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1 This article was downloaded by:[b-on Consortium - 27] On: 15 October 27 Access Details: [subscription number ] Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Food Additives & Contaminants Publication details, including instructions for authors and subscription information: Statistical modelling as an aid to the design of retail sampling plans for mycotoxins in food Roy Macarthur a ; Susan Macdonald a ; Paul Brereton a ; Alistair Murray a a Central Science Laboratory, Sand Hutton, York, UK Online Publication Date: 1 January 26 To cite this Article: Macarthur, Roy, Macdonald, Susan, Brereton, Paul and Murray, Alistair (26) 'Statistical modelling as an aid to the design of retail sampling plans for mycotoxins in food', Food Additives & Contaminants, 23:1, To link to this article: DOI: 1.18/ URL: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

2 Downloaded By: [B-on Consortium - 27] At: 12:12 15 October 27 Food Additives and Contaminants, January 26; 23(1): Statistical modelling as an aid to the design of retail sampling plans for mycotoxins in food ROY MACARTHUR, SUSAN MACDONALD, PAUL BRERETON, & ALISTAIR MURRAY Central Science Laboratory, Sand Hutton, York, UK (Received 24 June 25; accepted 2 August 25) Abstract A study has been carried out to assess appropriate statistical models for use in evaluating retail sampling plans for the determination of mycotoxins in food. A compound gamma model was found to be a suitable fit. A simulation model based on the compound gamma model was used to produce operating characteristic curves for a range of parameters relevant to retail sampling. The model was also used to estimate the minimum number of increments necessary to minimize the overall measurement uncertainty. Simulation results showed that measurements based on retail samples (for which the maximum number of increments is constrained by cost) may produce fit-for-purpose results for the measurement of ochratoxin A in dried fruit, but are unlikely to do so for the measurement of aflatoxin B1 in pistachio nuts. In order to produce a more accurate simulation, further work is required to determine the degree of heterogeneity associated with batches of food products. With appropriate parameterization in terms of physical and biological characteristics, the systems developed in this study could be applied to other analyte/matrix combinations. Keywords: Mycotoxins, sampling, measurement, uncertainty, ochratoxin A, aflatoxin Introduction Appropriate sampling plans are essential to ensure that the analytically-derived mean concentration of a sample is representative of the true mean concentration of a lot. Sampling plans are particularly relevant in the area of mycotoxins where it is known that the contamination of a commodity can be heterogeneously distributed (Schatzki 1995a, Jewers et al. 1988, Sharman et al. 1994, MacDonald et al. 21, Johansson et al. 2b, Whitaker et al. 1994b, Schatzki 1995b, Sharkey et al. 1994). The design of a sampling plan needs to take this heterogeneity into account to ensure that the final aggregate samples are as representative of the entire lot as practicable and that false positive and false negative results are reduced to an acceptable minimum. False negatives, i.e. acceptance of a lot containing unacceptable levels of mycotoxins, will result in potentially contaminated produce being available to consumers. European Directives set analytical and sampling requirements for the enforcement of European legislation setting maximum permitted limits for mycotoxins in certain commodities (EC 1998, 22). These include prescribed sampling plans. The Directives describe sampling lots and are, in the main, intended to be applied to consignments for trade or import. Sampling at the retail stage is mentioned, with the statement sampling should be done where possible in accordance with the sampling provisions of the Directives. Where this is not possible other effective sampling procedures can be used provided that they ensure sufficient representativeness for the sampled lot (EC 22). No specific advice on what procedure should be used or what is sufficiently representative is given. One working definition of representative in this context can be taken to be that derived statistics (such as mean concentration of lot), are without bias, and estimate the properties of the sampled lot with precision fit for their intended purpose. If the intended purpose is the testing of food products for the presence of mycotoxins in bulk or retail lots against a legislative limit then a measurement method (sampling followed by analysis) has produced a sufficiently representative result if the Correspondence: Roy Macarthur. r.macarthur@csl.gov.uk ISSN X print/issn online ß 26 Taylor & Francis DOI: 1.18/

