Article pubs.acs.org/JAFC
Estimation of Sampling Uncertainty of Pesticide Residues Based on Supervised Residue Trial Data Zsuzsa Farkas,* Zsuzsanna Horváth, István J. Szabó, and Á rpád Ambrus† National Food Chain Safety Office, Directorate for Food Safety Risk Assessment, Tábornok u. 2, 1143 Budapest, Hungary ABSTRACT: Typical sampling uncertainties were calculated as the average of relative standard deviations (CV) of residues measured in individual crops tested in supervised residue trials and from their pooled variance for crop groups. The relative confidence intervals of the sampling uncertainty for different crops were estimated from the random duplicate composite samples generated with computer modeling from residues in 182 independent primary sample sets, each consisting of 100−320 residue data. The relative 95% confidence intervals were found to be independent from the CV of primary residue data populations; therefore, the calculated values are generally applicable. In view of the potentially serious consequences of underestimated sampling uncertainties, their upper confidence limits are recommended for practical use to verify the compliance of products and for planning statistically based sampling programs. Sampling uncertainties are reported for 24 crop groups and 106 individual crops. KEYWORDS: variability of pesticide residues, sampling uncertainty, uncertainty of residue data, supervised trials
■
INTRODUCTION Pesticide residues are heterogeneously distributed in individual crop units or small single-sample increments and can vary to a large extent within and between treated fields,1 due to different reasons such as environmental and weather conditions,2,3 agrotechnology,4,5 and the application method of pesticides.6 At the international level, the FAO/WHO Joint Meetings on Pesticide Residues (JMPR) carries out the safety evaluation of pesticide residues and recommends maximum residue levels for the Codex Committee on Pesticide Residues (CCPR) for elaboration of Codex Standards, which are used as food safety criteria within the World Trade Organization (WTO) Sanitary and Phytosanitary Agreement.7 The maximum residue levels, highest residues, and median residues are estimated on the basis of the results of so-called supervised trials, which are carried out to reflect the residues likely to occur if the pesticides are used in accordance with the maximum registered dosage and shortest time between last application and harvest (PHI). The results of the evaluation of pesticide residues are published annually. Since 1997, the JMPR has systematically reported the residue data that were used for the estimation of maximum residue levels.8 The supervised residue trials are very carefully planned9 and carried out on small experimental plots. Some examples of the plot sizes8 and sample sizes are shown in Table 1. Supervised trial samples are analyzed by specialized laboratories, where the residues are determined typically in hundreds of the same sample matrix with optimized methods. Consequently, they can achieve better reproducibility than the official control laboratories, where usually large numbers of different kinds of samples are analyzed a few times during a year. Nevertheless, the residue concentrations in samples taken from crops treated with similar dose rates and sampled within a confined time interval can significantly vary within the treated plot and between fields due to several uncontrollable factors mentioned above. Results of supervised trials provide an excellent and © XXXX American Chemical Society
readily accessible database for the analysis of distribution of pesticide residues. Knowledge of the expectable sampling uncertainty, which is generally the main contributor to the combined uncertainty of the measured residues,10 is of paramount importance for planning statistically based sampling plans to verify compliance of food with legal limits before they are placed on the market. The sampling uncertainty involved in the determination of pesticide residues has been estimated on the basis of the results of analysis of individual fruits and vegetables11 taken from independent lots12 or from specifically designed field trials.13 However, the available data enabled estimation of sampling uncertainty only for small-, medium-, and large-sized crops in general according to