Noncompartmental modeling analysis

E.M. Landau and J.J. DiStefano III, Multiexponential, multicompartmental and noncompartmental modeling II, Data analysis and statistical considerations, Am. J. Physiol. 246 (1984) R665-R677. 

A basic assumption related to both methods of analysis is that the elimination of drug from the body is exclusively from the sampling compartment (i. e., blood/ plasma), and that rate constants are first order. However, when some or all of the elimination occurs outside the sampling compartment - that is, in the peripheral or tissue compartment(s) - these types of analysis are prone to error in the estimation of Vss, but not CL. In compartmental modeling, the error is related to the fact that no longer do the exponents accurately reflect the inter-compartmental and elimination (micro) rate constants. This model mis specification will result in an error that is related to the relative magnitudes of the distribution rate constants and the peripheral elimination rate constant. However, less widely understood is the fact that this model mis specification will also result in errors in noncompartmental pharmacokinetic analysis. 

The noncompartmental model provides a framework to introduce and use statistical moment analysis... 

The premise of noncompartmental PK analysis is to utilize a universal approach to analyze plasma concentration data without making assumptions about a specific number of model compartments or type of absorption process. This generally involves fitting the measured plasma concentration data to an equation in the form of a sum of multiple exponential terms ... 

Jacquez, J.A. 1996. Compartmental Analysis in Biology and Medicine. 3rd ed., Biomedware, Ann Arbor, MI. Jacquez, J.A. and Simon, C.P. 1993. Qualitative theory of compartmental systems. Siam. Rev., 35 43-79. Landaw, E.M. and DiStefano III, J.J. 1984. Multiexponential, multicompartmental, and noncompartmental modeling. II. Data analysis and statistical considerations. Am. J. Physiol 246 R665-R677. 

Analysis of most (perhaps 65%) pharmacokinetic data from clinical trials starts and stops with noncompartmental analysis (NCA). NCA usually includes calculating the area under the curve (AUC) of concentration versus time, or under the first-moment curve (AUMC, from a graph of concentration multiplied by time versus time). Calculation of AUC and AUMC facilitates simple calculations for some standard pharmacokinetic parameters and collapses measurements made at several sampling times into a single number representing exposure. The approach makes few assumptions, has few parameters, and allows fairly rigorous statistical description of exposure and how it is affected by dose. An exposure response model may be created. With respect to descriptive dimensions these dose-exposure and exposure-response models... 

Two classical methods used in the analysis of pharmacokinetic data are the fitting of sums of exponential functions (2- and 3-compartment mammillary models) to plasma and/or tissue data, and less frequently, the fitting of arbitrary polynomial functions to the data (noncompartmental analysis). 

In contrast to noncompartmental analysis, in compartmental analysis a decision on the number of compartments must be made. For mAbs, the standard compartment model is illustrated in Fig. 3.11. It comprises two compartments, the central and peripheral compartment, with volumes VI and V2, respectively. Both compartments exchange antibody molecules with specific first-order rate constants. The input into (if IV infusion) and elimination from the central compartment are zero-order and first-order processes, respectively. Hence, this disposition model characterizes linear pharmacokinetics. For each compartment a differential equation describing the change in antibody amount per time can be established. For... 

Traditionally, linear pharmacokinetic analysis has used the n-compartment mammillary model to define drug disposition as a sum of exponentials, with the number of compartments being elucidated by the number of exponential terms. More recently, noncompartmental analysis has eliminated the need for defining the rate constants for these exponential terms (except for the terminal rate constant, Xz, in instances when extrapolation is necessary), allowing the determination of clearance (CL) and volume of distribution at steady-state (Vss) based on geometrically estimated Area Under the Curves (AUCs) and Area Under the Moment Curves (AUMCs). Numerous papers and texts have discussed the values and limitations of each method of analysis, with most concluding the choice of method resides in the richness of the data set. 

As mentioned above, many drugs do not conform to the simple one-compartment model. These cases may require a two- or three-compartment model characterized by a hi- or tri-exponential decline (8). Alternatively, a simpler, commonly used approach is noncompartmental analysis, in which the concentration time profile is treated descriptively by the method of... 

From previous chapters it is clear that the evaluation. of pharmacokinetic parameters is an essential part of understanding how drugs function in the body. To estimate these parameters studies are undertaken in which transient data are collected. These studies can be conducted in animals at the preclinical level, through all stages of clinical trials, and can be data rich or sparse. No matter what the situation, there must be some common means by which to communicate the results of the experiments. Pharmacokinetic parameters serve this purpose. Thus, in the field of pharmacokinetics, the definitions and formulas for the parameters must be agreed upon, and the methods used to calculate them understood. This understanding includes assumptions and domains of validity, for the utility of the parameter values depends upon them. This chapter focuses on the assumptions and domains of validity for the two commonly used methods — noncompartmental and compartmental analysis. Compartmental models have been presented in earlier chapters. This chapter expands upon this, and presents a comparison of the two methods. 

Conventional PK models, which describe a concentration-time profile at a given dose, can be applied either using noncompartmental or compartmental analysis. The most commonly used software is WinNonlin from Pharsight. 

Note that the final model was not to be further modified based on any diagnostics plots. Thus, it was comforting that Figure 16.1 suggested no specific misfits of the model. However, in general, many more diagnostic plots would be needed to assess goodness of fit of population models, if that were the primary focus. As an additional check of model performance, the model predicted AUC and C ax for the intensively sampled individuals were comparable with the noncompartmental analysis results. 

Analyze the problem. What data are available to solve the problem Given the data available can the problem be solved Has proper attention to study design and data collection been done to achieve the objective Question whether a model is even necessary. Perhaps a noncompartmental analysis of the data will suffice instead. If the goal is to model multiple-dose data from single dose data, then something simple like the superposition principle may be useful. 

One of the most common transformations is the natural logarithmic transformation of multiplicative models. Many pharmacokinetic parameters, such as area under the curve (AUC) and maximal concentration, are log-normal in distribution (Lacey et al., 1997), and hence, using the Ln-transformation results in approximate normality. The rationale is as follows (Westlake, 1988). For a drug that has linear kinetics and elimination occurs from the central compartment (the usual assumptions for a noncompartmental analysis) then... 

The relative advantages and disadvantages of linear system analysis (LSA) and noncompartmentally based pharmacokinetic (PK) modeling to other modeling... 

The two most commonly used methods for characterizing pharmacokinetic data are noncompartmental analysis and the fitting of compartmental models. The latter technique can range from simple one to three well-stirred compartments to physiologically-based pharmacokinetic (PBPK) models, which are covered in the next section. The choice of which method to utilize will be largely dictated by the goals and objectives of the analysis. For example, descriptions of major pharmacokinetic parameters for linear systems (i.e., net systemic exposure is dose-proportional) can be easily calculated from a noncompartmental... 

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