Untransformed regression approach

Once the study is completed and the plasma or serum samples are analyzed for drug concentrations and AUC and Cmax are determined for each subject. AUC and Cmax are treated as the dependent variables (Y) in the analysis. At this point, there are a number of ways to assess for dose proportionality. The Statisticians in the Pharmaceutical Industry/Pharmacokinetics UK Joint Working Party (SPI/PUK JWP) have reviewed the statistical methods used to assess dose proportionality and have published a summary of their findings (Gough et ah, 1995). These methods will now be summarized. In the untransformed regression approach, the simple linear model is fit to the data... 

Application of a least-squares method to the linearized plots (e.g., Scatchard and Hames) is not reasonable for analysis of drug-protein binding or other similar cases (e.g., adsorption) to obtain the parameters because the experimental errors are not parallel to the y-axis. In other words, because the original data have been transformed into the linear form, the experimental errors appear on both axes (i.e., independent and dependent variables). The errors are parallel to the y-axis at low levels of saturation and to the x-axis at high levels of saturation. The use of a double reciprocal plot to determine the binding parameters is recommended because the experimental errors are parallel to the y-axis. The best approach to this type of experimental data is to carry out nonlinear regression analysis on the original equation and untransformed data. 

None of the above approaches optimizes the relationship between NIR absorbances and analyte for a range of sample types. Derivative transformations have been found to be generally useful when stepwise multiple linear regression (SMLR) techniques are used. When multidimensional statistics are employed, e.g., partial least-squares (PLS), principal component regression (PCR), or neural nets, it has been observed in some cases that the untransformed log 1/R data can perform just as well in correlation coefficient and error terms as in any kind of transformation. It is considered that in some cases physical manifestations of the sample contained in the spectra provide valid and useful discriminant data. 

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See also in sourсe #XX -- [ ]

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