the Codex Sampling Guidelines,14 but a number of important crop groups, such as cereals and root vegetables, could not be covered. To fill partly the information gap, in the study of Farkas et al.,15 primary samples of parsley and carrot were taken and analyzed with the QuEChERS method applying LC-MS/MS detection. Modeling experiments were conducted to evaluate the applicability of range statistics for the calculation of sampling uncertainty and the relationship of the number of tested lots and the estimated sampling uncertainty. The results of the modeling indicated that the average sampling uncertainties estimated with simple random sampling and range statistics were practically the same. The confidence intervals of the sampling uncertainty decreased with the increasing number of replicate samples taken from one lot and the number of lots sampled. The estimated relative 95% confidence intervals of sampling uncertainty are independent from the relative standard deviation of the measurand in the Special Issue: IUPAC - Analysis of Residues in Food Received: November 14, 2014 Accepted: December 22, 2014
A
DOI: 10.1021/jf5055112 J. Agric. Food Chem. XXXX, XXX, XXX−XXX
Article
Journal of Agricultural and Food Chemistry Table 1. Examples for Different Crops, Sprayers, Plot Sizes, and Field Sample Sizes in the Supervised Trials crop
place
year
sprayer
plot size
alfalfa apple apple apple banana bean bean coffee cotton cotton grapefruit grape grape lemon onion onions orange peach peanut peanut pea
Australia Australia New Zealand USA Australia Costa Rica Europe Colombia Brazil Brazil New Zealand Australia Italy Australia Europe New Zealand Italy Australia Argentina Australia Europe
1988−1989 1991 1986 1987 1991 1998 2000−2001 1984 1997 2001 1985 1990 1989 1990 1999−2000 1987 1991 1991 1992 1997 1999−2000
60−240 m2 2 trees 9 m2 1 tree, 37−46 m2
peas rice
Europe USA
2004 1987−1988
soybean soybean sugar beet sugar beet sunflower
Brazil Europe Europe Europe Europe
2000−2002 2000−2001 1988 2000 2000
precision plot sprayer LPG-powered hand lance precision plot sprayer CO2-powered backpack, tractor-mounted CO2 sprayer precision plot sprayer CO2-powered backpack sprayer 3 m boom, knapsack sprayer, compressed air sprayer CO2-powered backpack CO2-powered backpack CO2-powered backpack precision backpack precision plot sprayer crystal sprayer, motor pump, and teejet precision plot sprayer 3 m boom, boom sprayers precision plot sprayer knapsack LPG-powered hand lance CO2 powered backpack precision plot sprayers hand-carried boom sprayer, motorized backpack, plot sprayer, 3 m boom, knapsack AUK plot sprayer aircraft, CO2 -powered backpack, small plot sprayers, 4-wheeled CO2powered sprayer CO2-powered handboom AUK plot sprayer, plot boom sprayer knapsack with teejet, flat nozzle sprayer boom sprayers boom sprayers
32 m2 45−90 m2 3 trees 24 m2 60−500 m2 10 m2 1 vine 10−40 m2 1 tree 42−93 m2 12 m2 3 trees 2 trees 11 m2 120 m2 44−90 m2
sample size
2 kg, 15 fruits 25 fruits 2 kg 1−2 kg 1−2 kg 2 kg 2 kg, >8 fruits 1 kg 1−2.3 kg 2 kg, 12 onions 24 fruits
1−6 kg
39−60 m2 37−3300 m2
0.3−1 kg
64−184 m2 30−60 m2 22−144 m2 42−45 m2 42−60 m2
2 kg 1−3 kg 5 plants 1−6 kg 1−1.3 kg
sampled commodity, which indicates that the results of modeling are applicable regardless of the characteristics of the residue distribution in the sampled population. Knowledge of the uncertainty of sampling enables the calculation of combined uncertainty of residue concentrations measured in composite samples, which then can be used to test compliance with maximum residue limits as part of the premarketing self-control program of the producers. The objective of this study is to utilize the extensive pesticide residue data obtained from supervised trials for estimation of average sampling uncertainty for all groups of fresh fruits and vegetables, primary feed commodities, and semiprocessed plant products included in the Codex Commodity Classification,16 as well as for some individual crops for which sufficient residue data were available.
■
MATERIALS AND METHODS Figure 1. Relative frequency distribution of different pesticide residues measured in composite samples of size 10 taken from different cabbage fields treated with different pesticides independently. Reprinted with permission from ref 18. Copyright 2014 WESSLING Beneficial Nonprofit Ltd.