3 Downloaded By: [B-on Consortium - 27] At: 12:12 15 October 27 uncertainty associated with a result does not encompass the legislative limit. Hence, enabling an analyst to decide with a high degree of confidence whether the lot true mean concentration of mycotoxin is above or below the legislative limit. The majority of sampling plans used in the mycotoxins area have been concerned with the control of aflatoxin concentrations in peanuts (Whitaker et al. 1995, 1994a, Whitaker & Dickens 1989, Knutti & Schlatter 1982) whilst others have studied aflatoxins in pistachios (Schatzki 1995a), maize (Jewers et al. 1988, Whitaker & Dickens 1983), and figs (Sharman et al. 1994). Previous work has shown the major source of uncertainty associated with the measurement of mycotoxins is due to sampling variance, which is particularly affected by the number of increments taken (Whitaker et al. 1994a). An increment is a sample taken from a single location in the lot. Increments are combined to form an aggregate sample. While the sampling patterns of some bulk materials have been studied, there has been little work done on studying sampling strategies for retail products. Coker et al. (1995) stress that special attention should also be paid to the development of sampling plans for finished foods, which reflect the distribution of aflatoxin amongst individual retail packs, thus protecting individual consumers from exposure to excessively high levels of contamination. A study of jars of peanut butter for aflatoxin found the distribution could be described by an Extreme Value Type II distribution (Dell et al. 2). MacDonald et al. (21) reported results of retail sampling investigations on currants and roasted coffee for ochratoxin A, and pistachios and paprika for aflatoxins. A sampling plan was defined by Johansson et al. (2b) as a mycotoxin test procedure combined with a sample acceptance limit. The test procedure consists of sampling from the target population, sample preparation (homogenization, sub-sampling), and analytical steps. Each of these three steps has an associated variance that contributes to the total variance of the testing scheme. In order to make objective choices of sampling strategy, each of these components must be measured and/or modelled and their relationship understood. The work described here describes the modelling and subsequent simulation study to provide initial operating characteristic (OC) curves to examine the plausibility of applying retail-sampling strategies to the measurement of mycotoxins in dried fruit and nuts. The work reported here comprised two parts: An exploration of historical data to elucidate the form and parameters of the statistical distribution of the concentration of ochratoxin A in samples of dried fruit and aflatoxin in samples of pistachio nuts; and a Monte Carlo Statistical modelling as aid to sampling plans for mycotoxins in food 85 simulation, using the distribution and parameters determined in the first part of the study, to examine how the uncertainty associated with measurement results could be expected to change with the number of increments used to form the aggregate sample. Experimental Analytical methodology The concentrations of ochratoxin A in dried fruit samples, and aflatoxin B1 in pistachio nut samples were determined using UKAS accredited quantitative Liquid Chromatography methodology incorporating immunoaffinity column cleanup and fluorescence detection (MacDonald et al. 23, Patey et al. 1991). Probability distributions Evaluation of candidate probability distributions. Initial statistical evaluation of candidate probability distributions was undertaken using a data set (n ¼ 673) comprising results of the measurement of ochratoxin A in dried vine fruit, i.e. currants, raisins or sultanas. Results were included in the data set if the following criteria were met: (1) The sample type was single variety fruit, i.e. no mixed fruit samples were included; (2) The