample Kolmogorov-Smirnov Test

2012.90000

.128

.128-.110.571.901.629c

.617

.642








count




The second part of statistical analysis compared the uncertainty from plating. The average of uncertainty from each pair of duplicate plates is 0.019687 with single plate serial-1 being 0.02863, serial-2 being 0.027116 and the average being 0.027873. This verified that the uncertainty reduced by a factor of 0.707 using duplicate plating. Using the results of Experiment-2, Figs. I.8 and I.9 show the fitness of the E. coli count in final suspension to the Poisson distribution Fig. I.8 SPSS statistical results for Goodness fit test of Poisson distribution among PEC plates

Unce rta inty from pla t ing. Compa rison of the Empiric a l Count wi th S ta nda rd

Poisson P robabi l i ty Densi ty Func t ion

0

0.02

0.04

0.06

0.08

0.1

0.12

0 5 10 15 20 25

Colony count

Pro

babi

lity

de

nsit

y

St. Poisson/mass 0.1ml from 250ml E-1 suspension

2006/9/15 17/40

Fig. I.9 SPSS statistical results for Goodness fit test of Poisson distribution among PEC plates


Ecdf vs Poisson (E. coli in plating suspension)

COUNT

15.00000

15.00000

14.00000

12.00000

11.00000

9.00000

7.00000

Cum

ulat

ive

prob

abili

ty

1.2

1.0

.8

.6

.4

.2

0.0

ECDF

POISSON

Effect of decimal dilution on results When decimal dilutions are made, each dilution stage is a random event that influences the number of CFU in subsequent dilutions. The number of CFU present in the highest dilution is determined by the number of CFU in the sample, and the random events that happened in the previous stages of the procedure. During this procedure, the number of CFU that is eventually present in the used diluted cell suspension may deviate from the number of CFU that was expected. Reinders et al. [5], through theoretical approach and verification with experimental data, concluded the simplified Poisson is acceptable to estimate uncertainties caused by decimal dilutions. Experiment-3 was designed to explore and verify the effect of decimal dilution series on the outcome of the uncertainty of PECs in quantitative tests of E. coli in minced beef. The results of the Experiment-3 chi-square test showed that in the five sets of results for 10-1

dilution, χ2=0.29 < χ2(0.05,4)=9.49; in the five sets of results for 10-2 dilution, χ2=3.9 <

χ2(0.05,4)=9.49; and in the five sets of results for 10-3 dilution, χ2=4 < χ2

(0.05,4)=9.49. This implies that E. coli is randomly distributed in the decimal dilution series. This conclusion can be further confirmed by applying the one-sample K-S test with Monte Carlo test of SPSS (p=0.393 in 10-1, p=0.97 in 10-2 and p=1.000 in 10-3).

2006/9/15 18/40

Table I.9 SPSS statistical results for Goodness fit test of Poisson distribution among decimal dilutions

One-Sample Kolmogorov-Smirnov Test

5 5 534.2000 4.6000 .8000

.337 .126 .049

.337 .095 .047-.292 -.126 -.049.753 .281 .110.622 1.000 1.000.393c .974c 1.000c

.381 .970 1.000

.406 .978 1.000








E-1 E-2 E-3




Applying the one-sample K-S test with Monte Carlo test (by SPSS) further confirmed that the distribution of E. coli among 10-1 and 10-2 dilutions also fit with Poisson distribution (p = 0.07). Table I.10 SPSS statistical results for goodness fit test of Poisson distribution between E-1&E-2 dilutions

Experiment 3 Goodness of fit of Poisson Distribution among E-1 and E-2 Dilutionsby One-Sample Kolmogorov-Smirnov Test

10401.0000

.380

.380-.2711.201

.112

.070c

.064

.077








wcount




Uncertainties caused from sub sample to sub sample within a large sample The uncertainty between sub samples from one source, for example a batch of minced beef from a local supermarket, was investigated. The simplified Poisson stated above is acceptable to estimate uncertainties caused from sub sample to sub sample within a large sample, except that clustering happened in the sample [5]. Experiment-4 of this study was undertaken to verify the same assumption, but for E. coli in minced beef using PEC plates. In Experiment-4, from 1130 g fresh minced beef, eight sets of sub samples were tested. The E. coli counts of these sub samples were then carried out. Poisson fitting test: the result of chi-square test is χ2=10.69 < χ2

(0.05,7)=14.07, implying that ECDF fitted with Poisson distribution. This can be confirmed by the one-sample K-S test with Monte Carlo test (p=0.401).

2006/9/15 19/40

Table I.11 SPSS statistical results for goodness fit test of Poisson distribution among sub samples Experiment 4 Goodness fit test of Poisson Distribution of E.coli among

sub-samples by One-Sample Kolmogorov-Smirnov Test

1611.1250

.180

.180-.127.720.678.401c

.388

.414








count




Fig. I.10 Graphic plot with ECDF among sub samples vs. Poisson distribution function

Figure I.10 is the comparison of cumulative probability between ECDF and the Poisson distribution, revealing similarity and providing confirmation and evidence for the conclusion: Poisson distribution is an acceptable function for the distribution of E. coli from sub samples within a large minced beef sample. Discussion 1. Reinders et al. [5] in their report concluded that steps of decimal dilutions are one of the major

sources of uncertainty in bacteria counting. In their study, for a 105 cfu/g sample with an error of ±2%, the error level in the E-1 dilution increased to ±6%, in the E-2 dilution to ±20%, and in the E-3 dilution to ±62%. The difference between the actual variation of 2% and the measured variation of at least 20% (E-1 dilution must be made during stomaching procedure) makes it difficult to estimate the actual variation among sub samples. The same conclusion was reached in this study. We propose reducing dilution steps by applying 1 ml and 0.1 ml inoculum from the final suspension to the PEC plates (1 dilution step reduced) as a method of

20.