Selection of Residue Database. For the evaluation of the withinfield variability of pesticide residues of different crops and crop groups, supervised residue trials reported by the JMPR between 1997 and 2010 8 were considered. In some of the trials, replicate samples were taken (duplicate samples in >99.95% of the cases) from the single-trial plots to get more accurate information on the average residue concentration of the treated field, according to the requirements of U.S. EPA.17 These residue data were collected and used in our study. The selected data set contained altogether 12087 replicate sample sets (25876 individual ones), comprising 706 pesticide−crop combinations formed from 66 different pesticides and 106 commodities, referred to as “crops” in the study. The Codex Classification of Foods and Animal Feeds,16 developed within the framework of the Codex Committee on Pesticide Residues
(CCPR), was primarily used for grouping the various crops. It takes into account, among other things, the nature of the crops and expectable level of pesticide residues; therefore, fresh and dry foods and semiprocessed foods and feeds were classified into different groups. It is intended to ensure the use of unambiguous description of various crops and to classify food commodities into groups for the purpose of establishing group maximum residue limits based on the B
DOI: 10.1021/jf5055112 J. Agric. Food Chem. XXXX, XXX, XXX−XXX
Article
Journal of Agricultural and Food Chemistry Table 2. Summary of Average CVA Values Obtained from Recovery Studies commodity groupa
typical commodity category
no.b
spike rangec
no.d
CVAw%e
1
pome fruit stone fruit bulb vegetables Brassica vegetables fruiting vegetables/cucurbits leafy vegetables and fresh herbs stem and stalk vegetables forage crops fodder crops fresh legume vegetables root and tuber vegetables or feed citrus fruit small fruits and berries other
2 3 1 3 5 4 2 9 6 4 4 3 5 1
0.01−2.0 0.02−4.0 0.02−0.3 0.01−5.0 0.01−11.4 0.01−5.0 0.02−10.0 0.01−40.0 0.01−20.0 0.01−5.0 0.01−2.0 0.01−5.0 0.01−2.0 0.02−0.5
115 149 24 223 723 227 32 623 632 474 225 526 446 28
7.75 9.62 8.70 11.86 8.77 10.30 14.13 9.35 9.01 8.18 8.70 7.00 7.56 10.94
2
tree nuts oilseeds
2 6
0.01−1.0 0.01−3.0
12 672
11.88 8.08
3
oily fruits and products
2
0.01−5.0
42
9.25
4
dry legume vegetables, pulses cereal grain and products thereof almond hull, cotton hull, peanut shell hops, dried, tea, coffee, sugar cane
2 5 3 4
0.01−1.0 0.01−20 0.01−7.5 0.01−20.0
362 691 81 160
7.04 7.45 10.68 7.38
5
sum grand weighted average
6467 8.56
a
1, high water content; 2, high oil content and very low water content; 3, high oil content and intermediate water content; 4, high starch and/or protein content and low water and fat content; 5, difficult or unique commodities. bNumber of commodities. cRange of spike concentration, mg/kg. d Number of recovery tests. eCVAw%, weighted average CVA value. standard deviation, CV. The use of CV values is more suitable than the standard deviation of the residues because the variability of pesticide residues in different data sets, expressed with their CV value, is comparable regardless of their average concentration. Previous studies revealed that the relative frequency distributions of pesticide residues are very similar and independent from the type of the pesticide (Figure 1); therefore, the average of the CV values of different data sets is considered to be the best estimate for the uncertainty of the measured residues.18 From the combined uncertainty of the measured residues (CVR) and the uncertainty of the laboratory phase of the determination of residues19 (CVL), the uncertainty of sampling (CVS) can be calculated as
CVR =
Figure 2. Relationship of relative difference of the 95% range of estimated relative standard deviations based on duplicate samples (p2) of size 10 taken from L lots.