data had passed the analytical Quality Control criteria at the time of analysis and recovery data were available; (3) No kind of pre-selection of the samples had taken place (some samples are received for confirmation of a positive screening test); and (4) The sample mass was known. The measurements were made on samples taken from many sources over a period of years, thus the sampling variation displayed by the results incorporated between-lot variation and represents a likely, but not definite, overestimate for the amount of variation that might be expected to be displayed between samples taken from the same lot. Simulation model The simulation of sampling and analysis used the following algorithm: For N increments of mass M:. Decide, using probability p, whether the increment is contaminated;. If the increment is contaminated assign a concentration to it using a value selected from the gamma distribution with shape parameter and scale parameter ;. Calculate mean concentration of n increments;

4 Downloaded By: [B-on Consortium - 27] At: 12:12 15 October R. Macarthur et al.. Derive an aggregate sample with concentration of analyte equal to the mean of the increments;. Simulate the measurement of the aggregate sample using a method with limit of detection Ld and relative standard uncertainly Ru;. Output measurement result for aggregate sample. An Excel VBA macro was used to carry out the simulation. The macro employed published and, where appropriate peer-reviewed, methods for the production of pseudo-random numbers from uniform (L Ecuyer 1996), normal (Saucier 2) and gamma (Saucier 2) distributions. Parameter estimation Probability that an increment selected at random, contains mycotoxin. Measurement results from the mycotoxins databases were divided into groups by sample mass. The number of samples containing mycotoxin above the limit of detection, and the number not found to contain mycotoxin in each group were recorded. The likelihood function for the probability that a 1 kg sample contains mycotoxin ( p) was given by: Lð pþ ¼ Y 1 ð1 pþ m i xi ð1 pþ m iðn i x i Þ i ðfrom Tebbs & Swallow 23Þ where m i ¼ mass of samples in group i n i ¼ number of samples in group i x i ¼ number of positive samples in group i The log likelihood function was given by Ið pþ ¼ X ¼ X 2 2 ¼ X i x i Ln 1 ð1 pþ m i þ m i ðn i x i ÞLnð1 pþ c i n i ðð1 pþ m i ð 1Þþx i Þ ð1 pþ m ; i ð 1Þðp 1Þ 1 ðð1 pþ m i 1Þ 2 ðp 1Þ 2c i ni ð1 pþ m i 1 2 þ m i ð1 pþ m i þð1 pþ m i 1 x i For each set of results the most likely value of p ( p M ) was estimated iteratively, using Newton s method, by the convergence of: p kþ1 ¼ 2 I=@p 2 An approximate 95% confidence interval for p was estimated using the convergence (two values) of: p kþ1 ¼ p k Iðp kþ Iðp M k Shape and scale parameters for gamma function describing concentration of mycotoxin that may be expected to be found a 1 kg increment. Shape and scale parameters for the gamma distribution describing the concentration of mycotoxins in contaminated 1 kg samples were found using the maximum likelihood method described above by applying the log likelihood function: Iðm,cÞ ¼ Xn i¼1 1 c 2 Logðmc 2 Þþ 1 c 2 1! Logðx i Þ ðmc 2 Þx i Log 1 c 2 where n ¼ number of values in data set, x i ¼ the value of data set, c ¼ estimate of coefficient of variation associated with data set, m ¼ estimate of mean value of data set. This likelihood function employs a gamma distribution with parameters transformed from the usual shape and scale parameters ( and ) to mean and coefficient of variation (m and c) using: ¼ 1 c 2 and ¼ mc 2 Maximum likelihood estimates of m and c are less correlated than maximum likelihood estimates of and. This avoids the problems reported by Giesbrecht and Whitaker (1998) with the likelihood function of the gamma distribution based on the untransformed parameters. Limit of detection and relative standard uncertainty of analytical method used to measure concentration of mycotoxin. Estimates of limit of detection associated with the measurement of ochratoxin A in dried fruit and aflatoxin B1 in nuts were gained from the signal to noise ratio of chromatograms produced by blank samples. Estimates of the relative standard uncertainty associated with the measurement results were gained from in-house validation studies in accordance with the Eurachem guide to quantifying uncertainty in analytical measurement (Eurachem 2).