0

018.

0

015.

0

012.

0 0

11.

0 0 10.

0

010.

0 0

10.

0 0

10.

0 0

9.0

0

8.0

0

7.0

0 4.0

0 3.0

0 count

1.00

00 0.80

00 0.60

00 0.40

00 0.20

00 0.00

00

p

poiss

on

ed

cf

2006/9/15 20/40

lowering the level of uncertainty. 2. Using duplicate plates reduces this uncertainty by a factor of 0.707 compared with a single

plate test. 3. Clustering of E. coli was detected in one experiment by Reinders et al. [5]. Berg and

Hildebrandt [15] reported that immediately after grinding the total mesophilic aerobic plate count of minced beef is randomly distributed. However, after storage for 7 days at 5℃, ANOVA (Analysis of Variance) showed that in many lots clustering had occurred. At the start of the experiment the Poisson distribution could be used to describe the variations from sub sample to sub sample, but after a week’s storage the lognormal distribution was more appropriate. If growth should explain the clustering of E. coli, this would suggest that meat was subjected to temperature higher than about 4℃. This is the minimum growth temperature calculated by extrapolation of empirical data [19].

In Experiments 1-A and1-B with minced pork and beef, with storage at 4±2℃ for 1 day, clustering did not occur. However, another experiment showed that clustering happened when the time gap between sampling and analysis was over 30 minutes without temperature control (room temperature 20±2℃). The test result in this instance is fitted to lognormal distribution. It is recommended that enough distribution fitting experiments are carried out before any final statement is made.

Conclusion Selection of suitable distribution functions for estimation of SMPOU is essential. Poisson, binomial and lognormal are the frequently used options. The lognormal distribution has proved to be a convenient distribution function for the description of uncertainty in the test results, especially for APC tests with suitable density of microflora (SPC) or target organisms found clustering in the sample. Lognormal distribution cannot give insight into underlying mechanisms [5]. Poisson distribution is acceptable for modeling the variation of the PEC method in minced meat examination. The cumulative distribution curves provide insight into the variation of the levels of contamination of the samples from one lot. Evaluation of variability caused by matrix effect WM It is generally accepted that the solids in a food sample can lower the value of recovery of target bacteria from the sample. To estimate the value, spiking with pure cultures and testing for recovery seems to be the only approach [18]. ANOVA (Analysis of Variance) test of parallel certificate reference material (CRM) spiked samples can be used to determinate the uncertainty of the matrix effect (WM). ANOVA is used to compare the mean of the colony counts of spike blank samples (Cspike..blank) and the mean of the difference of colony counts of spike samples and normal samples (Cspike..sample－Csample), The sum of square between groups in the ANOVA test, includes the effects of matrix. Appling formula I.25 below, WM can be separated from the effects shown in the fishbone chart below.

2006/9/15 21/40

Fig. I.11 Fishbone chart showing the components of the sum of square between groups in the ANOVA test.

WST

W(count.spike.sample)

WA(media yield)

WZ (1/Z)

W(count sample)

WZ (1/Z)

WA(media yield)

WCRM

Wdilution factor

Wcertificate value

WV

Wm ??

W(count spike.blank)

WA(media yield)

WZ (1/Z)Wdilution factor

Wcertificate value

WV

WCRM

(variance between treatment from ANOVA)

W(spike sample)

W(spike blank) 2

.2

.2

samplespikeblankspikeST WWW += (I.18)

222).(

2..

2. CRMAblankspikeZblankspikecountblankspike WWWWW ++== (I.19)

22

.2

..2

. Msamplecountsamplespikecountsamplespike WWWW ++= (I.20)

222).(

2.. CRMAsamplespikeZsamplespikecount WWWW ++= (I.21)

22)(

2. AsampleZsamplecount WWW += (I.22)

22.

2.

2VfactordilutionvalueecertificatCMR WWWW ++= (I.23)

2222

)(2

).(2

.(2 23 MCRMAsampleZsamplespikeZblankspikeZST WWWWWWW +×+×+++= (I.24)

)23( 222

)(2

).(2

.(2

CRMAsampleZsamplespikeZblankspikeZSTM WWWWWWW ×+×+++−= ( I.25)

Φ= ST

ST

MSW (I.26)

2006/9/15 22/40

Table I.12 Definitions in Fig. I.11 WST relative uncertainty from mean of square between groups in ANOVA test MSST mean square SDST square root of MSST i.e. standard deviation Φ mean value WST SDST / Φ Wspike.blank relative uncertainty from spike blank samples Wcount.spike.blank relative uncertainty from colony count of CRM spike blank samples WA relative uncertainty of media yield, (Part III ) Wcertificate.value certified value of relative uncertainty of CMR Wdilution factor relative uncertainty from dilution factor Wv relative uncertainty from inoculum (Part II) WCRM relative uncertainty from CRM Wspike.sample relative uncertainty from spike samples Wcount.spike.sample relative uncertainty from colony count of CRM spiked normal samples Wount.sample relative uncertainty from colony count of normal samples Wz relative uncertainty from Poisson scatter In this study, CRM with 30 cfu, 550 cfu or 10,000 cfu (Bioball™) are selected for recovery tests in accordance with the level of bacterial contamination of the sample. In Experiment-6A, 12 sets samples of spike-blank, spike-sample and normal sample were tested to estimate the matrix effect. All samples were fresh minced beef collected from local retailers. The minced beef can be considered as heavily contaminated. Certificate reference material with count = 10,583 .7cfu and WCertificate.value= 10.01% was used in tests. WST was obtained from SPSS ANOVA test result. Table I.13 SPSS ANOVA test results (comparing the means of colony counts) Colony counts ANOVA

Sum of Squares df Mean Square F Sig.

