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Chapter 7 : Statistics of Sampling for Microbiological Testing of Foodborne Pathogens
Authors:
T. Ross1,
P. M. Fratamico2,
L. Jaykus3,
M. H. Zwietering4
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Affiliations:
1: Tasmanian Institute of Agricultural Research, School of Agricultural Science, University of Tasmania, Private Bag 54, Hobart 7001, Tasmania, Australia;
2: U.S. Department of Agriculture—Agricultural Research Service, Eastern Regional Research Center, Wyndmoor, PA 19038;
3: Department of Food, Bioprocessing and Nutrition Sciences, North Carolina State University, Raleigh, NC 27695-7624;
4: Laboratory of Food Microbiology, Agrotechnology & Food Sciences Group, Wageningen Agricultural University, Postbus 8129, 6700EV, Wageningen, The Netherlands
Content Type: Monograph
Publication Year:
2011
Category: Applied and Industrial Microbiology; Food Microbiology
Book DOI:
10.1128/9781555817121
Chapter DOI:
10.1128/9781555817121.ch7
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Abstract:
This chapter describes the assessment of the microbiological safety of foods, and the assessment of microbiological quality. Even with the widespread implementation of preventative strategies such as hazard analysis and critical control point (HACCP) and related food safety management strategies, there are still many situations in which food safety assurance mainly relies on microbiological testing. End product testing might be needed in some circumstances, for example, when there are no critical control points in a process (e.g., raw or minimally processed ready-to-eat foods) or when the history of a product is unknown. Equally, food safety objectives and performance objectives may nominate microbiological criteria to be met. The chapter presents basic concepts of sampling plan nomenclature, design, and interpretation to complement the rapid microbiological detection, identification, and enumeration technologies. Additionally, it presents recently introduced concepts concerning the numerical interpretation of microbiological presence/absence testing and a discussion of sample compositing.
Citation:
Ross T, Fratamico P, Jaykus L, Zwietering M.
2011.
Statistics of Sampling for Microbiological Testing of Foodborne Pathogens,
p 103-120.
In
Hoorfar J (ed),
Rapid Detection, Characterization, and Enumeration of Foodborne Pathogens.
ASM Press, Washington, DC.
doi: 10.1128/9781555817121.ch7
Figures
Statistics of Sampling for Microbiological Testing of Foodborne Pathogens
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Citation:
Ross T, Fratamico P, Jaykus L, Zwietering M.
2011.
Statistics of Sampling for Microbiological Testing of Foodborne Pathogens,
p 103-120.
In
Hoorfar J (ed),
Rapid Detection, Characterization, and Enumeration of Foodborne Pathogens.
ASM Press, Washington, DC.
doi: 10.1128/9781555817121.ch7
/content/10.1128/9781555817121.ch07.ch07fig01
FIGURE 1
OC curves. (A) Effect of the number of samples on the probability of detecting a defective unit (e.g., a contaminant) as a function of the prevalence of defective units in the lot for a scheme in which any positive leads to rejection of that batch (i.e., c = 0). (B) Sampling plan with c = 5 and n = 10, 20, or 50 showing the influence of the number of samples on the difference between the producer’s risk (shown as 95% probability of acceptance, upper dashed line) and the consumer’s risk (95% probability of rejection, lower dashed line). As n increases, the difference between the consumer’s risk and the producer’s risk is reduced. (C) Influence of the number of positive results permitted by the sampling scheme on the probability of acceptance of the lot, using a sampling plan based on n = 30 samples.
10.1128/9781555817121/f0110-01_thmb.gif
10.1128/9781555817121/f0110-01.gif
FIGURE 1
OC curves. (A) Effect of the number of samples on the probability of detecting a defective unit (e.g., a contaminant) as a function of the prevalence of defective units in the lot for a scheme in which any positive leads to rejection of that batch (i.e., c = 0). (B) Sampling plan with c = 5 and n = 10, 20, or 50 showing the influence of the number of samples on the difference between the producer’s risk (shown as 95% probability of acceptance, upper dashed line) and the consumer’s risk (95% probability of rejection, lower dashed line). As n increases, the difference between the consumer’s risk and the producer’s risk is reduced. (C) Influence of the number of positive results permitted by the sampling scheme on the probability of acceptance of the lot, using a sampling plan based on n = 30 samples.