CVS2 + CV2L → CVS =
CV2R − CV2L
(1) 20
As the database used contained replicate samples, range statistics was applied to calculate the relative standard deviation of the measured residues in one replicate sample set (CV1), and their average was considered as the characteristic uncertainty of measured residue values in a given crop (CVR1). For replicate samples from one trial
residues in/on representative commodities, which then can be extrapolated to the so-called minor commodities belonging to the group. In addition, we also took into account the sampling aspects in grouping of crops: for example, small-, medium-, and large-sized fresh fruits and vegetables. The crops included in the supervised trial residue database belonged to 24 groups having similar characteristics. In addition to the determination of sampling uncertainties for individual crops, the typical sampling uncertainty was also calculated for crop groups aiming to provide initial estimates for the expectable sampling uncertainties for minor commodities, belonging to the given group, for which supervised trial residue data are not available. Estimation of Sampling Uncertainty. The characteristic withinfield variation of the residues in/on a crop is expressed as the relative
CVR1 =
⎛ R max − R min ⎞ ⎜ ⎟/d ⎝ ⎠ 2 R
(2)
where Rmax, Rmin, and R̅ are the maximum, minimum, and mean residue values in replicate samples taken from one trial site and d2 is the corresponding factor of 1.128, 1.693, or 2.059, for two, three, or four replicate samples, respectively.21 Because the d2 values are different, the CV values were calculated separately for replicate sample sets consisting of two, three, or four residue values, and their average was calculated afterward. For a single ith commodity from ki trials C
DOI: 10.1021/jf5055112 J. Agric. Food Chem. XXXX, XXX, XXX−XXX
Article
Journal of Agricultural and Food Chemistry ∑i CVR1
CVRi =
ki
CVSsf =
(3)
The supervised trial reports include the validation data, but the details of concurrent recoveries obtained during the analysis of samples are usually not included in the FAO evaluations. Therefore, we collected the recovery data obtained during the validation of the methods used for analyzing samples from supervised trials by the specialized laboratories reported in the FAO evaluations.8 The recovery studies were generally conducted at spike levels from 0.01 to 10 mg/kg with three to eight replicates. The CVA obtained from the recovery studies generally ranged between 2 and 12%, with higher values up to 20% occurring in very few cases. There was no observable correlation between the spike level and the CVA values of recoveries of various pesticide residues of different chemical structures and physicochemical properties from different sample matrices. Therefore, the weighted average of reported CVA values was considered as the best practical estimate for the expectable variability of the results derived from the analysis phase. The results are summarized in Table 2. The grand weighted average (CVAw) of CVA of recoveries obtained from various pesticide−crop combinations was calculated as
CVAw =
∑ (dfi × CV2Ai) ∑ dfi
LCL =
(df × CVS2/χ0.975 )
(8)
UCL =
(df × CVS 2/χ0.025 )
(9)
df, the degree of freedom, is the number of replicate sample pairs of a crop or a crop group, and χ0.975 and χ0.025 are the tabulated values for the 97.5th and 2.5th percentiles of the χ2, distribution, respectively. The χ2 values were calculated with linear interpolation in cases where they were not available to the corresponding df. 24 Calculation of Confidence Limits by Using the Results of Modeling Experimental Data. According to the results of our previous study,15 the 95% relative confidence interval of the sampling uncertainty is independent from the relative standard deviation of the measured residues in the sampled commodity, and it decreases with the increasing number of lots sampled. The modeling was carried out with only up to 20 independent lots to determine the confidence intervals of the CVS1adj values. However, in the case of supervised residue trials, the number of trial sites from which replicate samples were taken