Mean bias

Accuracy, precision, and linearity of standards — The linear dynamic range was established as 10.22 pg/mL to 2.037 ng/mL with coefficient of determination (r2) below 0.996190 when using 1/x2 weighing for three consecutive accuracy and precision runs. The lower limit of quantitation (LLOQ) was accurate (inter-run mean bias = 1.1%) and precise (inter-run mean CV = 14.1%). Three levels of QCs were prepared. The inter-run mean bias varied from -4.3 to 1.0% and the inter-run mean CV varied from 4.6 to 6.6% for all QC levels. 

Standards performance — The assay performed well. Mean bias at LLOQ was -0.2% and for other standards varied from -1.2 to 1.0%. Coefficient of determination (r2) was greater than 0.989372 for all batches run. 

QC performance — The mean bias for three levels of QCs varied from -0.7 to 0.8%. Representative diagrams of QC performance are shown in Figure 2.6. 

Bias corrections are sometimes applied to MLEs (which often have some bias) or other estimates (as explained in the following section, [mean] bias occurs when the mean of the sampling distribution does not equal the parameter to be estimated). A simple bootstrap approach can be used to correct the bias of any estimate (Efron and Tibshirani 1993). A particularly important situation where it is not conventional to use the true MLE is in estimating the variance of a normal distribution. The conventional formula for the sample variance can be written as = SSR/(n - 1) where SSR denotes the sum of squared residuals (observed values, minus mean value) is an unbiased estimator of the variance, whether the data are from a normal distribution... 

Fig. 6 (a) Mean bias (%) of ME samples from 15 pL spotting on FTA Elute cards and partial punches, (b) Mean bias (%) of ME samples from 15 pL spotting on VWR 237 paper and partial punches, (c) Mean bias (%) of ME samples from 15 pL spotting on FTA Elute cards and full punches, (d) Mean bias (%) of ME samples from 15 pL spotting on VWR 237 paper and full punches... 

Site Method Bias. Method bias, defined as derived weekly minus measured weekly values, and relative mean bias, the bias per mean derived weekly value, were calculated for each site. The average of the collocated pair results for each daily and weekly sample was used. Figure 2 shows the distribution of the method bias for hydrogen ion and sulfate for each site. The median, mean, and... 

The Georgia site, although having the most significant bias results, has relative mean bias values under 8% for all the observ-ables except CaT for which the bias is 11.5%. For Kansas, the relative mean bias values are 10% or less, except for H+, K+ and Mg+. For Vermont, the values of the relative bias are less than 11%, except for K+. The relative weekly bias for hydrogen ion and sulfate are compared for the three sites in Figure 3. All extreme points are truncated at the 50% difference level. It is evident that most of the data lie within the 10% range. 

A one-way ANOVA detected significant differences in the mean bias for only H+ and Na+ among the sites, as indicated in Table I. 

The small differences in the weekly bias results among the three sites for all the other observables were not declared statistically significant since they are small relative to the random fluctuations in the measurements at each site. For the observables other than H " and Na+, the method bias is expected to be similar at the three sites. Except for K+, the differences between the relative mean bias for weekly and daily composited samples are generally under 12% for the major ions, NhJ, SO and NO3, the method bias is typically much smaller (<8%). 

Observable Median Bias Mean Bias Relative Bias (%)a Median Bias Mean Bias Relative Bias (% ) Median Bias Mean Bias Relative Bias (%)... 

Figure 14-7 Outline of basic error model for measurements by a field method. Upper part The distribution of repeated measurements of the same sample, representing a normal distribution around the target value (vertical line) of the sample with a dispersion corresponding to the analytical standard deviation, Oa- Middle part Schematic outline of the dispersion of target value deviations from the respective true values for a population of patient samples, A distribution of an arbitrary form is displayed.The vertical line indicates the mean of the distribution. Lower part The distance from zero to the mean of the target value deviations from the true values represents the mean bias of the method.

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... 

For example, the chromogenic creatinine method may on average determine creatinine values 15% too high, which then constitutes the mean bias. For individual samples, the particular bias may be slightly higher or lower than 15% depending on the actual chromogenic content. 

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... 

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

Thus the total error is composed of a mean bias, a random matrix-related interference component, and finally a random measurement error element. The latter component can be assessed from repeated measurements of the given sample by the method in question and can be expressed as a standard deviation (i.e., the analytical standard deviation as previously described [either within or between runs]). Estimation of the other elements requires parallel measurements between the method in question and a reference method as outlined in detail later. 

When the mean bias is considered, one should distinguish between specific (systematic) sample-related interference (e.g., the influence of hemolysis on a photometric assay) in which a clear concentration dependent effect is present and general nonspecificity of the assay. The former can be handled appropriately, either by systematic corrections or by setting limits for allowed degrees of hemolysis. ... 

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. 

Parameter estimate mean bias (%) Lower 90% Cl Upper 90% Cl... 

Method precision (random error, variation) and accuracy (systematic error, mean bias) for LBAs should be evaluated by analyzing validation samples (QC samples) that are prepared in a biological matrix that is judged scientifically to be representative of the anticipated study samples [18]. This topic has been reviewed in other publications [3 6,9,10,20]. These performance characteristics should be evaluated during the method development phase, taking into consideration the factors known to vary in the method (e.g., analysts, instruments, reagents, different days, etc.). Several concentrations are required during the method development phase and are assayed in replicates. Factors known to vary between runs (e.g., analyst, instrument, and day)... 

FIGURE 5.1 Example of measurement error profile. The central dotted line is the mean bias (trueness). The outer lines are obtained by connecting the upper and lower limits of the tolerance intervals. Open circles represent the values obtained from individual validation samples from multiple experimental runs. 

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