Citation:
Ross T, Fratamico P, Jaykus L, Zwietering M.
2011.
Statistics of Sampling for Microbiological Testing of Foodborne Pathogens,
p 103-120.
In
Hoorfar J (ed),
Rapid Detection, Characterization, and Enumeration of Foodborne Pathogens.
ASM Press, Washington, DC.
doi: 10.1128/9781555817121.ch7
/content/10.1128/9781555817121.ch07.ch07fig02
FIGURE 2
OC curves for selected sampling plans. (A) Probability of batch acceptance as a function of contamination levels, for different numbers of samples and sizes of analytical units for c = 0 (i.e., no positives permitted) sampling plans. The dotted line represents a plan comprising 20 25-g samples. The solid line represents a sampling plan comprising five 25-g samples. The dashed line represents a sampling plan comprising five 10-g samples. Though not shown, a plan with 50 10-g samples has the same OC curve as that for 20 25-g samples (i.e., the dotted-line OC curve), showing that compositing has no effect on plan sensitivity (subject to the caveats described in the text). (B) Effect of the mean and standard deviation of the distribution on the expected prevalence of defects determined as a proportion of samples above the criterion. In the plot, an arbitrary threshold of 1 CFU ‧ g–1 (0 log CFU ‧ g–1) is shown. Three distributions are shown as probability density (black) and corresponding cumulative probability curves (grey). The distributions shown (mean ± standard deviation in log CFU ‧ g–1) are as follows: solid lines, –1 ± 0.8; dotted lines, –2.5 ± 0.8; dashed lines, –2.5 ± 1.2. The proportions that have unacceptably high microbial loads are represented by that part of the distribution to the right of the vertical line representing the threshold. This proportion can be deduced most easily from the cumulative probability curves (grey lines). The point at which cumulative probability curves cross the threshold value gives the proportion of samples below the threshold and, by inference (1 –proportion below the threshold), the proportion above the threshold. It can be seen that the proportion of defectives is a function of both the mean and standard deviation of the distribution.
10.1128/9781555817121/f0117-01_thmb.gif
10.1128/9781555817121/f0117-01.gif
FIGURE 2
OC curves for selected sampling plans. (A) Probability of batch acceptance as a function of contamination levels, for different numbers of samples and sizes of analytical units for c = 0 (i.e., no positives permitted) sampling plans. The dotted line represents a plan comprising 20 25-g samples. The solid line represents a sampling plan comprising five 25-g samples. The dashed line represents a sampling plan comprising five 10-g samples. Though not shown, a plan with 50 10-g samples has the same OC curve as that for 20 25-g samples (i.e., the dotted-line OC curve), showing that compositing has no effect on plan sensitivity (subject to the caveats described in the text). (B) Effect of the mean and standard deviation of the distribution on the expected prevalence of defects determined as a proportion of samples above the criterion. In the plot, an arbitrary threshold of 1 CFU ‧ g–1 (0 log CFU ‧ g–1) is shown. Three distributions are shown as probability density (black) and corresponding cumulative probability curves (grey). The distributions shown (mean ± standard deviation in log CFU ‧ g–1) are as follows: solid lines, –1 ± 0.8; dotted lines, –2.5 ± 0.8; dashed lines, –2.5 ± 1.2. The proportions that have unacceptably high microbial loads are represented by that part of the distribution to the right of the vertical line representing the threshold. This proportion can be deduced most easily from the cumulative probability curves (grey lines). The point at which cumulative probability curves cross the threshold value gives the proportion of samples below the threshold and, by inference (1 –proportion below the threshold), the proportion above the threshold. It can be seen that the proportion of defectives is a function of both the mean and standard deviation of the distribution.
Citation:
Ross T, Fratamico P, Jaykus L, Zwietering M.
2011.
Statistics of Sampling for Microbiological Testing of Foodborne Pathogens,
p 103-120.
In
Hoorfar J (ed),
Rapid Detection, Characterization, and Enumeration of Foodborne Pathogens.