amounted to over several hundred; therefore, the modeling has been performed again with the same methodology utilizing 182 primary residue data sets obtained from commercial lots12 or specifically designed field trials: (1) 19 residue data sets,15 each consisting of 104−120 residue values, comprising the combinations of 7 different pesticide active ingredients present in carrot or parsley leaves. (2) 68 lots, assumed to contain crops of the same origin, imported from various countries or grown locally in the United Kingdom were selected in logistic centers, and 100−100 individual fruits were randomly taken from each lot. The fruits were analyzed with multiresidue methods to detect all residues present in the fruits. The 68 data sets comprised apple, banana, kiwi, orange, peach, plum, potato, and tomato.12 24 different pesticide residues were detected in the samples. (3) 95 data sets were obtained from a coordinated research program, including field studies, to determine residues in individual items of leafy vegetables, small and large crops in 13 countries, representing the actual agricultural practice worldwide. Twenty-five pesticide active ingredients were analyzed from black currant, cherry, cabbage, chicory, kale, cucumber, grape, lettuce, mango, papaya, strawberry, and zucchini samples.13 10−10 residue values were selected with random sampling procedure with replacement 1000 times from each of the 182 primary residue data set. The average of the 10 randomly selected residue values were calculated and considered as the residue concentration in one composite sample. The procedure was repeated two times to obtain two databases for assessing the effect of taking duplicate samples to reflect the situation of the supervised trials database, containing mostly duplicate samples. The CV values were calculated from the composite samples with eq 2, applying the corresponding factor of 1.128. Calculation of 95% Confidence Limits. The P0.025 and P0.975 percentiles of ranked CV values calculated from 1000 duplicate samples drawn from each of the 182 individual primary residue populations and the corresponding average CV values were taken to calculate the relative confidence intervals from one data set:
(4)
(5)
The adjusted CVS1 values (CVS1adj) were calculated as
CVS1adj = CVS1 × f
(7)
Calculation of Confidence Limits with Chi Distribution. The confidence intervals of the sampling uncertainties, the upper and lower confidence limits of CVS and CVS1adj values were calculated by applying the Chi2 distribution:
CVprim n
∑ dfi 2
where dfi is the degree of freedom for the CVAi of the ith pesticide residue−crop combination. The chopping and grinding of sample materials and their homogenization are generally carried out very carefully in the presence of dry ice, and the consequent sample processing error is usually negligible compared to CVA. The uncertainty of the analytical results varied from trial to trial; therefore, on the basis of the typical performance characteristic of analytical methods applied, we assumed an average value of 0.1 for the uncertainty of the laboratory phase (CVL) and used eq 1 to get the uncertainty of sampling (CVS1) from each calculated CVR1 value of a crop. In cases when the uncertainty of the measured residues (CVR1) was lower than the assumed CVL of 0.1, as a conservative approach, 0.1 was considered as the uncertainty of sampling. Because the sampling uncertainty was usually much larger, this assumption did not practically affect the results of our calculations. The sample sizes (number of individual crop units or sample increments) making up a composite sample) were not systematically reported by the JMPR (Table 1). The mass of the sample is often indicated instead of the number of primary samples making up a composite sample. We assumed that the protocols of pesticide manufacturers, specifying typically large samples (24 units for smalland medium-sized and 12 for large-sized crops), were generally followed, but at least the minimum sample sizes recommended by the FAO guidelines were satisfied.22 For official control, taking a minimum of 10 primary samples for small- and medium-sized and 5 for largesized crops, respectively, is recommended according to the relevant Codex standards;14 therefore, the CVS1 values calculated for each crop in supervised residue trials were adjusted with a factor of 1.55 (f = √24/√10 = √12/√5 = 1.55) based on the central limit theorem (eq 5), which is applicable for the far from normal distributions of residues in primary crop units (CVprim) according to the study of Horváth et al.23
