**7. Accuracy**

124 Analytical Chemistry

As mentioned earlier, the precision of the method is referred to as uncertainty. The uncertainty of results is a parameter that describes a range within which the measured value is expected to lie (Miller and Miller 2000). Intuitively, we associate this parameter with precision. Therefore, method precision has been viewed as the most important performance characteristic. Typically, method precision has been assessed from replicate analyses of the same sample. The work of Hayashi and Matsuda on FUMAI theory (Hayashi, Rutan et al. 1993; Hayashi and Matsuda 1994; Hayashi and Matsuda 1994; Hayashi and Matsuda 1995; Hayashi, Matsuda et al. 2002; Hayashi, Matsuda et al. 2004) demonstrated that the precision of chromatographic methods can be predicted from noise and the height and width of the signal (peak). However, due to the complexity associated with the required Fourier transformation of chromatograms and the parameterization of the power spectrum called for in implementation of this theoretical construct to the determination of precision, the

Apostol et al. (Apostol, Kelner et al. 2012) proposed a new approach to assessing the uncertainty of purity analyses that uses a more holistic approach that is called Uncertainty Based on Current Information (UBCI). The model allows for real-time assessment of all performance characteristics using the results of the specific separation of interest. A fundamental, underlying principle of this approach recognizes that the execution of a purity method is always associated with specific circumstances; therefore, uncertainty about the generated results needs to account for both the operational conditions of the method and the hardware. The authors demonstrated that noise levels, instrument and software settings can be linked directly to all method performance characteristics. Such simplification makes it easy to implement this procedure in a daily operation, and can provide a valuable live assessment of uncertainty instead of extrapolating uncertainty from historical

The UBCI model approximates the maximal uncertainty of the measurement associated with the actual conditions of analysis (test). The obtained precision corresponds to the uncertainty under the most unfavorable conditions, including the highest variability of injection, maximal numeric integration error, expected variability of the peak width, and the most unfavorable contribution of the noise. UBCI shows that the uncertainty of results is not only a function of the method (composition of the mobile phase, gradient, flow rate, temperature), but also is influenced by the hardware associated with the execution of the method (pump pulsation, detector range, status of the lamp, etc.), and the software settings used to acquire the output in the form of chromatograms. Information about these parameters can be extracted from individual chromatograms; therefore, the assessment of method performance characteristics (uncertainty) can be performed realtime, which can be considered as a 'live validation' associated with each individual test

It is important to note that historical qualification/validation approaches do not take this fundamental principle into account, such that performance drift may occur over time due to hardware differences and even due to differences in analyst skill levels, such that the

FUMAI theory approach has not been widely applied.

qualification/validation studies.

result.

The determination of accuracy for protein purity methods presents significant challenges. Since it is difficult to establish orthogonal methods for proteins to measure the same quality attribute, it is hard to assess the truthfulness of the accuracy measurements. For example, although SEC-HPLC results can be verified by analytical ultra centrifugation (AUC) techniques, these techniques are based on very different first principles, and may not provide comparable results (Carpenter, Randolph et al. 2010; Svitel, Gabrielson et al. 2011). Therefore, in most cases, the accuracy of purity methods for proteins is inferred when other performance characteristics meet expectations, which is consistent with the principles of ICH Q2R1(ICH 2005).
