Linear calibration curve transformed data

Figure 4.38. Validation data for a RIA kit. (a) The average calibration curve is shown with the LOD and the LOQ if possible, the nearly linear portion is used which offers high sensitivity, (b) Estimate of the attained CVs the CV for the concentrations is tendentially higher than that obtained from QC-sample triplicates because the back transformation adds noise. Compare the CV-vs.-concentration function with the data in Fig. 4.6 (c) Presents the same data as (d), but on a run-by-run basis, (d) The 16 sets of calibration data were used to estimate the concentrations ( back-calculation ) the large variability at 0.1 pg/ml is due to the assumption of LOD =0.1.

In some instances, calibration test data may need to be subjected to some kind of mathematical transformation, prior to the regression analysis, in order to obtain linear calibration plots. In some cases, however, such as in immunochemical assays, linearity cannot be demonstrated even after any transformation. The use of nonlinear calibration curves for analysis has been discussed (27). 

When an assay presents a nonlinear calibration curve (Fig. 16.4), the data can be linearized using standard functions.4 The log-logit function transforms a sigmoid curve with a single point of inflection into a straight line, and is used extensively with data from competitive immunoassays. 

Similar to conventional CE, HT-CE and HT-ME are applicable to quantitative analyses, as the calibration curve constructed from the transformed data shows good linearity even at concentrations less than the concentration limit of detection obtained using conventional CE (18, 29). HT-CE has been used in the analysis of actual samples. For instance, McReynolds et al. have successfully applied the HT-CE method with UV detection to the analysis of nitrates and nitrites in biological samples (30). We have also shown that the HT... 

Non-linear sensor responses can be modeled using linear equations with the same assumptions as the ordinary least-squares approach. Using a polynomial to fit curves is better in most cases than using transformations to linearize the data. For example, the following equation can be used to estimate a curvilinear calibration curve ... 

The analysis of the image requires the knowledge of the correspondence between composition and color (if that is not linear, a calibration curve is required). Furthermore, if diffusion has not altered the composition at the various points, then each pixel is made dark (e.g., minor component) or light (e.g., major component) based on a threshold value. The power spectrum is now calculated from the composition data and an FFT algorithm. The correlation function is then calculated by using the inverse Fourier transform of the power spectrum and the scale and intensity of segregation are then... 

When we draw a scatter plot of all X versus Y data, we see that some sort of shape can be described by the data points. From the scatter plot we can take a basic guess as to which type of curve will best describe the X—Y relationship. To aid in the decision process, it is helpful to obtain scatter plots of transformed variables. For example, if a scatter plot of log Y versus X shows a linear relationship, the equation has the form of number 6 above, while if log Y versus log X shows a linear relationship, the equation has the form of number 7. To facilitate this we frequently employ special graph paper for which one or both scales are calibrated logarithmically. These are referred to as semilog or log-log graph paper, respectively. 

Differences in calibration graph results were found in amount and amount interval estimations in the use of three common data sets of the chemical pesticide fenvalerate by the individual methods of three researchers. Differences in the methods included constant variance treatments by weighting or transforming response values. Linear single and multiple curve functions and cubic spline functions were used to fit the data. Amount differences were found between three hand plotted methods and between the hand plotted and three different statistical regression line methods. Significant differences in the calculated amount interval estimates were found with the cubic spline function due to its limited scope of inference. Smaller differences were produced by the use of local versus global variance estimators and a simple Bonferroni adjustment. 

---