CVn =
2 ∑ (dfi × CVS1adj, i)
CI rel, i = (6)
CVP0.975 − CVP0.025 CVi
(10)
As shown in our previous study, the calculated confidence intervals are independent from the CV value of the parent population.15 Figure 2 shows the fitted curve for the 95% relative difference of the CV values obtained from the 1000 duplicate composite samples generated from the 182 lots. The regression equation obtained was (R2 = 0.981)
The characteristic sampling uncertainty, CVS, of a crop group consisting of i crops is calculated from the pooled variances of the CVS1adj values of the crops belonging to one group, without excluding any CVS1adj,i values. For instance, for the group of small fruits (sf) D
DOI: 10.1021/jf5055112 J. Agric. Food Chem. XXXX, XXX, XXX−XXX
Article
Journal of Agricultural and Food Chemistry Table 3. Estimated CV Values of Individual Crops and Upper Confidence Limits Calculated with the New Approach crop group
crop name
ka
CVR1
CVS1
CVS1adjb
UCLc
small fruits
plum strawberry cherry
344 215 189
0.25 0.24 0.18
0.23 0.22 0.15
0.35 0.33 0.23
0.38 0.38 0.27
bush berries
blueberry cranberry raspberry blackberry
74 55 22 15
0.16 0.14 0.16 0.15
0.12 0.09 0.13 0.11
0.19 0.14 0.20 0.17
0.23 0.18 0.29 0.26
medium fruits
apple peach orange pear lemon grapefruit banana mandarin avocado nectarine Japanese apricot (pitted fruit)
636 409 328 316 195 99 47 36 10 9 8
0.17 0.24 0.18 0.18 0.19 0.23 0.21 0.27 0.35 0.15 0.13
0.14 0.22 0.15 0.14 0.16 0.20 0.18 0.25 0.34 0.11 0.08
0.22 0.34 0.23 0.22 0.25 0.31 0.28 0.39 0.52 0.17 0.13
0.24 0.37 0.26 0.25 0.29 0.37 0.35 0.51 0.85 0.29 0.22
large fruits
grape mango pineapple papaya
494 32 21 13
0.22 0.16 0.25 0.32
0.19 0.13 0.22 0.30
0.30 0.20 0.35 0.46
0.32 0.27 0.49 0.72
legume vegetables
bean bean (green) plant pea (succulent seeds) pea (edible podded) hops (fresh) bean (lima) soybean
72 40 36 18 17 15 13
0.20 0.29 0.23 0.28 0.21 0.27 0.20
0.18 0.27 0.20 0.26 0.19 0.25 0.17
0.27 0.42 0.32 0.41 0.29 0.38 0.27
0.33 0.55 0.41 0.59 0.43 0.58 0.42
medium vegetables
tomato pepper onion (green) onion (bulb)
624 503 29 44
0.25 0.26 0.25 0.30
0.23 0.23 0.23 0.28
0.36 0.36 0.35 0.44
0.38 0.39 0.48 0.56
Brassica vegetables
cabbage (head only) broccoli cauliflower Brussels sprout
398 205 73 22
0.25 0.20 0.22 0.24
0.23 0.17 0.20 0.22
0.35 0.27 0.31 0.34
0.39 0.30 0.37 0.47
cucurbits
cucumber squash melon cantaloupe eggplant (whole fruit)
111 77 74 64 11
0.24 0.29 0.25 0.27 0.09
0.21 0.27 0.23 0.25 0.10
0.33 0.42 0.35 0.39 0.15
0.39 0.51 0.42 0.48 0.25
leafy vegetables
leaf lettuce mustard green spinach sugar beet (top) radish tea (fresh) mint leaves (intended for processing) endive rape greens basil (fresh) beetroot (top)
769 345 304 261 61 52 18 16 16 12 8
0.23 0.14 0.20 0.21 0.19 0.48 0.16 0.12 0.17 0.11 0.12
0.20 0.10 0.18 0.19 0.16 0.47 0.12 0.06 0.14 0.05 0.07
0.31 0.16 0.27 0.29 0.25 0.73 0.19 0.09 0.21 0.07 0.12
0.34 0.17 0.30 0.32 0.31 0.92 0.28 0.13 0.32 0.12 0.20
E
DOI: 10.1021/jf5055112 J. Agric. Food Chem. XXXX, XXX, XXX−XXX
Article
Journal of Agricultural and Food Chemistry Table 3. continued crop group
crop name
ka
CVR1
CVS1
CVS1adjb
UCLc
root and tuber vegetables
potato sugar beet root carrot radish (root) turnip beetroot (root)
104 51 39 28 9 8
0.16 0.28 0.30 0.21 0.16 0.19
0.12 0.26 0.28 0.18 0.13 0.17
0.19 0.40 0.43 0.28 0.20 0.26
0.22 0.51 0.56 0.39 0.34 0.44
stalk and stem
celery artichoke
267 8
0.16 0.11
0.13 0.04
0.20 0.07
0.23 0.12
pulses
bean (dry) soybean (dry) pea (dry) lima bean (dry)
137 128 68 13
0.33 0.26 0.21 0.26
0.31 0.24 0.18 0.24
0.48 0.37 0.28 0.37
0.56 0.43 0.35 0.57
cereal grains
wheat (grain) rice (grain) barley (grain) paddy rice (husked grain) sorghum (grain)
86 64 63 62 27
0.21 0.13 0.16 0.15 0.15
0.19 0.09 0.13 0.12 0.11