5 Downloaded By: [B-on Consortium - 27] At: 12:12 15 October 27 Results Evaluation of heterogeneity Table I summarizes the vine fruit data set. The empirical distribution of analytical data were extremely skew as shown in Figure 1. Note that the maximum value is some 2 times the mean and more than 4 times the median; 7% of values are less than 3.7 mg/kg (mean ¼ 3.93 mg/kg) so the right-hand tail is very sparse. This means that, even in a large data set such as this one, there is little information to determine which of the candidate distributions is the best fit to the data. Several statistical distributions have been postulated to describe the probability distribution of results of mycotoxin measurements. These include Gamma, compound Gamma, log-normal, Negative Binomial, and Extreme Value. All the distributions that were explored provided statistically reasonable fits to the data, so it was necessary to take account of other factors in choosing a suitable model. The compound Gamma distribution was chosen because it:. Fits very well to mycotoxin data sets in peanuts, corn (Johansson et al. 2b, Giesbrecht & Whitaker 1998, Whitaker et al. 21) and dried fruit; Statistical modelling as aid to sampling plans for mycotoxins in food 87. Allows for finite probability at zero and thus avoids underestimation;. Readily scales with sample mass;. Has a plausible generating mechanism that relates to our biological understanding of the process whereby mycotoxin contamination occurs;. Is widely used in the USA to underpin sampling plans for regulatory purposes (Johansson et al. 2a, Whitaker et al. 1996, Giesbrecht & Whitaker 1998, Whitaker et al. 21). Table II summarizes the pistachio nut data set. The empirical distribution of analytical data was even more skew than the vine fruit data (Figure 2). The maximum value is some 35 times the mean and 2 times the median; 88% of values are less than the mean so the right-hand tail is extremely sparse. Estimated values of parameters of compound gamma distribution Probability that an individual increment, selected at random, contains mycotoxin. The Maximum Likelihood assessment of available measurement results (i.e. observed proportion of positive and Table I. Summary of ochratoxin A in vine fruit data. Summary statistics for vine fruit Number of values 673 Mean (mg/kg) 3.93 Median (mg/kg) 1.8 Minimum (mg/kg).4 Maximum (mg/kg) 81.2 Lower quartile (mg/kg).6 Upper quartile (mg/kg) 4.66 Standard deviation (mg/kg) 6.61 Coefficient of variation (%) 168 Skewness 4.99 Table II. Summary of the pistachio nut data set. Summary statistics for pistachio nuts Number of values 299 Mean (mg/kg) 5.8 Median (mg/kg).1 Minimum (mg/kg). Maximum (mg/kg) 2 Lower quartile (mg/kg).1 Upper quartile (mg/kg).4 Standard deviation (mg/kg) 21. Coefficient of variation (%) 366 Skewness Frequency 15 1 Frequency Concentration µg/kg Concentration (µg/kg) Figure 1. Empirical distribution of results of measurement of ochratoxin A in dried vine fruit. Figure 2. Empirical distribution of results of measurement of aflatoxin B1 in pistachio nuts.

6 Downloaded By: [B-on Consortium - 27] At: 12:12 15 October R. Macarthur et al. negative samples for different sample masses) led to an estimated probability of contamination of.896 (95% confidence interval ) for a 1 kg increment of vine fruit. The probability of contamination for a 1 kg increment of pistachio nuts was lower,.287 (95% confidence interval ). Shape and scale parameters for gamma distribution describing concentration of mycotoxin that may be expected to be found in an individual contaminated increment. The shape parameter for the gamma distribution describing the concentration of ochratoxin A that may be expected to be found in contaminated 1 kg increments of dried fruit was estimated to be.96 (95% confidence interval ). The scale parameter was estimated to be equal to 5.7 mg/kg (95% confidence interval mg/kg). The shape parameter for the gamma distribution describing the concentration of Aflatoxin B1 that may be expected to be found in contaminated 1 kg increments of pistachio nuts was estimated to be.57 (95% confidence interval ). The scale parameter was estimated to be equal to 2.2 mg/kg (95% confidence interval mg/kg). Limit of detection and relative standard uncertainty of analytical method used to measure concentration of mycotoxin. The limit of detection associated with the measurement of ochratoxin A in dried fruit was estimated to be equal to.2 mg/kg. The relative standard uncertainty associated with the measurement results was estimated to be equal to.22. The limit of detection associated with the measurement of aflatoxin B1 in nuts was estimated to be equal to.1 mg/kg. The relative standard uncertainty associated with the measurement results was estimated to be equal to.21. determine whether the concentration of mycotoxin in bulk or retail lots exceeded the relevant legislative limit. Parameters were modified from those estimated from the data sets in order to simulate a batch of product with the appropriate concentration. This was done in two ways chosen to represent extreme cases of the way in which different mean concentrations can arise in bulk or retail lots. The first kind of modification (Scenario 1) was carried out by assuming that