Nonlinear regression case studies

NONLINEAR REGRESSION CASE STUDY PHARMACOKINETIC MODELING OF COCAINE AFTER INTRAVENOUS, SMOKING INHALATION ( CRACK COCAINE ), AND INTRANASAL ( SNORTING ) ADMINISTRATION... 

NONLINEAR REGRESSION CASE STUDY PHARMACOKINETIC MODELING OF A NEW CHEMICAL ENTITY... 

NONLINEAR REGRESSION CASE STUDY ASSESSING THE RELATIONSHIP BETWEEN DRUG CONCENTRATIONS AND ADVERSE EVENTS USING LOGISTIC REGRESSION... 

Martin H) has written a perceptive analysis of the possible ways in which an ionized species may behave in various models and contribute to or be responsible for a given activity. QSAR studies that have dealt with ion-pair partitioning include a study of fibrinolytics ( ) and the effect of benzoic acids on the K ion flux in mollusk neurons ( ). Schaper (10) recently reanalyzed a large number of absorption studies to include terms for the absorption of ionized species. Because specific values were not available for log Pj, he let the relation between log Pi and log P be a parameter in a nonlinear regression analysis. In most cases he used the approximation that the difference between the two values is a constant in a given series. This same assumption was made in the earlier studies (, ) Our work suggests that the pKa of an acid can influence this differential (see below). The influence of structure on the log P of protonated bases or quaternary ammonium compounds is much more complex (11,12) and points out the desirability of being able to easily measure these values. 

Figure 8 shows a plot of the concentration of methanol produced by the hydrolysis of SiQAC at pH 4.07 in water and the nonlinear regression curve of equation (18) assuming three consecutive, irreversible first-order reactions. A summary of the observed rate constants at each pH studied is shown in Table 4. Regression fits produced R2 values of better than 0.99 for all the pH values investigated. Plots of the observed values of k, k2, and k3 vs. pH are linear in all cases, with R2 values greater than 0.99, and with slopes of -0.997, -0.992 and -0.999, respectively. The ratio of kt k2 k3 is approximately 20 3 1. 

Nord and Jacobsson [97] proposed several approaches to interpret ANN models. The results were compared with those derived from a PLS regression model where the contributions of variables were studied. Notably, they employed simple architectures composed of a unique hidden layer. They discovered that the variable contribution term in ANN models is similar to that in PLS models for linear relationships, although this may not be the case for nonlinear relations. In such cases, the proposed algorithms can give additional information about the models. 

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