Pharmacokinetics moment analysis

Stage 1 Pharmacokinetic (PK) data from the healthy subject studies (studies 1 and 2) were analyzed using the statistical moments analysis approach. From the results of the analysis, peak concentration (Cmax) and area under the plasma concentration curve (AUC) were selected for exploring the relationship between exposure and safety data (biomarker elevation). 

Moment analysis provides the means to determine a model independent characteristic of the absorption rate or dissolution rate (Riegelman and Collier 1980). A single value characterising the rate of the entire dissolution or absorption process is obtained, which is called the mean absorption or dissolution time (MAT and MDT, respectively). These parameters can be determined without any assumptions regarding absorption or disposition pharmacokinetics, apart from the general prerequisites of linear pharmacokinetics and absence of intraindividual variability described above. MAT/MDT can be interpreted as the most probable time for a molecule to become absorbed/dissolved, based on a normal Gaussian distribution. 

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. 

Wu, Z., Rivory, L.R, and Roberts, M.S., Physiological pharmacokinetics of solutes in perfused rat hindlimb characterisation of the physiology with changing perfusate flow, protein content and temperature using statistical moment analysis, J. Pharmacokinet. Biop-harm., 1993, 21, 653-688. 

In recent years, non-compartmental or model-independent approaches to pharmacokinetic data analysis have been increasingly utilized since this approach permits the analysis of data without the use of a specific compartment model. Consequently, sophisticated, and often complex, computational methods are not required. The statistical or non-compartmental concept was first reported by Yamaoka in a general manner and by Cutler with specific application to mean absorption time. Riegelman and Collier reviewed and clarified these concepts and applied statistical moment theory to the evaluation of in vivo absorption time. This concept has many additional significant applications in pharmacokinetic calculations. 

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... 

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. 

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. 

Moments of a function will play an essential role in estimating specific pharmacokinetic parameters. The modern use of moments in the analysis of pharmacokinetic data and the notions of noncompartmental or integral equation analysis can be traced to Yamaoka et al. (10), although these authors correctly point out that the formulas were known since the late 1930s. 

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 ... 

In many cases pharmacokinetic data (i.e. plasma drug concentration versus time data) cannot be fitted to an explicit equation equivalent to a system containing a discrete number of compartments into which dmg distributes. This data analysis requires some form of non-compartmental analysis (also referred to as model-independent analysis.) This is achieved by the use of statistical moment theory. 

This first moment (or, more strictly speaking, according to Yamaoka et al., the unnormalized first moment) is called the AUMC (area under the [first] moment curve). It is estimated by the trapezoidal approximation of the area under the curve having the product of plasma drug concentration multiplied by time on the ordinate and time on the abscissa. AUMC is rarely used per se in pharmacokinetics. However, the ratio of AUMC/AUC is widely used in non-compartmen-tal pharmacokinetic analysis. This ratio, the MRT, is described in considerable detail below. 

Finally, the successful application of congener analysis in casework requires considerable experience not only regarding laboratory analysis but also controlled drinking experiments. Studies of this kind furnish the information needed about the pharmacokinetics of specific congener, their interactions with ethanol metabolism and urine/blood relationships. Consequently, much basic research is necessary before embarking in actual casework, this expertise, at the present moment is available at only a few institutes of legal medicine on Germany. 

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