Random bias

The study of the precision of a method is often the most time and resource consuming part of a method validation program, particularly for methods that are developed for multiple users. The precision is a measure of the random bias of the method. It has contributions fi om the repeatability of various steps in the analytical method, such as sample preparation and sample injection for HPLC [5-9], and from reproducibility of the whole analytical method fiom analyst to analyst, fiom instrument to instrument and fiom laboratory to laboratory. As a reproducibility study requires a large commitment of time and resources it is reasonable to ensure the overall ruggedness of the method before it is embarked upon. 

Because the amounts of co-determined substances may vary from sample to sample, the bias is likely to differ somewhat from sample to sample. For a representative set of patient samples, we may describe the biases associated with the individual samples by the central tendency (mean or median) and the dispersion (Figure 14-7). Thus the bias may be split into an average amount the mean bias, and a random part, random bias. For an individual sample, we have... 

Taking mean bias and random bias into account, we obtain the following expression for an individual measurement of a given sample by a field method... 

Xj - Targett F Gj — Truei F A4ean-Bias F Random-Bias/ F g,-... 

Total error ofx,- = Mean-Bias + Random-Bias,- F Gj... 

The random error components may be expressed as SDs, and generally we can assume that random bias and analytical components are independent for each analyte yielding the relations... 

The random bias components for method 1 and 2 may not necessarily be independent. They may also not be normally distributed, which is less likely as regards the analytical components. Thus when applying a regression procedure, the explicit assumptions to take into account should be considered. In situations without random bias components of any significance, the relationships simplify to... 

Another methodological problem concerns the question whether the dispersion of the random error components is constant or changes with the analyte concentration as considered previously in the difference plot sections. For most clinical chemical compounds, the analytical SDs vary with the measured concentration, and this relationship may also apply to the random-bias components. In cases with a considerable range (i.e., a decade or more), this phenomenon should also be taken into account when applying a regression analysis. Figure 14-20 schematically shows how the dispersions may increase proportionally with concentration. 

Figure 14-25 Simulated examples that illustrate the effect of sample-related random interferences in a scatter plot with regression analysis. A, xl and x2 are subject to only analytical errors. B, Additional random bias of the same magnitude is present, which results in a wider scatter around the line.

As mentioned earlier, the matrix-related random interferences may not be independent. In this case, simple addition of the components is not correct, because a covariance term should be included. However, we can estimate the combined effect corresponding to the bracket term, which then strictly refers to the CV of the differences (CV b2-rb])- As in the case with constant standard deviations, information on the analytical components is usually available, either from duplicate sets of measurements or from quality control data, and the combined random bias term in the second bracket can then be derived by subtracting the analytical component from CV21. Systematic and random errors can then be determined, and it can be decided whether a new field method can replace an existing one. Figure 14-31 shows an example with proportional random errors around the regression line. 

We consider here decision levels of 3 and 6mmol/L and suppose in the present example that the SDa is 0.09mmol/L, which corresponds to a CVa of 2% at the mean (4.5 mmol/L) of the considered range. In the present example we set the random bias component to zero. Thus the systematic difference that should be detected is ... 

When comparing the two approaches briefly outlined, the latter is the more informative. Using a series of patient samples instead of a pooled sample, individual random bias components are included in the uncertainty estimation, assuming the patient samples are representative. Also, natural patient samples are preferable to a stabilized pool that perhaps is distributed in freeze-dried form that may introduce artifactual errors in some analytical systems. Using a CRM, on the other hand, is more practical and in many situations the only realistic alternative. 

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