the new lot was similar to the observed lot but that contaminated increments contained (on average) a different concentration of mycotoxin (i.e. by modifying the parameter and keeping the parameter constant at the observed value). The second modification (Scenario 2) was carried out by assuming that changes in mean concentration were driven by changes in the incidence of contamination (i.e. by modifying the parameter and keeping the parameter constant at the observed value). Hence, OC curves describing the relation between the probability that a lot is accepted as containing less than the legislative limit of mycotoxin and the true mean concentration of mycotoxin were produced for each product type for measurements based on 1, 1 and 3 increments, for simulated lots based on each scenario. Uncertainty associated with sampling from a lot described by data-set Ochratoxin A in dried fruit. The variation displayed by simulation results based on 1 increments was much larger than analytical uncertainty. This showed that sampling variation was significant compared to analytical uncertainty for measurements employing aggregate samples produced from 1 increments. However, variation due to sampling became insignificant compared to analytical uncertainty (i.e. overall variation analytical uncertainty) for measurements based on 6 increments. Simulation results are shown in Figure 3. Demonstration of use of simulation to estimate effect of number of increments on measurement reliability Estimates of the parameters: prevalence of contaminated 1 kg increments; and shape and scale parameters of the gamma distribution describing concentration of mycotoxins that may be expected to be found in contaminated 1 kg increments were used in a simulation to examine the effect of the number of increments on the uncertainty associated with measurement results. This was achieved by simulating the analysis of aggregate samples produced by between 1 and 2 increments of 1 kg each. Simulated OC curves were also produced to examine the effect of the number of increments on the reliability of using measurement results to Aflatoxin B1 in Pistachio nuts. The variation displayed by simulation results based on 5 increments was much larger than analytical uncertainty. This showed that sampling variation was significant compared to analytical uncertainty for measurements employing aggregate samples produced from 5 increments. Variation due to sampling remained significant when compared to analytical uncertainty for all measurements simulated (up to 2 increments). Simulation results are shown in Figure 4. Operation characteristic curves Ochratoxin A in dried fruit. The OC curves produced by simulated measurement of ochratoxin A in dried

7 Downloaded By: [B-on Consortium - 27] At: 12:12 15 October 27 Simulated measurement results (µg/kg) Number of increments Lot true mean 2.5th percentile 97.5th percentile Analytical uncertainty Figure 3. Effect of number of increments on measurement uncertainty, OA in dried fruit; calculated by simulation based on a single analysis of an aggregate sample derived from 1 kg increments taken from a lot with properties estimated from the data set. Simulated measurement results (µg/kg) Number of increments Lot true mean 2.5th percentile 97.5th percentile Analytical uncertainty Figure 4. Effect of number of increments on measurement uncertainty, aflatoxin B1 in pistachio nuts; calculated by simulation based on a single analysis of an aggregate sample derived from 1 kg increments taken from a lot with properties estimated from the data set. Statistical modelling as aid to sampling plans for mycotoxins in food 89 Probability of acceptance Scenario1 Scenario2 Figure 5. OC curve showing relation between lot true mean contains less than the legal limit of 1 mg/kg OA in dried fruit by employing a single analysis of an aggregate sample formed from a single (1 kg) increment. Probability of acceptance (%) Scenario 1 Scenario 2 Figure 6. OC curve showing relation between lot true mean contains less than the legal limit of 1 mg/kg OA in dried fruit by employing a single analysis of an aggregate sample formed from 1 (1 kg) increments. fruit (see Figures 5 7) showed that measurements based on single increments led to high probabilities of both the acceptance of lots containing more than the legislative limit (1 mg/kg) (false negative result) and the rejection of lots containing less than the legislative limit (false positive result) under both Scenario 1 and Scenario 2 when compared to the OC curve produced by considering analytical uncertainty alone (i.e. the performance produced by the analysis of perfectly representative samples). For simulated measurements based on 1 increments the probability of a false negative result was less than 5%, under both Scenario 1 and Scenario 2 for lots containing 24 mg/kg. For simulated measurements based on 3 increments the probability of a false negative result was less than 5%, under both scenarios, for lots containing 18 mg/kg. Probability of acceptance (%) Scenario 1 Scenario 2 Figure 7. OC curve showing relation between lot true mean contains less than the legal limit of 1 mg/kg OA in dried fruit by employing a single analysis of an aggregate sample formed from 3 (1 kg) increments.

