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Chapter 7 : Statistics of Sampling for Microbiological Testing of Foodborne Pathogens
Category: Applied and Industrial Microbiology; Food Microbiology
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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.
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.
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.
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.
Terminology associated with sampling plans used in food microbiology
Example of a risk-based sampling plan scheme a