Analytical measurement range

Linearity refers to the relationship between measured and expected values over the analytical measurement range. Linearity may be considered in relation to actual or relative analyte concentrations. In the latter case, a dilution series of a sample may be studied. This is often carried out for immunoassays, in which case it is investigated whether the measured concentration declines as expected according to the dilution factor. Dilution is usually carried out with the appropriate sample matrix (e.g., human serum [individual or pooled serum]). 

The analytical measurement range (measuring interval, reportable range) is the analyte concentration range over which the measurements are within the declared tolerances for imprecision and bias of the method. In practice, the upper limit is often set by the linearity limit of the instrument response and the lower limit corresponds to the lower limit of quantitation (LoQ—see below). Usually, it is presumed that the specifications of the method apply throughout the analytical measurement range. However, there may 

When the true sample concentration equals LoB, 50% of the measurements exceed LoB. B, At a true sample concentration equal to LoD, (100% 3) (here 95%) of the sample measurements exceed LoB. 

In case the sample distribution is not normal, the 5 percentile of the sample distribution can be estimated non-parametrically in the same way as the LoB. However, parametric estimation is more efficient and should be used when possible. 

It is important to realize the exact meaning of the LoD. The LoD expresses a capability of the method and should not be used for direct comparison with actually measured sample values. These should be related to the LoB. 

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C, Illustrates a mixed situation with constant SD in the low range and a proportional relationship in the rest of the analytical measurement range. 

Comparison of measurements by two methods is a frequent task in the laboratory. Preferably, parallel measurements of a set of patient samples should be undertaken. To prevent artificial matrix-induced differences, fresh patient samples are the optimal material. A nearly-even distribution of values over the analytical measurement range is also preferable. In... 

Nonparametric limits may also be considered. The distribution of the differences as measured on the y-axis of the coordinate system corresponds to tlie relations outlined for the DoD plot, which represents a projection of the differences on the y-axis. A constant mean bias over the analytical measurement range changes the average concentration away from zero. The presence of random matrix-related interferences increases the width of the distribution. If the mean bias depends on the concentration or if the dispersion varies with the concentration or both, the relations become more complex, and the interval mean 2 SD of the differences may not fit very well as a 95% interval throughout the analytical measurement range. 

Figure 14-19 Outline of the relation between xl and x2 values measured by two methods subject to random errors with constant standard deviations over the analytical measurement range. A linear relationship between the target values (XI Target.. X2Targeti) Is presumed.The xlj and x2,- values are Gaussian distributed around Xi Target and X2Targeti. respectively, as schematically shown. 021 (Oyx) is demarcated.

Figure N-21 The model assumed in ordinary OLR.The x2 values are Gaussian distributed around the line with constant standard deviation over the analytical measurement range.The x values are assumed to be without random error. 021 is shown.

The estimated slope and intercept provide an estimate of the systematic difference or error between two methods over the analytical measurement range. Additionally an estimate of the random error is important. As mentioned above, it is commonplace to consider the dispersion around the line in the vertical direction, which is quantified as SD, ( (here denoted SD21). SD21 has originally been introduced in the context of OLR, but it may as well be considered in relation to Deming regression analysis. 

Figure i4-34 Top, Scatter plot showing an example of nonlinearity in the form of downward deviating x2 values at the upper part of the range. Bottom, Plot of residuals showing the effect of nonlinearity. At the upper end of the analytical measurement range, a sequence (run) of negative residuals is present from x= ISO to 200,... 

The necessary sample sizes for a series of standard method comparison situations in clinical chemistry have been tabulated (Tables 14-13 and 14-14). A Type I error (significance level) of 5% and a power of 90% have been assumed. Table 14-13 concerns the situation with constant SDs over the analytical measurement range, and Table 14-14 covers cases with proportional SDs. 

We first decide on the critical differences that should be detected For convenience, we take as a basis the GLIA 88 demand, which amounts to 0.5mmol/L throughout the analytical measurement range. Notice that CLIA 88 demands relate to the total error in relation to a target value of a quality control sample ... 

We may now consider the various factors in the estimation of sample size. The first factor to consider is the analytical measurement range 3 to 6 mmol/L (i.e., a range ratio of 2). We suppose as mentioned above that both methods have constant SDs corresponding to a CV% of 2% at the middle of the range (i.e, 0.09 mmol/L). We are now able to convert the slope delta value to a standardized value ... 

Let us now consider the conditions an analytical measurement range of 600 mg/L to 3000 mg/L (i.e.> a range ratio of 5) the midpoint of the interval (x, ) = 1800 mg/L and for both methods, proportional SDaS with CVaS = 0.03, The regression procedure is weighted Deming regression analysis with a significance level (Type I error) of 5% and a statistical power of 90%. 

The second method is an acceptable alternative. The laboratory must identify an established laboratory that is willing to share its reliable median values. Then, 25 to 50 specimens are assayed at each laboratory. These specimens are selected so that their results span the analytical measurement range. The two sets of values can then be compared using linear regression analysis (after appropriate transformations) to establish the relationship between the two assays. The regression equation can then be applied to the reliable set of median values to derive a set of medians appropriate for the laboratory. These median values can be used temporarily until values from 300 to 500 patients are available for the analysis provided earlier. 

The commercial fluorescence polarization test, TDx FLM II (Abbott Laboratories, Abbott Park, lU.), has an analytical measurement range of 0 to 160 mg surfactant/g albumin. Uncentrifuged amniotic fluid is used for this method. If... 

NBD-PC Fluorescence Polarization Method The NBD-PC method, also called FPol, is described in detail on the Evolve site that accompanies this book. The specimen is amniotic fluid that has been centrifuged at 400 Xg for 2 minutes. Results are expressed using artificial units of mil-lipolarization (P x 1000, mP). The analytical measurement range is 150 to 350 mP. No calibrators are used, but use of a Triton XlOO control assures that the temperature is correct and that the dye is not degraded. Comparison of the TDx FLM II and the NBD-PC assay reveals, as expected, a strong nonlinear, inverse correlation ... 

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