ASM Press, Washington, DC.
doi: 10.1128/9781555817121.ch7
/content/10.1128/9781555817121.ch07.ch07fig03
FIGURE 3
Illustration of sampling errors in microbiology, showing a two-dimensional depiction of a food sample contaminated with microbial cells, shown as shaded circles. Each square or diamond represents a sample drawn from the food. The cells are evenly distributed at a concentration of 1 cell per square centimeter, and the sample size is exactly 1 square centimeter, so that it would be expected that every sample would capture one cell, as is shown in panels A and B. However, it is easy to see that by chance a sample might not capture a cell, as shown in panel C. Similarly, even though the cells are perfectly homogenously distributed at a concentration equivalent to one per sample, more than one cell could be captured in a sample (panel D). In reality, cells would be randomly distributed as shown in panel E, and this would exacerbate the situation depicted in panels A through D so that even if the average concentration is one cell per sample, some samples will contain no cells while others will contain multiple cells.
10.1128/9781555817121/f0118-01_thmb.gif
10.1128/9781555817121/f0118-01.gif
FIGURE 3
Illustration of sampling errors in microbiology, showing a two-dimensional depiction of a food sample contaminated with microbial cells, shown as shaded circles. Each square or diamond represents a sample drawn from the food. The cells are evenly distributed at a concentration of 1 cell per square centimeter, and the sample size is exactly 1 square centimeter, so that it would be expected that every sample would capture one cell, as is shown in panels A and B. However, it is easy to see that by chance a sample might not capture a cell, as shown in panel C. Similarly, even though the cells are perfectly homogenously distributed at a concentration equivalent to one per sample, more than one cell could be captured in a sample (panel D). In reality, cells would be randomly distributed as shown in panel E, and this would exacerbate the situation depicted in panels A through D so that even if the average concentration is one cell per sample, some samples will contain no cells while others will contain multiple cells.
Citation:
Ross T, Fratamico P, Jaykus L, Zwietering M.
2011.
Statistics of Sampling for Microbiological Testing of Foodborne Pathogens,
p 103-120.
In
Hoorfar J (ed),
Rapid Detection, Characterization, and Enumeration of Foodborne Pathogens.
ASM Press, Washington, DC.
doi: 10.1128/9781555817121.ch7
References
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Baird-Parker, A. C. 2000. The production of microbiologically safe and stable food, p. 3–18. In B. M. Lund,, A. C. Baird-Parker, and, G. W. Gould (ed.), The Microbiological Safety and Quality of Food. Aspen Publishers Inc., Gaithersburg, MD.
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Codex Alimentarius Commission. 1997. Principles for the Establishment and Application of Microbiological Criteria for Foods ( CAC/GL 21-1997). http://www.codexalimentarius.net/download/standards/394/CXG_021e.pdf. Accessed 2 September 2010.
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Codex Alimentarius Commission. 2004. General Guidelines on Sampling ( CAC/GL 50-2004). http://www.codexalimentarius.net/download/standards/10141/CXG_050e.pdf. Accessed 2 May 2010.
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Codex Alimentarius Commission. 2007. Principles and Guidelines for the Conduct of Microbiological Risk Management ( MRM). ( CAC/GL 63-2007). http://www.codexalimentarius.net/download/standards/10741/cxg_063e.pdf. Accessed 6 September 2010.
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Food and Agriculture Organization/World Health Organization. 2004. Risk Assessment of Listeria monocytogenes in Ready-to-Eat Foods. Technical Report. Microbiological Risk Assessment Series 5. Food and Agriculture Organization, Rome, Italy.
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Havelaar, A.,, M. J. Nauta, and, J. T. Jansen. 2005. Fine-tuning Food Safety Objectives and risk assessment. Int. J. Food Microbiol. 93: 11– 29.
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International Commission on Microbiological Specifications for Foods. 1986. Microorganisms in Foods 2. Sampling for Microbiological Analysis: Principles and Specific Applications, 2nd ed. Blackwell Scientific, Oxford, United Kingdom.
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International Commission on Microbiological Specifications for Foods. 2002. Microorganisms in Foods 7. Microbiological testing in food safety management. Kluwer Academic/Plenum Publishers, New York, NY.
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International Commission on Microbiological Specifications for Foods. 2011. Microorganisms in Foods: Use of Data for Assessing Process Control and Product Acceptance. Kluwer Academic/Plenum Publishers, New York, NY.
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Jarvis, B. 1989. Statistical aspects of the microbiological analysis of foods. Progress in Industrial Microbiology, vol. 21. Elsevier, Amsterdam, The Netherlands.