0.29 0.14 0.20 0.18 0.17
0.35 0.17 0.25 0.23 0.23
grasses, for sugar or syrup production
sugar cane
15
0.46
0.44
0.69
1.04
tree nuts
almond pecan
60 39
0.15 0.17
0.11 0.14
0.17 0.22
0.21 0.29
oilseeds
cotton seed peanut rape (seed) cotton (undelinted seed) sunflower seed
130 52 23 21 21
0.25 0.15 0.18 0.38 0.25
0.22 0.11 0.14 0.36 0.22
0.35 0.17 0.22 0.56 0.35
0.40 0.22 0.31 0.80 0.50
seeds for beverages and sweets
coffee (dry bean)
18
0.38
0.37
0.57
0.84
legume forage and fodder
soybean (forage) alfalfa (forage) bean forage peanut fodder
184 48 31 13
0.17 0.33 0.13 0.20
0.13 0.31 0.08 0.17
0.21 0.49 0.13 0.26
0.24 0.62 0.17 0.41
straw, hay (of legume feeds
soybean (hay) peanut (hay) barley straw alfalfa (hay) pea hay bean hay
199 133 85 64 28 14
0.18 0.27 0.18 0.25 0.18 0.26
0.15 0.25 0.15 0.23 0.15 0.24
0.24 0.39 0.23 0.36 0.23 0.37
0.27 0.45 0.28 0.45 0.31 0.56
cereal forage, fodder and straw
wheat (straw) corn forage wheat (forage) maize straw barley fodder (hay and straw) sorghum (fodder) rice (straw) rice (shoot panicle) rye straw oat foliage
353 247 191 110 93 72 66 16 12 9
0.18 0.25 0.18 0.25 0.21 0.24 0.26 0.12 0.25 0.05
0.15 0.22 0.15 0.23 0.19 0.22 0.24 0.06 0.23 0.10
0.24 0.35 0.23 0.36 0.29 0.33 0.37 0.10 0.35 0.15
0.26 0.39 0.26 0.42 0.35 0.41 0.45 0.15 0.55 0.26
grass forage
Bermuda grass (forage)
8
0.09
0.10
0.15
0.27
grass hay
Bermuda grass (hay)
8
0.09
0.10
0.15
0.27
F
DOI: 10.1021/jf5055112 J. Agric. Food Chem. XXXX, XXX, XXX−XXX
Article
Journal of Agricultural and Food Chemistry Table 3. continued crop group
crop name
dried herbs
hop (cones, dried) basil (dry)
byproducts for animal feed and miscellaneous products
almond (hull) peanut hulls cotton gin trash
ka
CVR1
CVS1
CVS1adjb
UCLc
87 9
0.18 0.07
0.15 0.10
0.23 0.15
0.28 0.26
238 89 58
0.19 0.14 0.18
0.16 0.09 0.15
0.25 0.15 0.24
0.28 0.18 0.30
a k, number of replicate sample pairs used for estimation of CVR1. bCVS1adj, relative standard deviation of residues in composite samples adjusted to the minimum sample size requirements of the Codex sampling procedure. cUCL, upper 95% confidence limit of CVS1adj calculated with the new approach.
Table 4. Estimated CVS Values of Crop Groups and Confidence Limits Calculated with Different Methods calculated from chi2 distribution a
b
N
crop group
k
CVSc
4 12 4 4 4 7 4 5 11 6 2 4 6 1 2 5 1 4 6 10 2 1 2 3
small-sized fruits medium-sized fruits large-sized fruits medium-sized vegetables bush berries legume vegetables Brassica vegetables cucurbits leafy vegetables root and tuber vegetables stalk and stem vegetables pulses cereal grains grasses, for sugar or syrup production tree nuts oilseeds seeds for beverages and sweets legume forage and fodder straw, hay (of legume feeds) cereal forage, fodder, and straw grass forage grass hay dried herbs byproducts for animal feed
768 2139 560 1211 171 211 698 337 1872 256 276 346 340 15 101 247 22 288 523 1176 19 18 99 391
0.33 0.27 0.30 0.36 0.18 0.33 0.32 0.37 0.29 0.30 0.20 0.40 0.21 0.71 0.19 0.33 0.55 0.28 0.30 0.29 0.22 0.15 0.23 0.23
new approach
LCL
UCL
CI
LCL
UCLmodd
CI
0.31 0.26 0.28 0.35 0.16 0.31 0.31 0.34 0.28 0.28 0.18 0.38 0.20 0.52 0.17 0.30 0.42 0.26 0.27 0.28 0.17 0.12 0.20 0.21
0.34 0.28 0.32 0.38 0.20 0.37 0.34 0.40 0.31 0.33 0.22 0.44 0.23 1.09 0.23 0.36 0.78 0.31 0.30 0.30 0.32 0.23 0.26 0.24
0.03 0.02 0.03 0.03 0.04 0.06 0.03 0.06 0.02 0.06 0.04 0.06 0.03 0.57 0.05 0.06 0.35 0.05 0.03 0.02 0.15 0.11 0.06 0.03
0.30 0.25 0.28 0.34 0.16 0.30 0.30 0.33 0.28 0.27 0.18 0.37 0.19 0.53 0.17 0.30 0.43 0.26 0.26 0.27 0.17 0.12 0.20 0.21
0.35 0.28 0.32 0.38 0.20 0.38 0.35 0.40 0.31 0.34 0.22 0.45 0.23 1.06 0.23 0.37 0.77 0.31 0.31 0.32 0.32 0.23 0.27 0.25
0.04 0.02 0.05 0.04 0.05 0.08 0.05 0.07 0.03 0.07 0.04 0.08 0.04 0.53 0.06 0.07 0.35 0.06 0.05 0.05 0.15 0.11 0.07 0.04
a
N, number of commodities considered. bk, number of replicate sample sets used for estimation of CVS. cCVS, relative standard deviation of residues in composite samples meeting the minimum sample size requirements of the Codex sampling procedure. dUCLmod, upper 95% confidence limit of the estimated sampling uncertainty (CVS) calculated with the new approach.