Between Groups 253.500 1 253.500 6.170 .021

Within Groups 903.833 22 41.083

Total 1157.333 23

Table I.13 shows the difference between means of Cspike..blank and Cspike..sample－Csample has statistical significance(P=0.021) and MSST = 253.5. With Φ= 43.17 (derived from SPSS descriptive test) , in accordance with formula I.26, we got WST = 0.3688

2006/9/15 23/40

Alternatively, WST can be obtained by comparing the mean of two recovery rates, blank spike Krcya and sample spike Krcym. Krcya is defined as:

valueCRM

blankspikea C

CKrcy

.

.= (I.27)

Cspike.blank = counting of spiked blank sample (blank diluent) CCRM value = certificated colony count of CRM

Krcym is defined as:

valueCRM

samplesamplespikem C

CCKrcy

.

. −= (I.28)

Cspike.sample = counting of spiked sample Csample = counting of the sample CCRM value = certificated colony count of CRM

. WST was obtained in SPSS ANOVA test result Table I.14 SPSS ANOVA test results (comparing means of recovery rates)

Recovery rates ANOVA

Sum of Squares df Mean Square F Sig.

Between Groups .091 1 .091 6.170 .021

Within Groups .323 22 .015

Total .413 23

Table I.14 shows the difference between means of Krcya and Krcym has statistical significance(P=0.021) and MSST = 0.023. With Φ= .815720 (derived from SPSS descriptive test) , in

accordance with formula I.26, we got WST = 0.368842. The comparison of two methods is shown in Table I.15 below. Table I.15 Comparison of ANOVA tests

Item Compare means of

colony counts Compare means of

recovery rates

MSST 253.500000 0.090524 SDST 15.921683 0.300872 Φ 43.170000 0.81572

WST 0.368814 0.368842

WST2 0.136023 0.136044

2006/9/15 24/40

Table I.15 shows that there is only a very small difference between WST generated by two methods and can be ignored. The advantage of the second method is WST is independent from the absolute value of CRM. This feature enables the accumulation of chronicle data of same sample matrix for further wM estimation. Besides, these two recovery rates are important parameters in quality control of analytical works especially applied with quality control charts. With WA=7.33% (see Part III), we got WM=10.01% in accordance with formula I.18 – I.25. Not fewer than 8 sets of valid replicate tests have to be carried out during the set-up stage of a monitoring program, say, the quality control of the product at the outlet of a production line as an example, or a sample without any chronicle data of matrix effect. The result data set is use to calculate WM. The data set of each trial is then added to a chronicle database of the relative sample type. The data of the database is used to build a x Quality control chart of Krcym . For each routine trail, a set of data is obtained and a single sample Krcym is calculated according to the formula I.27 and I.28 above. If the single sample Krcym falls in the 95% confidence interval, i.e. UCL(upper control limit) and LCL (lower control limit) of the x control chart, the data set including Cspike.blank, , Cspike.sample , Csample together with CCRM value , is then added to the chronicle database. Data from the database are used to calculate WM ,. If the single sample Krcym falls out of the 95% confidence interval, at least 8 replicate recovery tests should be carried out on the reserved sample as if it was a first trial sample, and the matrix effect evaluated from this set of data. The reason for the outranged Krcy should be analyzed and the database reviewed or update if necessary. Evaluation of variability caused by sample stability Ws The microbial concentration may change a% between the sampling and analysis of the sample. The level of a depends on microorganisms, food type, and the environmental condition of the sample. It is different from case to case and it is necessary to accumulate empirical data for evaluation of the uncertainty caused. In Experiment-5, we try to find out a described above in minced beef. Samples of fresh minced beef were purchased from a local retailer (heavily contaminated) and tested every 2 hours for 6 hours. Samples were kept aseptically at room temperature before analysis. For N plates

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=∑

=−

N

yY

N

ii

11)ln(

ln (I.29) 1

1

YYY

a N −= (I.30)

2006/9/15 25/40

The estimation of Ws has to be based on rectangular distributions (Niemelä [18]).

Ws=3

a (I.31)

Fig. I.12 Relation between time delay and counting

Trend of E.coli count in minced beef

Y = 0.2405x + 7.1545

R2 = 0.9028

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10

time delay (hour)

LN

(CFU

/ml)

Fig I.13 Relation between time delay and uncertainty from sample stability

Time delay vs Ws

0%

50%

100%

150%

200%

250%

300%

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Time delay (hours)

Discussion

According to the results shown above, the concentration of E. coli in heavily contaminated minced beef develops exponentially under room temperature (20±2℃) respective to the time gap between sampling and analysis. If the sample is left untreated for 30 minutes, it will lead to adding a standard relative uncertainty of 18% to the test result.

……………………………………………………………….end of Part I

2006/9/15 26/40

Part II Procedure Oriented Uncertainties—PRCOU The basic work flow of E. coli testing using PEC plate is shown in Fig. II.1 Fig.II.1 The basic work flow of E. coli testing using PEC plate

Evaluation of variation caused by homogenization of Sample Stomacher and blender are two major instruments for homogenizing food samples for bacteriological examinations. The stomacher has advantages over the blender, of not generating high temperatures during operation, being cost effective, and being easy to operate and maintain. In general, both methods perform equally well for most kinds of samples including pork, beef, poultry

[20], and many other foods [21]. Some studies have reported that stomacher tends to give higher counts for milk powder, but lower counts for sausages [22]. Jay and Margitic [21] reported a higher recovery of total aerobics by stomacher than by blender, except in particular gram-negative microorganisms from beef, including ground beef. Usually the problem comes from foods that contain high concentrations of fat [22]. After homogenization the sample suspension contains two fractions, fluid and slurry. Because the particles in the slurry portion always clog up the pipette-tip, only the fluid fraction can be handled in the process of analysis. Based on the assumption that microorganisms are equally divided over both fractions, a sample of the fluid is taken as representative for the whole sample suspension. Reinders et al. [5] designed experiments to estimate this error. The experiments revealed the following points:

The APC of the slurry was significantly higher than the APC of the fluid for both stomached and blendered samples (P=0.014 and 0.015, respectively). Both methods showed a significant systematic error. The stomacher showed an underestimation of –38% (P=0.012), whereas the blender gave –8.2% underestimation (P=0.002). The difference between the systematic error of the stomacher or blender was not significant (P=0.057).

