Pharmacokinetics model-independent relationships

In pharmacokinetics, mathematical approaches are used to predict or describe certain events, usually for calculating a dosing regimen or predicting the serum drug concentration after a given drug dose. The mathematical tools most often used in clinical pharmacokinetics are compartmental models and model-independent relationships. 

Model-independent relationships are firequently used in evaluation of clinical pharmacokinetics, because there are fewer relationships to remember, fewer restrictive assumptions, a more general insight into elimination mechanisms, and easier computations. However, model-independent relationships are not without their disadvantages conceptualization of compartments or physiological spaces maybe lost, specific information that may be clinically relevant or pertinent to mechanisms of distribution or efimination can be lost, and the difficulty can be increased in constructing profiles of concentration versus time. 

There are several approaches to population model development that have been discussed in the literature (7, 9, 15-17). The traditional approach has been to make scatterplots of weighted residuals versus covariates and look at trends in the plot to infer some sort of relationship. The covariates identified with the scatterplots are then tested against each of the parameters in a population model, one covariate at a time. Covariates identified are used to create a full model and the final irreducible, given the data, is obtained by backward elimination. The drawback of this approach is that it is only valid for covariates that act independently on the pharmacokinetic (PK) or pharmacokinetic/pharmacodynamic (PK/PD) parameters, and the understanding of the dimensionality of the covariate diata is not taken into account. 

In the pharmacokinetic arena, there are many cases where the independent variable is measured with error and a classical measurement model is needed. Some examples include in vitro in vivo correlations, such as the relationship between Log P and volume of distribution (Kaul and Ritschel, 1990), in vivo clearance estimates based on in vitro microsomal enzyme studies... 

---