CI rel, i = 2.4679k−0.439
from them. In the cases of 16 and 20 lots, when the 182 data sets of CV values were not enough to get 15 repetitions, the 16 and 20 lots were selected following a random order of the data sets.
(11)
Equation 10 was used for the estimation of the relative confidence intervals for the calculated CVS1adj and CVS values taking into account the number of trial sites (number of replicate sets, k). The absolute confidence intervals, CIna, were calculated by multiplying the relative confidence limit values with the estimated average CVS1adj and CVS values. The estimated relative confidence intervals, obtained from the modeling experiment, were somewhat larger than those calculated with eqs 8 and 9. The upper confidence limit based on modeling (UCLmod) was calculated proportionally to that obtained from Chi2 distribution to take into account that CVS-LCL < UCL-CVS due to the asymmetrical nature of Chi2 distribution. The calculation of UCL described above is called the “new approach”. To evaluate the effect of the number of lots randomly selected for estimation of the sampling uncertainty and its upper confidence limit as well as to assess the reliability of the estimated relative confidence intervals, an additional modeling has been made. From the 182 primary sample data sets, 4, 8, 16, and 20 were chosen independently 15 times, and the CVS values and their relative confidence intervals were calculated from each of the duplicate composite samples drawn
■
RESULTS AND DISCUSSION The grand average of 8.56% calculated from 6467 recovery studies (Table 2) covering the most frequently occurring residue ranges of 0.01−10 mg/kg and the five typical commodity categories recommended for performing recovery studies as part of the method validation25 can be considered as a good estimate for the expectable uncertainty of the analysis (CVA) of residues. The average CVL of 10% used for the calculation of CVS from CVR (eq 1) includes an allowance for sample processing CVSP of 5.17%, which generally covers the contribution of sample homogenization procedures applied by the specialized laboratories analyzing samples from supervised trials. The uncertainty of sampling was determined for 106 individual crops (Table 3) and 24 different crop groups G
DOI: 10.1021/jf5055112 J. Agric. Food Chem. XXXX, XXX, XXX−XXX
Article
Journal of Agricultural and Food Chemistry
approach can be seen in Figure 3. The range of the confidence intervals depends on the number of replicate sample sets, and it is increasing with decreasing number of sample sets used for calculation of CVS (Figure 3). The modeling experiments carried out for assessing the effect of data sets on the estimated sampling uncertainty and their confidence limits revealed (Figure 4) that they are robust and only minimally affected by the concentration level and distribution of residues in the lots from which the samples were taken. The relative standard deviations of the calculated confidence intervals from 15 repetitions were 4.3, 3.8, 3.9, and 5.5% in the cases of 4, 8, 16, and 20 lots, respectively, with an average value of 4.4%. This finding is in agreement with the previous experiments15 showing that the relative confidence interval is practically independent from the variability of the parent population. Taking into account the potentially serious consequences of an underestimated sampling uncertainty, as the largest contributor to the combined uncertainty, and to get reliable results when testing the compliance of a product in at least 95% of the cases, we recommend using the upper confidence limit of the estimated sampling uncertainties calculated with the new approach in practical applications. Previous studies15,26 indicated that sampling uncertainty values calculated from a minimum of eight lots can be considered as a borderline for acceptable estimate, as below that the confidence interval is getting very large. Therefore, where the number of sampled lots was