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Jarvis, B. 2007. On the compositing of samples for qualitative microbiological testing. Lett. Appl. Microbiol. 45: 592– 598.
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Legan, J. D.,, M. H. Vandeven,, S. Dahms, and, M. B. Cole. 2001. Determining the concentration of microorganisms controlled by attributes sampling plans. Food Control 12: 137– 147.
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Membré, J.-M.,, J. Bassettand, and, L. M. Gorris. 2007. Applying the food safety objective and related standards to thermal inactivation of Salmonella in poultry meat. J. Food Prot. 70: 2036– 2044.
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Nauta, M. J.,, and A. H. Havelaar. 2008. Risk-based standards for Campylobacter in the broiler meat chain. Food Control 19: 372– 381.
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Ross, T.,, and C. Chan. 2002. Microbiological criteria and microbiological risk assessment, p. 214–247. In M. Brown and, M. Stringer (ed.), Microbiological Risk Assessment in Food Processing. Wood-head Publishing, Cambridge, United Kingdom.
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Stringer, M. 2005. Summary report: food safety objectives—role in microbiological food safety management. Food Control 16: 775– 794.
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Uyttendaele, M.,, K. Baert,, Y. Ghafir,, G. Daube,, L. De Zutter,, L. Herman,, K. Dierick,, D. Pierard,, J. J. Dubois,, B. Horion, and, J. Debevere. 2006. Quantitative risk assessment of Campylobacter spp. in poultry based meat preparations as one of the factors to support the development of risk-based microbiological criteria in Belgium. Int. J. Food Microbiol. 111: 149– 163.
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van Schothorst, M.,, M. H. Zwietering,, T. Ross,, R. L. Buchanan,, M. B. Cole, and the International Commission on Microbiological Specifications for Foods. 2009. Relating microbiological criteria to food safety objectives and performance objectives. Food Control 20: 967– 979.
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Whiting, R. C.,, A. Rainosek,, R. L. Buchanan,, M. Miliotis,, D. LaBarre,, W. Long,, A. Ruple, and, S. Schaub. 2006. Determining the microbiological criteria for lot rejection from the performance objective or food safety objective. Int. J. Food Microbiol. 110: 263– 267.
Tables
Statistics of Sampling for Microbiological Testing of Foodborne Pathogens
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Citation:
Ross T, Fratamico P, Jaykus L, Zwietering M.
2011.
Statistics of Sampling for Microbiological Testing of Foodborne Pathogens,
p 103-120.
In
Hoorfar J (ed),
Rapid Detection, Characterization, and Enumeration of Foodborne Pathogens.
ASM Press, Washington, DC.
doi: 10.1128/9781555817121.ch7
/content/10.1128/9781555817121.ch07.ch07tab01
TABLE 1
Terminology associated with sampling plans used in food microbiology
TABLE 1
Terminology associated with sampling plans used in food microbiology
Citation:
Ross T, Fratamico P, Jaykus L, Zwietering M.
2011.
Statistics of Sampling for Microbiological Testing of Foodborne Pathogens,
p 103-120.
In
Hoorfar J (ed),
Rapid Detection, Characterization, and Enumeration of Foodborne Pathogens.
ASM Press, Washington, DC.
doi: 10.1128/9781555817121.ch7
/content/10.1128/9781555817121.ch07.ch07tab01a
Untitled
Untitled
Citation:
Ross T, Fratamico P, Jaykus L, Zwietering M.
2011.
Statistics of Sampling for Microbiological Testing of Foodborne Pathogens,
p 103-120.
In
Hoorfar J (ed),
Rapid Detection, Characterization, and Enumeration of Foodborne Pathogens.
ASM Press, Washington, DC.
doi: 10.1128/9781555817121.ch7
/content/10.1128/9781555817121.ch07.ch07tab02
TABLE 2
Example of a risk-based sampling plan scheme
a
TABLE 2
Example of a risk-based sampling plan scheme a
Citation:
Ross T, Fratamico P, Jaykus L, Zwietering M.
2011.
Statistics of Sampling for Microbiological Testing of Foodborne Pathogens,
p 103-120.
In
Hoorfar J (ed),
Rapid Detection, Characterization, and Enumeration of Foodborne Pathogens.
ASM Press, Washington, DC.
doi: 10.1128/9781555817121.ch7