In Enterobacteriaceae counts, the difference between error in the stomacher and in the blender was statistically significant (P=0.036).

In coliform counts, the slurry was significantly lower than the counts in the fluid in both the stomached (P= 0.005) and the blendered samples (P=0.021). This resulted in a statistically significant overestimation of 10.1% (P=0.003) and 3.8% (P=0.014) for the stomached and blendered counts, respectively. The difference between the systematic error of the stomacher and blender was statistically significant (P=0.021). In general, the samples that were homogenized by the blender method yielded less slurry than the samples that were stomached.

W e ig h t 2 5 g m e a t s a m p le to th e s to m a c h e r b a g / b le n d e r ja r

A d d 2 2 5 g D L P T to th e s a m p le

H o m o g e n iz in g to o b ta in a 1 :1 0 d i lu t io n ( f in a l s u s p e n s io n )

P ip e t te 1 m l f in a l s u s p e n s io n d i r e c t in o c u la te d to P E C (E -1 )

P ip e t te 0 .9 m l D L P T + 0 .1 m l f in a l s u s p e n s io nin o c u la te to P E C (E -2 )

3 5 °C , 4 8 H

R e a d in g a n d re s u l t r e c o rd in g

2006/9/15 27/40

In Experiment-7 of this study, by applying Latin Square Design, the stomacher, low speed blender, and high speed blender are compared together with three treatments: immediate inoculation after homogenization, inoculation after 5 minutes, and suspension after filtration of filter stomacher bags; and three plating methods: PEC, VRBA-MUG pour plate and VRBA-MUG spread plate. Two successful trials (1 and 3) were carried out. Summary of these experiments is as follows: Table II.1 The Latin Square Design plan

H.method(i)

Plating(j) Media(k) Stomacher

Low speed

blender

High speed

blender

Direct Test 1 A PEC Test 2 B VRBA-P Test 3 C VRBA-S After 5 min (liquid only) Test 4 C VRBA-S Test 5 A PEC Test 6 B VRBA-P

Filtered Test 7 B VRBA-P Test 8 C VRBA-S Test 9 A PEC Results Variance Analysis In both trials, no statistically significant difference was found between treatments. If bias existed, it was most probably created by the particles and fibers of tissue, which caused difficulty in pipetting, leading to the bias of the test portion. Table II.2 Trial 1 Analysis of Variance (ANOVA) to a Latin Square Design

Source of variance Degree of freedom (v) Variance (l) Mean of variance (MS) F

Media (k) 2 0.1673518 0.0836759 3.3622483 Homogenization (i) 2 0.0264828 0.0132414 0.5320629 Plating method (j) 2 0.0916714 0.0458357 1.8417607 Error 2 0.0497738 0.0248869 Total variance 8 0.3352798

v1 = 2, v2 = 8, F0.05(2,8) = 4.46 , F0.01(2,8) = 8.65

Table II.3 Trial 3 Analysis of Variance (ANOVA) to a Latin Square Design

Source of variance Degree of freedom (v) Variance (l) Mean of variance (MS) F Media (k) 2 0.077369403 0.038684702 2.48570498 Homogenization (i) 2 0.11725094 0.05862547 3.767009088 Plating method (j) 2 0.054175952 0.027087976 1.740551526 Error 2 0.031125739 0.015562869 Total variance 8 0.279922034

v1 = 2, v2 = 8, F0.05(2,8) = 4.46 , F0.01(2,8) = 8.65

Discussion Homogenization is one of the most important steps in microbiological examinations; uncertainty may be caused in this step. Due to the difficulty of collecting empirical data for measuring the uncertainty quantitatively, the only way to operate is to set up and follow a well-designed and quantitatively validated standard procedure. The systematic errors of the stomacher are higher than the systematic errors of the blender. In addition, the blender causes less variation than the stomacher [5]. Although the experiment in this

2006/9/15 28/40

study cannot verify this point, using a blender may be a good option to minimize factors of the problem while manipulating a complex case. Uncertainty of the bacterial count caused by homogenization of a sample of minced meats depends on the size and type of the bacterial population, so it will be covered by the main source of uncertainty SMPOU. The Uncertainty of the Test Portion Volume WV

The uncertainty of the test portion volume is usually expressed as a standard deviation noted as SD or uv, or alternatively as a relative standard deviation noted as RSD (relative standard deviation ) or wv often expressed as a percentage. The three main sources of volumetric uncertainty are:

The specification of the manufacturer giving the limits of the true volume; Temperature effect; Fill-in/empty operation.

