Fitting Considerations for Nonlinear Pharmacometrics
M. Katzper, CDER, FDA, Rockville, MD 20857
When rich data sets are available for pharmacokinetic data, the standard two-stage approach is used to estimate population characteristics. This involves fitting of individual data followed by averaging over the parameters of all the individuals. The reason given for not using a one-stage naïve pooled data approach is that grouping and fitting the averaged data does not distinguishing the variability within and between individuals. Using scenarios without any intra-individual variability it can be demonstrated that the one-stage pooled data approach, when used for non-linear models, is inherently flawed in defining a population average irrespective of variability. An example is constructed using exponential decay for a number of individuals with differing clearances and perfect data with no variability. Such a group has a clearly defined parametric average. A transformed linearized fit can be used to calculate the average, which coincides with the parametric average. A non-linear least-squares fit of the untransformed data does not yield the parametric average.