C HARACTERIZATION OF THE U NCERTAINTY AND B IAS OF THE M ETHODS The interpretation of the results and making correct decisions require information on

5.1.2 C HARACTERIZATION OF THE U NCERTAINTY AND B IAS OF THE M ETHODS The interpretation of the results and making correct decisions require information on

the accuracy and precision of the measurements. The measurement process is subjected to a number of influencing factors which may contribute to random, 9,10 systematic, and gross errors.

The quality control of the process aims to monitor the uncertainty (repeatability, reproducibility) and trueness of the measurement results.

* Synonymous with the term analytical quality control (AQC) and performance verification.

128 Analysis of Pesticides in Food and Environmental Samples

5.1.2.1 Uncertainty of the Measurement Results The uncertainty of the measurements is mainly due to some random effects. The

uncertainty ‘‘estimate’’ describes the range around a reported or experimental result 11 within which the true value can be expected to lie within a defined level of probability.

This is a different concept to measurement error (or accuracy of the result) which can

be defined as the difference between an individual result and the true value. It is worth noting that, while the overall random error cannot be smaller than any of its contrib- uting sources, the resultant systematic error can be zero even if each step of the determination of the residues provides biased results. Another important difference between the random and systematic errors is that once the systematic error is quanti-

fied the results measured can be corrected for the bias of the measurement, while the random error of a measurement cannot be compensated for, but its effects can be reduced by increasing the number of observations.

The combined uncertainty is calculated as 10 v u ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

u(y(x i , j, ... )) ¼ t

c i c k u(x i ,y k ) , ( 5:1)

i¼1

i ,k¼1

where u i is the standard uncertainty of the ith component

c i and c k are the sensitivity coefficients u (x i ,y k ) is the covariance between x i and y k (i 6¼ k)

The covariance can be calculated with the regression correlation coefficient r i,k : u (x i ,x k ) ¼ u(x i ) 3 u(x k )3r ik .

The uncertainty components of a residue analytical result may be grouped according to the major phases of the determination 12 (external operations: sampling (S S ), packing, shipping, and storage of samples; preparation of test portion: sample preparation and sample processing (S Sp ); analysis (S A ): extraction, cleanup, evapor- ation, derivatization, instrumental determination). The major sources of the random and systematic errors 13 are summarized in Table 5.1. Their nature and contribution to the combined uncertainty of the results will be discussed in the following sections. The general equation can be simplified for expression of the combined relative standard uncertainty (CV Res ) of the results of pesticide residue analysis.

Res ¼ CV 2 2 2 S 2 þ CV L and CV L ¼ CV Sp þ CV A , ( 5:2) where CV S is the uncertainty of sampling and CV L is the combined uncertainty of the

q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q CV ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

laboratory phase including sample processing (Sp) and analysis (A). The preparation of portion of sample to be analyzed 14 as part of the sample preparation step (such as gentle rinsing or brushing to remove adhering soil, or taking outer withered loose leaves from cabbages) cannot be usually validated and its contribution to the uncer- tainty of the results cannot be estimated. If the combined uncertainty is calculated from

Quality TABLE 5.1

Major Sources of Random and Systematic Errors in Pesticide Residue Analysis a

Assurance Sampling

Sources of Systematic Error

Sources of Random Error

Wrong sampling design or operation

Inhomogeneity of analyte in sampled object

Degradation, evaporation of analytes during preparation, Varying ambient (sample material) temperature during transport and storage transport and storage

Varying sample size

Sample The portion of sample to be analyzed (analytical sample) The analytical sample is in contact and contaminated by other portions of the sample preparation

may be incorrectly selected Rinsing, brushing is performed to various extent; stalks and stones may be

differentially removed Nonhomogeneity of the analyte in single units of the analytical sample Sample processing

Decomposition of analyte during sample processing, Nonhomogeneity of the analyte in the ground=chopped analytical sample cross-contamination of the samples

Variation of temperature during the homogenization process Texture (maturity) of plant materials affecting the efficiency

of homogenization process Varying chopping time, particle size distribution

Extraction=cleanup Incomplete recovery of analyte Variation in the composition (e.g., water, fat, and sugar content) of sample materials

taken from a commodity

Interference of coextracted materials (load of the adsorbent)

Temperature and composition of sample=solvent matrix

Quantitative Interference of coextracted compounds Variation of nominal volume of devices within the permitted tolerance intervals determination

Incorrectly stated purity of analytical standard

Precision and linearity of balances

Biased weight=volume measurements

Variable derivatization reactions

Determination of substance which does not originate Varying injection, chromatographic and detection conditions (matrix effect, system from the sample (e.g., contamination from the

inertness, detector response, signal-to-noise variation, etc.)

packing material)

Operator effects (lack of attention)

Determination of substance differing from the

Calibration

residue definition Biased calibration

129 Some processes and actions may cause both systematic and random error. They are listed where the contribution is larger.