The first two items relate to the nature of the equipment determined by the material, manufacture quality and status of calibration. This is usually provided by the manufacturer or calibration laboratory and must be considered as an element of the total volumetric uncertainty of the analysis. The third item is related to operation. If operation is automatic, the accuracy of the equipment has to be taken into account. If operation is manual, the uncertainty wmvr created by human error must be evaluated and added to the total uncertainty. The human error from individual or group is estimated in a repeated gravimetric test (DIN EN ISO 8655). Experiment-8 is a performance test of volumetric measuring following a standard procedure of gravimetric test. The standard variance and the relative standard variance of the total volume ( 22 , VV wu ) is the sum of the squares of the component uncertainties including umvr, wmvr:

2222

21 ... mvrvnvvV uuuuu ++++= (II.1) 222

221 ... mvrvnvvV wwwwW ++++= (II.2)

where umvr, wmvr refer to the standard uncertainty and relative standard uncertainty created by the error of measuring operation. Discussion Although in reality the inaccuracy caused by ignoring the additional dilution steps is normally insignificant, improving the volumetric operation is still an important step to lower the level of uncertainty. For each fill-in/empty operation, a portion of uncertainty was added to the wV.. Minimizing the number of operational steps in any one analysis is an important consideration. Using the automatic dilution making pipette, it is possible to inoculate up to 10 plates in single filling operation with certificated accuracy. Another consideration is that instead of weighing a 25 g sample into a pre-autoclaved dilution bottle with 225 ml dilution fluid, weigh a 25g sample and 225 ml autoclaved dilution fluid on sequence into the sterile stomacher bag, jar, or bottle. This is because measuring the 225 ml diluents into a dilution bottle and then into an autoclave will introduce great error. During autoclaving the quantity of diluents will be lost by up to 3.5 ml/99 ml, about 3.5% [5]. Furthermore, weighing with a suitable balance provides much higher accuracy.

2006/9/15 29/40

Uncertainty from dilution factor wF (literature review) Dilution factor F

Dilution factor F denotes the number of steps by which the sample was diluted to obtain the final suspension. It is the reciprocal of the dilution. If the dilution = 10D

DF10

1= (II.3)

F is used as a multiplier for calculating the bacterial count of the sample zFc •=

if 10D = 10-2, z = 20 then, c = 100*20 = 2.0x103cfu/ml

A single dilution step is made by mixing a small volume a of a microbial suspension with volume b of sterile diluent. The dilution factor of one dilution step is therefore

a

baf += (II.4)

Should calibration measurements indicate that the true volumes differ from the nominal ones then a and b in the formula should be replaced with the true volumes a’= a+Δa and b’ = b+Δb. The standard uncertainties in volume scale remain unchanged but the relative uncertainties change as much as a and b do. A dilution factor consisting of k successive dilution steps is calculated as the product

kk

kkk fff

aba

aba

aba

F •••=+

••+

•+

= • ........... 212

22

1

11 (II.5)

If a, b remain unchanged then the total dilution factor equals k

kk a

bafF ⎟⎠⎞

⎜⎝⎛ +== (II.6)

Uncertainty of the dilution factor WF

The numerator and denominator in the formula for calculating the dilution factor are correlated (same a). Therefore, it is not completely correct to apply the rules of combining independent components of uncertainty when estimating the uncertainty of a dilution factor. The uncertainty variance of a dilution step is obtained from:

4

22

2

2

4

22222

aub

au

aubua

u ababf +=

+= (II.7)

( ) ( )( )22

2

2

2

2222

22 1

abab

f wwba

ba

ubuaba

W ++

=⎥⎦

⎤⎢⎣

⎡ ++

+= (II.8)

a = suspension transfer volume b = dilution blank volume ua= standard uncertainty of a or a’ ub=standard uncertainty of b or b’ wa= relative standard uncertainty of a or a’ wb= relative standard uncertainty of b or b’

If the total dilution consists of k similar steps the combined RSD squared of the dilution factor is calculated from:

2006/9/15 30/40

22fF kwW = (II.9)

If the steps differ in their volume configuration, the relative uncertainty of each step should be separately estimated and the results compounded as the sum of RSD squared:

222

22 ......11 kffF wwwW +++= (II.10)

(Excerpt from Niemelä 2003 [18]) Discussion The dilution factor uncertainty is one of the major components in the combined uncertainty of the analysis. An example is given by Reinders et al. [5] and is shown in following table: Table II.4 Effect of dilution steps on uncertainty

Measured number of CFU Statistics Actual number of CFU 10-1 dilution 10-2 dilution 10-3 dilution

Mean 10,000 10,000 10,000 10,000 s.d. 100 316 1,000 3,162 Lower 95% limit 9,840 9,380 8,000 4,000 Upper 95% limit 10,196 10,620 12,000 16,000 ± Error (%) 2 6 20 62

From the table above we can see how the dilution factor affects the uncertainty of the test result. It means that the test result is no longer reliable, or is even meaningless, after a series of dilutions. To lower the uncertainty of this element the only course of action is to decrease the number of dilution steps. Uncertainty from counting error WT The result of the plating method, say, the PECs example, is based on observation and counting of the number of colonies. Error generated by the human eye and mind lend to the readings a lack of repeatability, termed counting error or tally error. Uncertainty caused by tally operation can be classified into two categories: personal level and laboratory-specific level.

2006/9/15 31/40

Personal uncertainty of counting Uncertainty caused by an individual can be estimated by a periodical test. Each analyst reads and notes down results of her/his repeated reading (z1 ,z2) of plates from routine analysis within a time span insufficient to cause real changes in the colony counts. The reading results are then filled in to the table and computed. For PEC the range of colonies is better within 15 to 80 cfu/plate, usually not less than 10 plates. Table II.5 Calculation table for single person counting error

Plate (i) zi1 zi2 Ln(zi1) Ln(zi2) Ln(zi1)-ln(zi2)1 2 : : n

∑=

−=

n

i

iiT n

zzW

1

2212

2)ln(ln

(II.11) (Seppo I.Niemelä 2003)

Laboratory-specific uncertainty of counting Suppose that four technicians involved in daily routine microbiological analysis (A,B,C,D) read the same ten randomly selected plates independently. The results are filled in to the following table and computed. Table II.6 Calculation table for group counting error

The sum of squared wt is the sought estimate of the average relative variance of reading in the laboratory as a whole, without regard to any person in particular. Experiment-15 is a series of experiments for the above purpose. Important note: if taking the counting error WT in this section into account, then the system personal yield WH (see

Part III) should not be applied at the same time.