8 Downloaded By: [B-on Consortium - 27] At: 12:12 15 October 27 9 R. Macarthur et al. Probability of acceptance (%) Scenario 1 Scenario 2 Figure 8. OC curve showing relation between lot true mean contains less than the legal limit of 2 mg/kg aflatoxin B1 in pistachio nuts by employing a single analysis of an aggregate sample formed from a single (1 kg) increment. Probability of acceptance (%) Scenario 1 Scenario 2 Figure 9. OC curve showing relation between lot true mean contains less than the legal limit of 2 mg/kg aflatoxin B1 in pistachio nuts by employing a single analysis of an aggregate sample formed from 1 (1 kg) increments. The similarity of the 3 increment OC curve and the analytical only OC curve shows that if further improvement in measurement performance is required then this should be achieved by improving analytical performance rather than by increasing the number of increments. Aflatoxin in pistachio nuts. The OC curves produced by the simulated measurement of aflatoxin (see Figures 8 to 1) showed that measurements based on up to 3 increments led to a high probability of false negative results under both Scenario 1 and Scenario 2 (for example a 2% probability of accepting a lot containing twice the legal limit of 2 mg/kg). Discussion The form of the statistical distribution of mycotoxin between increments of fruit and nuts has been elucidated using available measurement results. Probability of acceptance (%) Scenario 1 Scenario 2 Figure 1. OC curve showing relation between lot true mean contains less than the legal limit of 2 mg/kg aflatoxin B1 in pistachio nuts by employing a single analysis of an aggregate sample formed from 3 (1 kg) increments. A simulation has been constructed based on these parameters and parameters describing analytical uncertainty that can be used to objectively model the quality of results that will be produced by any measurement (sampling and analysis) design for these products. It is important to remember that the measurement results used to provide estimates of the size of variation associated with sampling were produced by the analysis of samples from different lots. However, they have been used as estimates of within-lot variability. Hence, conclusions about the number of increments necessary to produce fit for purpose results represent a likely, but not definite, upper limit to this number. Further study of the variability of mycotoxin concentration within-lots, based on the measurement of mycotoxins in individual increments, will be necessary to substantiate the specific quantitative estimates of sampling and measurement uncertainty presented in this paper. For lots based on the observed parameters the variability associated with simulated measurement results was much larger than the uncertainty associated with analysis alone for measurements based on 1 or less increments for ochratoxin A in dried fruit, and for measurements based on 5 increments or less for the measurement of aflatoxin B1 in pistachio nuts. However, this observation does not mean that results based on small numbers of increments are not fit for any purpose. For example, if the uncertainty associated with a measurement result is large, but does not encompass a legislative limit, then the result is fit for the purpose of testing against the limit. This observation shows that if the uncertainty associated with results based on small numbers of increments (less than 1 for ochratoxin A in dried fruit, less than 5 for aflatoxin B1 in pistachio nuts) is too large then the only way to reduce uncertainty is