130 Analysis of Pesticides in Food and Environmental Samples the linear combination of the variances of its components, according to the Welch –

Satterthwaite formula the degree of freedom of the estimated uncertainty is

X S i(y)

i¼1

with n P N

i¼ 1 n i . The S c ( y) ¼u c ( y) values may be replaced with S c (y) =y (CV) values where the combined uncertainty is calculated from the relative standard deviations. 11

eff

The CV L can be calculated from CV Sp and CV A obtained during the method validation, or from the results of reanalysis of replicate test portions of samples containing field-incurred residues, as part of the internal quality control. Reference materials are not suitable for this purpose as they are thoroughly homogenized. If the relative difference of the residues measured in replicate portions is R Di ¼

2(R i 1 R i 2 )=(R i 1 þR i 2 ), then CV L is

v ffiffiffiffiffiffiffiffiffiffiffiffiffi u u P n u R 2 t

where n is the number of measurement pairs, and the degree of freedom of the corresponding standard deviation is equal to n.

The analytical phase may include, for instance, the extraction, cleanup, evapor- ation, derivatization, and quantitative determination. Their contribution to the uncer- tainty of the analysis phase (CV A ) can only be conveniently determined by applying

14 C-labeled compounds, 15,16 but it is usually sufficient to estimate their combined effects by the recovery studies. The repeatability of instrumental determination,

which does not take into account the effect of preparation of calibration from different sets of standard solutions, can be easily quantified. However, the determin- ation of the total uncertainty of the predicted concentration based on the approxima-

tions described, for instance, by J.N. Miller and J.C. Miller, 9 or Meier and Zünd 17 require special software to avoid tedious manual calculations.

5.1.2.2 Systematic Error—Bias of the Measurements The systematic errors can occur in all phases of the measurement process. However,

it practically cannot be quantified during the external, field phase of the process. Once the sample is taken, the most accurate and precise determination of the system- atic error including that caused by the efficiency of extraction and dispersion of residues in the treated material can be carried out with radiolabeled compounds. Unfortunately, routine pesticide residue laboratories very rarely have access to facil- ities suitable for working with radioisotopes. Nevertheless, very useful information on stability of residues during storage, efficiency of extraction, and distribution of residues can be found in the FAO=WHO series of Pesticide Residues —Evaluations, which are published annually by FAO, and can be freely downloaded from the

Quality Assurance 131 Web site of the Pesticide Management Group. 18 Another source of information is the

data submitted to support the claim for registration of the pesticides. Though the whole package is confidential, that part relating to the analysis of residues could be made accessible for laboratories analyzing pesticide residues.

Alternately, laboratories may test the bias of their measurement results with performing recovery studies usually spiking the test portion of the homogenized sample with a known amount of the analyte (R 0 ) before the extraction. It should be born in mind that the recovery tests can provide information on the systematic error and precision of the procedure only from the point of spiking. Thus, following the usual procedure it will not indicate the loss of residues during storage and sample processing. The recovery studies are normally performed with untreated samples. Where untreated samples are not available or the final extract of blank sample gives detectable response, the analyte equivalent of the average instrument signal obtained from the unspiked sample shall be taken into account. When the average recovery is statistically significantly different from 100%, based on t-test, the results should 10,19 generally be corrected for the average recovery.

It should be noted, however, that currently some regulatory authorities require results which are not adjusted for the recovery. It may lead to a dispute situation when parties testing the same lot applying methods producing different recoveries. For instance, the shipment may be simply rejected due to the lower recoveries of analytical method used in the exporting country. Another area, where reporting the most accurate result is necessary, is providing data for the estimation of exposure to pesticide residues. In this case the residues measured should be corrected for the mean recovery, if that is significantly different from 100%. In order to avoid any ambiguity in reporting results, when a correction is necessary, the analyst should give the uncorrected as well as the corrected value, and the reason for and the method of the correction. 20

CV

Q ¼ p n ffiffi A , affects the uncertainty of q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the corrected results CV 2

The uncertainty of the mean recovery, CV

Acor ¼ CV 2 A þ CV Q . On the one hand, the increase of the uncertainty of the residue values adjusted for the recovery can be practically

Acor

1.03 CV A ). On the other hand, if corrections would be made with a single procedural recovery, the uncertainty of the corrected result would be 1.41 CV A . Therefore, such correction should be avoided as far as practical. The recovery values obtained from performance verification usually symmetric- ally fluctuate around their mean, which indicates that the measured values are subjected to random variation. If the procedural recovery performed with an analy- tical batch is within the expected range, based on the mean recovery and within- laboratory reproducibility of the method, the analyst demonstrated that the method was applied with expected performance. Therefore, the correct approach is to use the typical recovery established from the method validation and the long-term perform- ance verification (within laboratory reproducibility studies) for correction of the measured residue values, if necessary.

Under certain circumstances, such as extraction of soil samples, the extraction conditions cannot be fully reproduced from one batch of samples to the next, leading occasionally to much higher within laboratory reproducibility than repeatability

132 Analysis of Pesticides in Food and Environmental Samples (3S r <S R ). In this case, the use of concurrent recovery for adjusting the measured

residues may provide more accurate results. Where correlation between the residue values observed, the uncertainty of the residue value adjusted for the recovery should

be calculated according to Equation 5.1. Where correlation between the results is quantifiable, it may be necessary to perform at least two recovery tests in one analytical batch covering the expected residue range, and use their average value for correction to reduce the uncertainty and improve the accuracy of the results.