…………………………………………………………………..end of Part II

Plate(i) A B C D Mean Std wt wt2

1 2 . . n

Σwt2= Std = standard deviation

wt = relative standard deviation (Std/Mean) WT =

2006/9/15 32/40

Part III System Oriented Uncertainties—SYMOU Uncertainty caused by culture medium WA

To derive the uncertainty caused by culture medium, CRM with certificate value CRM.value and standard deviation Sc is used to perform not fewer than 8 replicate tests to each batch of culture medium. The result of the tests is then used for the following calculations:

n

n

iix

x∑

== 1__

(III.1) 1

1

2_

−

⎟⎠⎞

⎜⎝⎛ −

=∑

=

n

xxu

n

ii

a (III.2)

CI=n

Su ca22

2 +• (III.3) %100•=x

CIWA (III.4)

xi = individual count −x = mean CI = 95% confidence interval

In Experiment-12, 12 replicate tests are carried out on PEC. With CRMvalue = 32.1, Sc= 3.0, wA of the batch under testing is 8.43%. Discussion Theoretically, each batch of the medium should be tested for uncertainty by the quality assurance system. Critical growth support and recovery tests must be performed prior to starting to apply a culture medium or other ingredient to be used over an extended time. In our study, wA is one of the major sources of uncertainty (see the figure “Source of the total combined uncertainty” at the end of this document). Actual dilution factor F’ and its uncertainty As a rule, laboratories seem to assume the nominal pipette and dilution blank volumes to be true, and base the calculation of the dilution factor on the nominal volumes. Should calibration measurements indicate otherwise this should be taken into account by inserting the actual volume in the formulae for computing the dilution factor and its uncertainty, as in Part Two of this study. The actual dilution factor F’ may differ markedly from the nominal one F when a high degree of dilution is necessary (see Part Two, Uncertainty from dilution factor wF) a’ = a+Δa and b’ = b+Δb (III.5) Usually Δa and Δb …are derived from equipment specifications, calibration information and the statistics of chronic quality control data, so this element is assigned to SYMOU. Important note: if taking the actual dilution factor WF’ in this section into account, then the dilution factor WF (see

Part II) should not be applied at the same time.

2006/9/15 33/40

Uncertainty from incubation faults In this study a Latin Square Design experiment was set up to explore the effect of incubation condition on the uncertainty of the test result. Table III.1 The Latin Square Design plan for incubation faults

Temp.(i)

Time(j) Humidity(k) 30℃ 35℃ 37℃

18 h Test 1 A highTest 2 B normal

Test 3 C low 24 h Test 4 C low Test 5 A high Test 6 B normal

48 h Test 7 B normalTest 8 C low Test 9 A high

Table III.2 Statistics results of Trail 1-ANOVA test for incubation fault

Source of variance Degree of freedom (v) Variance (l) Mean of variance (MS) F Humidity (k) 2 0.00210691 0.00105345 0.21678849 Temperature (i) 2 0.05282721 0.0264136 5.43561637 Time (j) 2 0.00631805 0.00315903 0.65009119 Error 2 0.00971871 0.00485936 Total variance 8 0.07097088

v1 = 2, v2 = 8, F0.05(2,8) = 4.46 , F0.01(2,8) = 8.65 Table III.3 Statistics results of Trail 2 -ANOVA test for incubation fault

Source of variance Degree of freedom (v) Variance (l) Mean of variance (MS) F

Humidity (k) 2 0.0032548 0.0016274 0.09759513 Temperature (i) 2 0.02344961 0.0117248 0.7031372

Time (j) 2 0.04980246 0.02490123 1.49332838 Error 2 0.03334997 0.01667499

Total variance 8 0.10985684 v1 = 2, v2 = 8, F0.05(2,8) = 4.46 , F0.01(2,8) = 8.65

Table III.4 Statistics results of Trail 3-ANOVA test for incubation fault

Source of variance Degree of freedom (v) Variance (l) Mean of variance (MS) F Humidity (k) 2 0.00939306 0.00469653 2.36150045

Temperature (i) 2 0.00825401 0.00412701 2.07513476 Time (j) 2 0.00159244 0.00079622 0.40035435

Error 2 0.00397758 0.00198879 Total variance 8 0.02321709

v1 = 2, v2 = 8, F0.05(2,8) = 4.46 , F0.01(2,8) = 8.65 Discussion From the statistics above, it can be seen that only the temperature factor in trial 1 has statistical significance, in contrast with the other factors. From practical experience, humidity is also a very important factor affecting the results of tests. This may be caused by some bias during setting up of experimental conditions. Conclusion Although we cannot get strong evidence from our experiments, it is widely accepted that temperature and humidity are two major factors affecting test results. We cannot find in any literature quantitative data of uncertainty for these two factors.

2006/9/15 34/40

The confirmation rate p and its uncertainty Wp The confirmation rate p of E. coli on PEC plate should be based on different sample types. To estimate the true value of p, an estimated confirmation rate p̂ can be obtained by testing a subset of random presumptive colonies. NOTE. Placing the symbol “ ^ ” above a letter is a statistical convention for denoting an estimate of the quantity which that letter denotes. Thus, p̂ refers to an estimate of p. pzx = (III.6) x is the confirmed count p is the confirmation coefficient (true positive rate) z is the count of presumptive positive In Experiment-14, by using NA-MUG or VRBA-MUG the presumptive colonies were confirmed, estimating the confirmation rate p. Estimated confirmation rate p̂ :

nkp =ˆ (III.7)

k is the number of colonies confirmed n is the number of presumptive colonies tested z is the colony count

RSD squared of the estimated confirmation rate 2p̂w :

kn

knWp−=2

ˆ (III.8)

Variance of the confirmed count 2xu :

3

222 )(

nznkknkzux

+−= (III.9)

RSD squared of the confirmed count 2xw :

nkzkn

knzx

uW x

x1111

2

22 ++=−+== (III.10)

Seppo I.Niemelä 2003 [18] In this study, p̂ =0.995 and pw ˆ =0.533% Conclusion According to the empirical result of Experiment-14, p̂ = 99.5%, with pW ˆ = 0.533%. The fact implies the positive rate of the confirmation test is approximately 100% with very low uncertainty. As a result, confirmation of typical colonies on PEC plate is not necessary in minced beef or pork analysis.

