Evaluating measurement uncertainty for dioxins in routine analysis by the accuracy profile approach. Gauthier Eppe 1 , Bruno Boulanger 2 , Philippe Hubert 3 , Marie-Louise Scippo 4 , Guy Maghuin-Rogister 4 and Edwin De Pauw 1
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Evaluating measurement uncertainty for dioxins in routine analysis by the accuracy profile approach
Gauthier Eppe1, Bruno Boulanger2, Philippe Hubert3, Marie-Louise Scippo4, Guy Maghuin-Rogister4 and Edwin De Pauw1
1CART Mass Spectrometry Laboratory, Chemistry Department, University of Liège, Allée de la Chimie 3, B-6c Sart-Tilman, B-4000 Liège, Belgium
2Lilly Development Centre, Statistical and Mathematical Sciences, rue Granbompré, 11, B-1348 Mont-Saitn-Guibert, Belgium
3Department of Analytical Pharmaceutical Chemistry, Institute of Pharmacy, University of Liège, CHU, B36, B-4000 Liège 1, Belgium
4CART Laboratory of Analysis of Foodstuffs of Animal Origin, University of Liège, Boulevard de Colonster B-43bis Sart-Tilman, B-4000 Liège, Belgium
Ministère de la Région Wallonne
Very different approaches for evaluating measurement uncertainty (MU) are found in the literature and in dedicated guidelines[1-3]. The one published by Eurachem in 2000 was dedicated to analytical chemists and illustrated with practical examples. It defines uncertainty as ‘a parameter associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand’. The parameter can be a standard deviation or the width of a confidence interval. This confidence interval represents the interval on the measurement whithin which the true value is believe to lie at a specified probability if all relevant sources of error have been taken into account (i.e. represented by the expanded uncertainty U(x) with a coverage factor k). Within this interval, the result is regarded as being accurate, i.e. precise and true. However, one should note that MU is different from error. The error (random and systematic) is the difference between an analytical result and the true value while the uncertainty (derived from the errors) is a range and no part of the uncertainty can be corrected for.
Recently, Boulanger, Hubert and co-workers introduced a concept based on the expectation tolerance interval  and on the concept of total error called the accuracy profile [5, 6]. Basically, the idea behind this approach is that a result X which differs from the unknown true value µ of an analyzed sample is less than an acceptability limit . depends on the objectives of the analytical procedure. Initially, the accuracy profile was dedicated to the validation of an analytical method and the profile was constructed from the available estimates of the bias and precision of the method at each concentration level. This confidence interval corresponds to the expectation tolerance interval introduced by Mee . In addition, Feinberg et al demonstrated that the uncertainty as defined in the ISO/TS 21748 document  and limited to statistical estimation equals the total variance of the -expectation tolerance interval . It was then possible to use this variance as an estimate of the MU for each concentration in the accuracy profile. Thus, all these concepts are fully in agreement with the ISO definition of MU and its interval within which a result is regarded as being accurate. It is however possible to extend this concept of accuracy profile to the environment of routine analysis and quality control.
Three spiked quality control of beef fat at levels below and above the maximum levels (i.e. 3pg-TEQ/ g lipids) were selected. For each level, a series of ten replicates was performed in order to estimate the repeatability standard deviation (sW) of the method. In addition, The IQCs were afterwards implemented as statistical quality control with routine series of samples for long term intermediate method precision and bias assessment. 7 grams of fat were loaded on a Power-Prep system for clean-up. Analyses were performed by GC/HRMS
Results and Discussion
Periodically, results were added in a QC chart (MultiQC, quality control software, Metz, France) to check the stability, the trends or the drift of the method according to ISO 17025 requirements. Figure 1 illustrates the QC charts of TEQ data. The three levels were 1.69 pg-TEQ/g lipid (level 1, n=50); 5 pg-TEQ/g lipid (level 2, n=80) and 10 pg-TEQ/g lipid (level 3, n=88). Each data point represented one IQC introduced with the series of routine samples (except the ten replicates). The data recorded were spread over a period of more than 6 months. The central green line defines the mean value while the upper and lower control limits (set at m3sM) are drawn in red. The red curve with its control limits (red dashed lines) represents the Exponentially Weighted Moving Average (EWMA) with a smoothing factor of 0.2. It is a useful method for detecting small shifts or bias in the mean of a process.