9 Downloaded By: [B-on Consortium - 27] At: 12:12 15 October 27 to take more increments. Improving analytical performance will not improve measurement performance. However, the simulation results also suggest that increasing the number of increments beyond 5, given the current analytical uncertainty, would lead to little improvement in measurement uncertainty for ochratoxin A in dried fruit. Curves produced for the measurement of mycotoxins in dried fruit and nuts using identical sampling and analytical plans revealed a large difference in the reliability of plans for testing compliance against legislative limits for mycotoxins in the two products. This highlights the problems that may arise where measurement designs are not properly researched and optimised. For example, a design that is effective for the measurement of ochratoxin A in dried fruit is likely to leave consumers largely unprotected were it to be applied to the measurement of aflatoxins in pistachio nuts, and a design that is effective for the measurement of aflatoxin B1 in pistachio nuts would represent a waste of resources if applied to the measurement of ochratoxin A in dried fruit. A measurement design that has not been adequately researched cannot be said to offer effective protection or value for money. Conclusions The model demonstrated in this study can be used to estimate uncertainty associated with results of the measurement of mycotoxins based on small numbers of increments. Hence, the model can be used to test whether retail sampling plans, for which the number of increments is inevitably constrained by cost, meet the condition of ensuring sufficient representativeness in accordance with Directive 22/26/EC. Applying the model to historical results of the measurement mycotoxins in dried fruit and pistachio nuts has shown that measurements based on retail samples may produce fit for purpose results for the measurement of ochratoxin A in dried fruit, but are unlikely to do so for the measurement of aflatoxin B1 in pistachio nuts. The observation that the fitness for purpose of mycotoxin measurement plans is product-dependent is important. It means that in order to demonstrate that plans adequately protect the public and offer value for money, plans should be properly validated against objective fitness for purpose criteria by, for example, using the model presented in this paper. The conclusions of this study should be substantiated using measurements of mycotoxins in large numbers of individual increments taken from single lots to provide better estimates of the size of within-lot variability. Statistical modelling as aid to sampling plans for mycotoxins in food 91 Acknowledgements The authors would like to thank Dr Gavin Ross of Rothamsted Statistics Department for performing the non-linear modelling using Maximum Likelihood Program software. They gratefully acknowledge support from the UK Food Standards Agency (FSA) for funding this work. The statements and conclusions are the responsibility of the authors and should not be taken to represent the opinion of the FSA. References Coker RD, Nagler MJ, Blunden G, Sharkey AJ, Defize PR, Derksen GB, Whitaker TB Design of sampling plans for mycotoxins in foods and feeds. Natural Toxins 3: Dell MPK, Haswell SJ, Gay C, Coker RD. 2. Analytical methodology for the determination of aflatoxins in peanut butter: The validation of a suitable sampling model. EC Commission Directive 98/53/EC. Methods on sampling and analysis for the control of certain contaminants in food. Official Journal of the European Communities L21:93. EC 22. Commission Directive 22/26/EC. Laying down the sampling methods and the methods of analysis for the official control of ochratoxin A in foodstuffs. Official Journal of the European Communities L75: Eurachem/CITAC 2. Quantifying uncertainty in analytical measurement. 2nd edition. Giesbrecht FG, Whitaker TB Investigations of the problems of assessing aflatoxin levels in peanuts. Biometrics 54: Jewers K, Bradburn N, Sharkey AJ Aflatoxin distribution studies on a four tonne batch of maize. International Biodeterioration 24: Johansson AS, Whitaker TB, Giesbrecht FG, Hagler WM, Young JH. 2a. Testing shelled corn for aflatoxin, Part III: Evaluating the performance of aflatoxin sampling plans. Journal of the Association of Official Analytical Chemists International 83: Johansson AS, Whitaker TB, Giesbrecht FG, Hagler WR, Young JH. 2b. Testing shelled corn for aflatoxin, Part II: Modelling the observed distribution of aflatoxin test results. 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