6.3 Avoiding/minimizing bias and correcting for bias

There is an important difference between precision and trueness. Although the repeatability and/or reproducibility standard deviation can be decreased, they cannot be fully eliminated. In contrast, elimination of bias is in principle possible, although care must be exercised. In practice, bias correction (1) is frequently done or at least attempted. In very broad terms, a distinction can be made between avoiding/minimizing bias and correcting for bias is applicable.

Minimizing (in favourable cases avoided/eliminated) bias can in the case of LC-MS methods be most effectively done via the isotope-labeled internal standard (ILIS) method. This approach means that at an as early as possible stage of the analysis, an accurately measured amount of the ILIS is added to the sample and instead of just using the analyte signal S_Analyte for the quantitation, the ratio of the analyte and the ILIS signals, S_Analyte/S_ILIS, is used. If some of the heavy atoms (i.e. not hydrogen atoms) in the ILIS are labeled (which is preferred as opposed to replacing hydrogen by deuterium) then the extraction, adsorption, etc properties of the analyte and the ILIS are almost indistinguishable. As a consequence, extraction losses, retention time, co-eluting interferents and consequently matrix effects for the ILIS will be almost indistinguishable from the analyte and will be cancelled out if the above-mentioned ratio will be used for quantification. At the same time the m/z values are different, enabling separate MS measurement of the signals S_Analyte and S_ILIS, even if their retention times are the same. For this reason, the use of ILIS is one of the most powerful approaches of assuring quality of LC-MS results. The three main drawbacks of the ILIS are (a) non-availability of ILIS-s for many analytes, (b) difficulties in dispersing the ILIS into the sample in such a way that it will be in the same molecular environment as the native analyte and (c) in most cases they are very expensive when a mixture of different analytes is considered and more than one ILIS is needed.

If ILIS is successfully used, then the remaining bias can be negligible, even though process efficiency (PE) and/or recovery (R) may be below 100% (sometimes significantly). In this case PE, R, etc. cannot be called bias constituents anymore. In this course, most of the discussion related to bias is given from a wider point of view and does not assume that ILIS has been used.

Correcting for bias. If ILIS cannot be used, then bias can be determined as explained in the previous sections and thereafter results can be corrected for bias. There can in broad terms be three cases with respect to bias correction [ref 22]: (a) correction may be required (e.g. by some regulations), in which case it has to be carried out; (b) correction may be forbidden, in which case it must not be done or (c) correction may be allowed. In the latter case, it is not easy to decide, whether or not to correctthe results, therefore a careful consideration is needed. The main reasons for this are:

• In many cases accurate determination of a systematic effect (accurate determination of bias) can involve a very large effort and because of this can be impractical. This means that the determined bias is not accurate (has high uncertainty) and does not enable reliable correction.
• In the case of correcting results with bias, the uncertainty of bias has to be included into the result’s uncertainty budget. It can happen that the uncertainty of the correction is not much smaller than the uncertainty due to possible bias.
• It is possible that the bias determined using a matrix similar (but not exactly the same) to the sample matrix will be so much different from the real bias that correction makes the result more wrong than it was before correction.

For this reason it is useful to check the following four criteria and carry out bias correction only if all of them are fulfilled [ref 21, ref 22]:

• There is evidence of a significant effect (i.e. no need to correct when bias is close to 1).
• The cause of bias can be identified (i.e. bias correction should never be used for solving problems of unknown origin).
• Bias can be reliably determined for the particular analyte-matrix combination (otherwise the result can become even more wrong!).
• Useful reduction of combined uncertainty is achieved (as compared to inclusion of the possible bias into uncertainty)

Figure 6 in ref 22 presents the decision tree regarding bias correction.

If bias is not eliminated and is not corrected for, then the uncertainty due to the possible existence of bias has to be taken into account in the uncertainty estimate of the result!

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