Table 1 :
Table 1 summarises the relevant information from these QC charts. Among the results, it should be noted that the mean values for levels 1 and 2 show a negative relative bias of 3.2% and 3.9% respectively while the upper level demonstrates a positive bias of 8.5%. Moreover, sM increases with levels and it corresponds to intermediate precision in terms of RSDM lower than 10%.
Table 2 :
These data are subsequently used to compute the accuracy profile. For each QC level, trueness and precision are estimated to build the accuracy profile by computing equations (10), (11) and (12). It provides the lower and upper limits of the b-expectation tolerance interval (see Table 2 for relative values). Figure 2 gives an overview of the accuracy profile of the analytical method for the determination of PCDD/Fs in TEQ by GC/HRMS in beef fat. Each data point (i.e. level) corresponds to a QC chart. The grey area represents the tolerance interval within which the procedure is able to quantify with a known accuracy. The upper and lower tolerance limits are connected by straight lines between levels. They are called interpolating lines. The middle line characterizes the relative bias of the analytical procedure. The graph also indicates that the tolerance interval between level 1 and 3 is narrower than the acceptance limits set a priori at 35%.
The grey zone represents the relative expanded uncertainty of the method. It provides therefore an interesting visual tool of the MU covering the working range of the method. Calculated values of combined standard uncertainty, expanded uncertainty and relative expanded uncertainty by level are summarized in Table 5. We can conclude that the relative expanded uncertainty is quite constant across the working range and a relative U of 20% could reasonably be associated with values close to the maximum level (or the maximum residue level MRL).
Figure 2 :
The new concept of accuracy profile uses all the relevant information gathered either during a validation process or, in this paper, during an IQC process to support MU. It becomes a natural extension of the upstream validation phase or the downstream IQC process without any additional analyses or extra costs. In this context, the part played by the experimental design is of prime interest and must be underlined. The accuracy profile is a useful tool and it allows an estimation of the MU at different levels within the acceptance limits. This approach is not limited here to the MU assessment in toxic equivalents unit. It could also be applied to individual congeners if their levels in the pattern are sufficiently high to be exploited and to extract relevant information.
The main criticism of validation or of IQC approaches is that the MU assessed in toxicological units is linked to the congener profile of the material used during these steps, however the profile observed in real samples is not necessary identical, and nor is its corresponding MU. Thus, sometimes, the MU associated with a result is extrapolated.
 EURACHEM/CITAC (2000) guide: quantifying uncertainty in analytical measurement, 2nd edition.
 Hund E, Massart DL, Smeyers-Verbeke J (2001), TrAC, vol 20, 8, 394-406
 Taverniers, I, Van Bockstaele E, De Loose M (2004), TraC vol 23, 7, 490-500
 Mee RW (1984) Technometrics26(3): 251-253
 Boulanger B, Chiap P, Dewé W, Crommen J, Hubert Ph (2003) J. Pharmaceut Biomed 32: 753-765
 Hubert Ph, Nguyen-Huu J-J, Boulanger B, Chapuzet E, Chiap P, Cohen N, Compagnon P-A, Dewé W, Feinberg M, Lallier M, Laurentie M, Mercier N, Muzard G, Nivet C, Valat L (2004) J. Pharmaceut Biomed 36: 579-586
 ISO/TS 21748: 2004(E), Guidance for the use of repeatability, reproducibility and trueness estimates in measurement uncertainty estimation.
 Feinberg M, Boulanger B, Dewé W, Hubert Ph (2004) Anal. Bioanal. Chem.380: 502-514