Noncompartmental analysis

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). 

Noncompartmental analysis is limited in that it is not descriptive or predictive concentrations must be interpolated from data. The appeal of noncompartmental analysis is that the shape of the blood concentration-versus-time curve is not assumed to be represented by an exponential function and, therefore, estimates of metabolic and pharmacokinetic parameters are not biased by this assumption. In order to minimize errors in parameter estimates that are introduced by interpolation, a large number of data points that adequately define the concentration-versus-tie curve are needed. 

In pharmaceutical research and drug development, noncompartmental analysis is normally the first and standard approach used to analyze pharmacokinetic data. The aim is to characterize the disposition of the drug in each individual, based on available concentration-time data. The assessment of pharmacokinetic parameters relies on a minimum set of assumptions, namely that drug elimination occurs exclusively from the sampling compartment, and that the drug follows linear pharmacokinetics that is, drug disposition is characterized by first-order processes (see Chapter 7). Calculations of pharmacokinetic parameters with this approach are usually based on statistical moments, namely the area under the concentration-time profile (area under the zero moment curve, AUC) and the area under the first moment curve (AUMC), as well as the terminal elimination rate constant (Xz) for extrapolation of AUC and AUMC beyond the measured data. Other pharmacokinetic parameters such as half-life (t1/2), clearance (CL), and volume of distribution (V) can then be derived. 

An assumption concerning the number of compartments is, by nature, not required. For reliable results and precise parameter estimates, however, a relatively large number of data points per individual are required. Phase 1 studies of mAbs usually provide sufficient data for a noncompartmental analysis, but the assumption of linear pharmacokinetics is not valid for most mAbs. This prerequisite, however, was frequently neglected during the early years of therapeutic mAh development, and an overall estimate for CL, for example, was frequently reported in the literature. In dose-escalating studies, however, the concentration-time plots of the raw data clearly indicate that the slope of the terminal phase is not parallel for the different doses, but increases with increasing dose (Fig. 3.10). As a result, the listing of different clearance values for different doses can be found. For example, the clearance of trastuzumab was reported to be 88.3 mL/h for a 10-mg dose, 34.3 mL/h for a 50-mg dose, 25.0 mL/h for a 100-mg dose, 19.0 mL/h for a 250-mg dose, and 16.7 mL/h for a 300-mg dose. 

Despite these limitations, even today noncompartmental analysis approaches are sometimes the only way in which pharmacokinetic data of mAbs are analyzed. Especially for the mechanistic understanding of the behavior of mAbs in the body, a noncompartmental analysis cannot be recommended. 

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... 

Noncompartmental analysis to assess systemic effects in humans. The degree of systemic side effects can easily be measured for most inhalation drugs. This includes, for example, the change in plasma potassium levels [97,98] and increase in heart rate for beta-2-adrenergic drugs. Other parameters, such as lymphocyte numbers, the suppression of 24-hour urine cortisol [70,99] and 24-hour serum cortisol levels [100] (a more sensitive parameter) have been used for inhaled glucocorticoids. 

A true area under the curve (TRUE AUC) was calculated for each subject using the full concentration-time profile generated from the simulation. Sampling was performed at 0, 0.25, 0.5, 0.75,1, 2, 4, 6, 8,10,12,16, and 24 hours. All areas under the curve were calculated using the noncompartmental analysis module in WinNonlin Version 4.0, using the log/linear trapezoidal rule. 

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. 

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... 

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... 

Intravenous Drug Disposition. The estimation of primary pharmacokinetic parameters using noncompartmental analysis is based on statistical moment theory [45, 46]. The relationships dehned by this theory are valid under the assumption that the system is linear and time-invariant. For simplicity, we further assume that drug is irreversibly removed only from a single accessible pool (e.g., plasma space). Regardless of the route of administration, the temporal profile of plasma drug concentrations, Cp(t), can represent a statistical distribution curve. As such, the zeroth and first statistical moments (Mo and Mi) are defined as ... 

The noncompartmental analysis of pharmacokinetic data after extravascular drug administration, when coupled with that of IV dosing, can yield additional relevant pharmacokinetic parameters, particularly regarding absorption processes. For example, the systemic availability F), which represents the net fraction of the drug dose reaching the systemic circulation after extravascular administration, is defined as ... 

TABLE 6.5-2. Pharmacokinetic Parameters Estimated by Noncompartmental Analysis for (A) ATI and (B) ATF... 

Noncompartmental analysis of ATI plasma data indicated that ATI distributed into a steady-state volume of distribution of 110-200 mL/kg, and that ATI was cleared at a rate of 0.75-1.08mL/h/kg, with a terminal half-life of 105-154h. These values are similar to those reported by Bazin-Redureau et al. after single-dose (0.7mg/kg) i.v. administration of a monoclonal murine IgGl to rats [15]. In their study, they reported = 125 + 4.0mL/kg, systemic clearance = 0.48 0.05mL/h/ kg, and a terminal half-life = 194 + 19 h. 

Pharmacokinetic evaluation typically includes noncompartmental analysis to characterize pharmacokinetics in terms of AUC or clearance, V, and... 

The pre-exponential terms, Q, and the exponential terms, are used in the noncompartmental analysis to calculate a number of descriptive pharmacokinetic terms that describe the disposition of the drug. Each exponential term has a half-life associated with it. 

Some pharmacokinetic software packages perform noncompartmental analysis without fitting the entire response curve. These programs compute the elimination rate constant (k) for the terminal elimination phase of the data, and then use a trapezoidal rule with this elimination rate constant to compute AUC and AUMC. With these terms, the total body clearance, the steady-state volume of distribution, and the mean residence time in the body can be calculated. Without C , it is not possible to calculate the volume of distribution of the central compartment or the mean residence time of the sampling compartment. The latter term is therefore critical in accurately determining these parameter values and depends on an unbiased and close fit of the data to Equations 13.2 and 13.6. 

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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