Noncompartmental methods

Various PK parameters such as CL, Vd, F%, MRT, and T /2 can be determined using noncompartmental methods. These methods are based on the empirical determination of AUC and AUMC described above. Unlike compartmental models (see below), these calculation methods can be applied to any other models provided that the drug follows linear PK. However, a limitation of the noncompartmental method is that it cannot be used for the simulation of different plasma concentration-time profiles when there are alterations in dosing regimen or multiple dosing regimens are used. 

The notions of linearity and time invariance will be discussed in more detail later.) For a formal derivation of these equations/ the reader is referred to Weiss (11)/ Coveil ef al. (A), or Cobelli et al. (12). An understanding of the derivations is absolutely essential to understanding the domain of validity of the pharmacokinetic parameters obtained by noncompartmental methods/ no matter what method of evaluating the integrals or extrapolations is employed. 

The issue of inadequate sampling time is exemplified by monoclonal antibodies. As shown in Table 32.12/ the Vi and Vss are similar and are similar in size to a vascular space of 2-3 L/m. It is also important to note that for the most part/ in the studies submitted to support New Drug Application (NDA) approval/ Vgs was determined with methods assuming linear/ first-order kineticS/ and clearly this is not the case for the majority of the monoclonal antibodies currently marketed/ such as cetuximab (Erbitux). In fact/ the use of noncompartmental methods to describe the pharmacokinetics of mABs oversimplifies their complex properties. 

Average T1/2 based on noncompartmental methods and after subcutaneous administration [see Ref. (47)]. 

Hence, intravenous data were modeled first, followed by inhalational, then intranasal. Once the pharmacokinetics of each individual route of administration was established, all model parameters were then estimated simultaneously. Initial values for cocaine pharmacokinetics after intravenous administration were estimated using noncompartmental methods. Total systemic clearance was estimated at 100 L/h and volume of distribution at steady-state was estimated at 232 L. Central compartment clearance and intercompartmental clearance were set equal to one-half total systemic clearance (50 L/h), whereas central and peripheral compartment volumes were set equal to one-half volume of distribution (116 L). Data were weighed using a constant coefficient of variation error model based on model-predicted plasma concentrations. All models were fit using SAAM II (SAAM Institute, Seattle, WA). An Information-Theoretic approach was used for model selection, i.e., model selection was based on the AIC. 

Another internal validation technique is the posterior predictive check (PPC), which has been used in the Bayesian literature for years, but only recently reported in the PopPK literature by Yano, Beal, and Sheiner (2001). The basic idea is an extension of the predictive check method just described but include hyperparameters on the model parameters. Data are then simulated, some statistic of the data that is not based on the model is calculated, e.g., half-life or AUC by noncompartmental method, and then compared to the observed statistic obtained with real data. The underlying premise is that the simulated data should be similar to the observed data and that any discrepancies between the observed and simulated data are due to chance. With each simulation the statistic of interest is calculated and after all the simulations are complete, a p-value is determined by... 

Statistical moment analysis is a noncompartmental method, based on statistical moment theory, for calculation of the absorption, distribution, and elimination parameters of a drug. This approach to estimating pharmacokinetic parameters has gained considerable attention in recent years. 

The basis for noncompartmental methods for calculation of the parameters of each step of absorption, distribution, and elimination is the theory of statistical moments. The information required is the drug concentration in the central compartment versus time with concentrations taken past the absorptive phase and distributive phase of the curve. The area under the concentration versus time curve (AUC) is the zero moment. The first moment of the AUC is the area under the curve of the product of the concentration times time versus time... 

This method is chiefiy descriptive and requires no understanding of the underlying mechanisms. It permits quantitative characterization of the kinetics of the drug in the central compartment. The advantage is that sophisticated mathematics is unnecessary. This fact alone makes noncompartmental methods particularly useful in the clinical use of drugs. 

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). 

Typically, a PK study is composed of three phases, namely the in-life phase, bioanalysis, and data analysis. The in-life phase includes administering the compound to animals or humans and collecting samples from an appropriate matrix of interest such as blood or urine at predetermined time intervals for bioanalysis. The bioanalytical phase involves analysis of a drug and/or its metabohte(s) concentration in blood, plasma, serum, or urine. This analysis typically involves sample extraction and detection of analytes via LC-MS/MS. The third phase is data analysis using noncompartmental or compartmental PK computational methods. 

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. 

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. 

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. 

The quantitative parameters require not only a mathematical formalism but also data from which to estimate them. As noted, the two most common methods used for pharmacokinetic estimation are noncompartmental and compartmental analysis. A comparison of the two methods has been given by Gillespie (1). Comparisons regarding the two methodologies as applied to metabolic studies have been provided by DiStefano III (2) and Cobelli and Toffolo (3). Coveil et al. (4) have made an extensive theoretical comparison of the two methods. 

In comparing noncompartmental with compartmental models, it should now be clear that this is not a question of declaring one method better than the other. It is a question of (1) what information is desired from the data and (2) what is the most appropriate method to obtain this information. It is hoped that the reader of this chapter will be enabled to make an informed decision on this issue. 

In conclusion, noncompartmental models and linear, constant-coefficient models have different domains of validity. When the domains are identical, then the pharmacokinetic parameters estimated by either method should, in theory, be equal. If they are not, then differences are due to the methods used to estimate them. 

Noncompartmental analysis (NCA) is the most frequently used method and provides good information about the absorption rate. For example, the concept of partial area under the curve (AUC) has been evaluated in comparative PK studies, and these metrics had greater statistical power than the peak plasma drug concentrations (Cmax) (10). However, NCA requires more samples than are customarily available in Phase 2/3 studies. 

An early example of this methodology was presented by Burtin et al. (1996) who presented the results of a PopPK analysis from a 13 week toxicology study in male and female rats orally dosed once daily at four dose levels. Each animal provided one sample on the first day of dose administration and one sample after the last dose on Day 92 at one of five possible times (0.5-, 1-, 2-, 7-, and 24-h postdose) at the same time on each occasion. Two animals were sampled at each of the five times. They then compared the results of the PopPK analysis to a traditional noncompartmental approach. Both analysis methods came to similar conclusions, but the PopPK approach, resulted in greater mechanistic interpretations to the data. 

One must carefully interpret the volumes of distribution of peptides and proteins reported in the literature. Most studies rely on a so-called noncompartmental analysis to estimate primary pharmacokinetic parameters (see Section 3.2.3.1). However, this method is only valid for linear systems, assuming that the site of drug elimination is in rapid equilibrium with the sampling site (plasma). The former... 

Pharmacokinetic Analysis. Standard noncompartmental analyses were conducted to assess ATI and ATF pharmacokinetics using WinNonlin software (v. 2.1) (Pharsight, Mountain View, CA). The areas under the plasma concentration versus time curve from time zero to inhnity (AUCint) were determined via the log-linear trapezoidal method. The terminal half-life was determined from the relationship of ti/2 = In 2/, where k is the negative slope of the terminal phase of the InC versus time plot. Systemic clearance (CL) was estimated by dividing the administered dose by AUCint. The volume of distribution at steady state (Vss) was determined by the product of clearance and the mean residence time. 

An important finding is that if one has initial estimates of the basic parameters one can determine local identifiability numerically at the initial estimates directly without having to generate the observational parameters as explicit functions of the basic parameters. That is the approach used in the IDENT programs which use the method of least squares (Jacquez and Perry, 19W Perry, 1991). It is important to realize that the method works for linear and nonlinear systems, compartmental or noncompartmental. Furthermore, for linear systems it gives structural local identifiability. 

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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