2006/9/15 35/40

The System Personal Yield WH To estimate WH,, different sources of information can be used as reference: 1. The count of a laboratory expert; 2. The average count of a work group; 3. the average count of all analysts who take part in the analytical work of the test under

estimation. In this study the last option is selected. To estimate WH the relative difference d of the two counts should be computed for each pair (zavg, zx) of counts, where zx is the individual count and zavg is the mean of counts for all analysts of one test item.

avg

xavg

zzz

d−

= (III.11)

The standard uncertainty (standard deviation) of d (sd) is calculated according to the standard statistical practice (type A estimation). The standard deviation of the mean d (standard error) is an approximate estimate for the relative uncertainty wH

nS

W dH = (III.12)

The uncertainty of the general counting practice of the laboratory as a whole can be estimated with experiments in which all technicians read the numbers of colonies of the same plates. The standard uncertainty or standard uncertainty in ln scale is computed separately for the counts of each plate and their quadratic average is determined (refer to Part Two). Important note: if taking the system personal yield WH in this section into account, then the counting error WT (see part II) should not be applied at the same time. Uncertainty from overlap colonies WKL (Excerpt from Niemelä et al. 2003 [18]) The number of colonies observed in or on a plate is, at the most, equal to the number of so called colony forming unit CFU present in the test portion. Resulting from purely geometrical overlap incidents, the observed number of colonies (z) is generally smaller than the original number of CFU. Some colonies ‘disappear’ by merging indistinguishably with other similar colonies. This phenomenon is different from the loss of recovery caused by excessive background colonies. (Background growth sometimes not only masks but may also alter the appearance of the target colonies, changing some of them into false negatives.) The loss due to the geometrical overlap of target colonies is proportional to the space area occupied by the colonies, the coverage. The table below has been constructed from previously published data (Niemelä 1965 [23]) (sic), it applies to the membrane filtration and spread plate methods. With the pour plate technique the overlap phenomenon is only marginally observable and can be ignored.

zxK L += 1 (III.13)

(x: count of overlap colony)

If the true number (CFU) is not known, only an average expected value for KL can be quoted on the basis of the observed coverage (Table 1).

2006/9/15 36/40

Table III.5 Coverage and overlap rate Coverage area % KL Coverage area % KL

5 1.02 25 1.11 10 1.04 30 1.14 15 1.06 35 1.18 20 1.08 40 1.24

If coverage is over 40%, the result should be not valid. If x is not known, KL can be quoted on the basis of the observation of area covered by the overlap colonies and the average value of the relative uncertainty can be estimated to be of the order WKL = 0.05 ………………………………………………………………………………………………………………………..end of Part III

Summary: The Simplified Model in Minced Meat Test In this study, we tried to find out the feasible methods to quantify possible sources of variability/uncertainty in minced meat test, but we still failed in quantifying uncertainties caused by sample incubation fault, sample homogenization, and overlap colonies. For the first two factors, it is recommended that strict adherence to test standard procedures be enforced to minimize related uncertainty. We can only estimate the uncertainty caused by colony overlap in a semi-quantitative way; this problem can be minimized by choosing suitable dilution factor and improving counting technique including adequate computer image processing. In routine practice, we select System Personal Yield instead of Counting Error to estimate the uncertainty caused by human tally operation. We apply Adjust Dilution Factor F’ to estimate the uncertainty from dilution factor. In a general laboratory, the analytical work starts from receiving samples. If the handling of sample strictly follows the standard procedure, the variability caused by sample stability can be ignored. In this document, many factors which will introduce variability or uncertainty to the test result have been discussed, but the related correction action were not yet mentioned, because it will involve the modification of the reporting of standard methods even the regulations. The uncertainty estimation methods discussed in this document will not affect the figure of test result. Enumeration model Based on the assumption that Poisson distribution is an acceptable function for the distribution of Escherichia coli in minced meat, the test result is calculated from:

VZF

vz

FFcyi

i ===∑∑ (S.1)

The relative uncertainty of the test is estimated from

222222' ZVHMAFy WWWWWWW +++++= (S.2)

2006/9/15 37/40

General approximation of the 95% confidence interval

Upper limit )21( yH Wyy += (S.3)

Lower limit )2121

(2

y

yL W

Wyy

+−

= (S.4)

Approximate 95% confidence interval of results based on low counts (z<25)

Upper limit )122(' +++= zzVFyH (S.5)

Lower limit )122(' +−+= zzVFyL (S.6)

(Seppo I.Niemelä 2003) S.5 and S.6 can be used only when 1/2*SPMOU>(PRCOU2+SYMOU2)1/2

A simplified fishbone chart showing the main sources of uncertainty is shown below. Fig. S.1 Simplified fishbone chart showing sources of uncertainties minced meat analysis

