CC α and CC β estimation approaches

If an analytical method is used that demands a reliable parameter for interpre-tation of results in terms of whether the analyte is detected or not and for characterization of the method then it is recommended to use CC_α and CC_β. Here the approaches suggested in the guideline ISO 11843-2 [4] are discussed and the obtained CC_α and CC_β values are compared. The data collected for these

0 0,001 0,002 0,003 0,004 0,005 0,006 0,007

LoD (mg/kg)

Carbendazim Thiabendazole Imazalil

experiments follow the specific requirements given in that guideline. ISO 11843-2 allows calculation of CC_α and CC_β for homo- and heteroscedastic data with separate approaches and these results are compared. The approach that takes into account the heteroscedasticity of the data assumes that the standard deviation is linearly dependant on concentration. Moreover, the estimation procedure for this approach uses WLS in place of OLS [4]. As the CF uses multiple independent calibration solution preparations (in this case 2) separately (i.e. not averaged) for each calibration level then it is assumed that the same number of independent replicate sample preparations and measurements will be done for the future samples. To the authors’ knowledge these approaches are the most sophisticated approaches recommended in guidelines and take into account considerations that other LoD approaches do not (see Table 1). In addition, these approaches are quite widely used.

In comparison to these approaches the simple approaches for estimating CC_α and CCβ (group 6 in Table 1) can be recommended only when high reliability is not required, because they make similar assumptions to the LoD estimation approaches reviewed in the previous chapters. Keeping in mind that CCα and CCβ are usually used for making critical decisions, these simplified approaches are not discussed here.

The data range found in the previous chapter is used for calculations: (1) for the approach assuming homoscedasticity the homoscedastic and linear range is used, and (2) for the approach that assumes heteroscedasticity the linear range is used. Ideally in the first case the data is homoscedastic, but can in practice be somewhat heteroscedastic as some higher calibration level data must in some cases be added so that enough calibration levels could be used. Figure 10 presents the comparison of the two ISO 11843-2 approaches and the ICH approach using the Sy.x (group 4, Table 1). From paired t-test (similar to test used in chapter 4.3.2) of the results it is seen that for the given data the two approaches suggested by ISO 11843-2 do not give statistically different CCα

and CCβ (p = 0.05). The results of the t-test can be seen in Table 11. Although significantly more complex the approach that takes heteroscedasticity into account is more appropriate due to possible heteroscedasticity of the data used here. Moreover, the LoD value estimated from Sy.x is significantly different from the estimated CC_β value only for one compound. This can be due to the fact that the most important assumptions on linearity and scedasticity have been taken into account in both approaches. Therefore fairly accurate interpretation can be done with this LoD approach. However, in case reliable interpretation of results is needed the ISO 11843-2 approach is still preferable.

72 Figure 10. The ISO 11843-2 approaches to estimate CCα are compared (on the left) and the CCβ estimation approaches are compared to the approach using Sy.x (group 4, Table 1) (on the right). In both graphs the results are normalised to the propamocarb value obtained using the ISO 11843-2 approach for homoscedastic data. The LoD is estimated with the assumption of homoscedastic data with repeated measurements at each calibration level. In this graph the average LoD of the between-days results is compared to CCβ values. The error bars show the standard deviation of the mean.

0

0,005

0,010,015

0,020,025

CCα(mg/kg) CCα from homoscedastic dataCCα from heteroscedatic data

00,0050,010,0150,020,0250,030,0350,040,0450,05

CCβ(mg/kg) CCβ from homoscedastic dataCCβ from heteroscedastic data 3.3*Sy.x/b

Table 11. Three different pairs of estimates are compared to each other: (1) CCα

estimates from the two different approaches given in ISO 11843-2, (2) CCβ estimates from the two different approaches given in ISO 11843-2, and (3) the CCβ value from the ISO 11843-2 approach that uses heteroscedastic data and WLS is compared to the approach using Sy.x value (Table 1, group 4). These comparisons are numbered in the rows of the Table similarly.

The LC-MS/MS system parameters may significantly vary between days. Thus, the variability of LoD between days should be tested and between-days LoD should be used if necessary (see Chapter 2.1.5).

In order to estimate whether LoD changes significantly between days more than one estimate of LoD is necessary on each day. Therefore 4 separate CF-s were obtained with a single calibration point at each calibration level for obtaining 4 independent LoD estimates within a day.

With the data collected in the experiments, only the approaches in group 4 Table 1 that uses S_y.x or standard deviation of intercept can be used for finding several LoD estimates within one day (there are not enough data to use other approaches). Here only the approach using S_y.x was used. LoD values were calculated with the approach from 4 different calibration graphs on each 6 days (altogether 24 LoD values) for each compound. The same data was used as in chapter 4.3.1 where single measurement was made at each calibration level.

ANOVA (see general description of ANOVA in chapter 2.1.3.1) was performed on these data: the changing factor was taken to be time (meaning different days) and it was tested whether the variance of LoD results is significantly larger between days than within a day.

The results show that the between-day variance of LoD estimates is similar to within-day variance (Table 12). Therefore, from these data it cannot be said that LoD significantly differs between days. In this case it is therefore appro-priate to use the between-days LoD estimated because the LoD does not significantly differ between days and using a between-days LoD (calculated from data collected in many days) gives a more accurate representation of the methods capabilities. As discussed in chapter 2.1.5 if it would have been shown that the LoD significantly changes between days then the between-days LoD might not be best for use when interpreting result. This is so because in that case we would ignore the conditions of that specific day that significantly influences the LoD.