Total Variability/Uncertainty

PRCOU

SYMOU SMPOU

WeightingMeasuringaccuracy

Volume

Measuringaccuracy Individual

reading

Confirmation ErrorSystem Personnel Yield**

Overlap Colony

Media Effect

Adjusted Dilution Factor

Sample Stability

Bactetria Distrubution

Matrix Effect

Poisson Scatter

Counting Error **

** Exclusive items

Inoculation

……………………………………………………………..end of Part III

2006/9/15 38/40

Appendix I

An example of uncertainty estimation report

Estimation of Uncertainty in Microbiological Analysis

Process no. 0194/OUT (2006) Sample Type Fresh Minced Beef Parameter Escherichia coli Test Method Petrifilm EC Plate Method

F00000235800S

Basics of the test: Dilution factor of final suspension F 1.00E+01

Test portion volume (ml) V 2

Counting of colonies (cfu) Z 35

Source of Uncertainty

Class Factor W W2

SMPOU Primary count--microbial distribution Z 16.90% 0.0286SMPOU Food matrix effect M 10.01% 0.01002PRCOU Test portion V 0.03% 0.0000PRCOU Dilution factor F 0.05% 0.0000SYMOU Tally operation error T 0.00% 0.0000SYMOU Confirmation P 0.56% 0.0000SYMOU Personal yield H 3.25% 0.0000SYMOU Medium yield A 7.33% 0.0054

Test Result

Microbial content of the sample 1.8E+02

Total relative uncertainty of the test result

21.2%

95% confidence interval: If Z＞＝25 If Z＜25

Upper Limit

2.5E+02

Lower Limit

1.1E+02

22222'/

222AHPTFFVMZy WWWWWWWWW +++++++=

)21( yH Wyy += )122( +++= zzVFyH

)122( +−+= zzVF

yL)2121

(2

y

yH W

Wyy

+−

=

2006/9/15 39/40

Appendix II References [1] Teagasc–The National Food Center FSAI Ireland 2001-2002 [2] Gill CO, McGinnis JC & Badoni M (1996) Assessment of the hygienic characteristics of a beef

carcass dressing process. Journal of Food Protection, 59 (2), 136-40 [3] Gill CO, McGinnis JC & Badoni M (1996) Use of total or Escherichia coli counts to assess the

hygienic characteristics of a beef carcass dressing processes. International Journal of Food Microbiology, 31 (1-3) 181-96

[4] Gill CO & Penney N (1997) Penetration of bacteria into meat. Applied and Environmental Microbiology, 33 (6) 1284-6

[5] Reinders RD, Evers EG, de Jonge R & van Leusden FM (2002) RIVM report 149106009/2002. (RIVM: Rukinstituut Voor Volksgezondhed en Mileu, National Institute of Public Health and Environment Netherlands)

[6] Steel RGD & Torrie JH (1980) Principles and Procedure of Statistics: A Biometrical Approach (2nd edn). McGraw Hill Book Co, USA, 530-531

[7]張照寰, 詹紹康, (2003) 醫用統計方法第二版 (金丕煥主編) 第十五章中國上海:復旦大

學出版社 [8] Vose D.(1998) The application of quantitative risk assessment to microbial food safety. Journal

of Food Protection 61 640-8 [9] Vose DJ (2000) Risk Analysis – A Quantitative Guide (2nd edn). John Wiley & Sons Ltd,

Chichester, England [10] Moroney MJ (1962) Facts From Figures (3rd and revised edn, reprinted). Penguin Books Ltd,

Harmondsworth, Middlesex [11] Brown MH, Baird-Parker EL & Williamson JK (1982) The microbiological examination of

meat. In: Brown MH (ed) Meat Microbiology, Applied Science Publishers, 423-520 [12] Slob W (1994) Uncertainty analysis in multiplicative model. Risk Analysis 14 571-576 [13] ICMSF (2002) Microorganisms in Food 7 Microbiological Testing in Food Safety

Management. Kluwer Academic/Plenum [14] ICMSF (1986) Microorganisms in Food 2 Sampling for Microbiological Analysis: Principles

and Applications (2nd edn). University of Toronto Press [15] Berg C & Hildebrandt G (1996) Zur Streuung der maesophilen aeroben Gesamtkeimzahlung in

grob zerkleinerten Fleischerzeugnissen: Mettwurst, Hackfleisch un Hamburger Fleischwirtschaft. 76 (6) 644-8

[16] Simpson GG, Roe A & Lewontin RC (1960) Quantitative Zoology (revised edn). Hal-court, Brace, 311-312

[17] Farmiloe FJ, Cornford SJ, Coppock JPM & Ingram M (1954) The survival of Bacillus subtillis spores in the baking of bread. J.Sci Food Agric, 5:292-304

[18] Niemelä SI (2003) Uncertainty of quantitative determinations derived by cultivation of microorganisms, J4 Advisroy Commission for Microbiology, Helsink, 2003, Finland

[19] Presser KA, Ratkowsky DA & Ross T (1997) Modelling the growth rate of Escherichia coli as a function of pH and lactic acid concentration. Applied and Environmental Microbiology, 63 (6) 2355-60

[20] Thomas CJ, McMeekin TA (1980) A note on scanning electronic microscopic assessment of stomacher action on chicken skin. Journal of Applied Bacteriology, 49 339-44

[21] Jay JM, Margitic S (1979) Comparison of homogenizing, shaking and blending on the recovery of microorganisms and endotoxins from fresh and frozen beef as assessed by plate counts and Limulus amoebocyte lysate test. Applied and Environmental Microbiology, 38 (5) 879-84

[22] Purvis U, Sharpe AN, Bergener DM, Lachapelle G, Milling M & Spring F (1987) Comparison

2006/9/15 40/40

of bacterial counts obtained from naturally contaminated foods by means of stomacher and blender. Canadian Journal of Microbiology, 33 52-6

[23] Niemela S (1965) The quantitative estimation of bacterial colonies on membrane filters. Ann Acad Sci Fenn, Ser A.IV. Biologica, No.90

uncertainty measurement on quantitative examination ... · pdf fileuncertainty measurement on...

Documents