Statistical moment theory

It can readily be seen from this example that the contributions of the extrapolated areas to the total areas are relatively more important for the higher order moments. In this example, the contributions are 28, 61 and 72% for AUC, AUMC and AUSC, respectively. Because of this effect, the applicability of the statistical moment theory is somewhat limited by the precision with which plasma concentrations can be observed. The method also requires a careful design of the sampling process, such that both the peak and the downslope of the curve are sufficiently covered. 

The alternative to compartmental analysis is statistical moment analysis. We have already indicated that the results of this approach strongly depend on the accuracy of the measurement process, especially for the estimation of the higher order moments. In view of the limitations of both methods, compartmental and statistical, it is recommended that both approaches be applied in parallel, whenever possible. Each method may contribute information that is not provided by the other. The result of compartmental analysis may fit closely to the data using a model that is inadequate [12]. Statistical moment theory may provide a model which is closer to reality, although being less accurate. The latter point has been made in paradigmatic form by Thom [13] and is represented in Fig. 39.16. 

P.R. Mayer and R.K. Brazell, Application of statistical moment theory to pharmacokinetics. J. Clin. Pharmacology, 28 (1988) 481-483. 

Riegelman S, Collier P. The application of statistical moment theory to the evaluation of in vivo dissolution time and absorption time. J Pharmacokinet Biopharm 1980 8 509-534. 

Unfortunately, most of the correlation efforts to date with IR dosage forms have been based on the correlation Level C approach, although there also have been some efforts employing statistical moment theory (Level B). Level A correlation approach is often difficult with IR dosage forms because of the need to sample intensively in the absorptive region of the in vivo study. Thus, Levels B and C are the most practical approaches for IR dosage forms, even though they are not as information-rich and therefore more limited in their application. 

Non-compartmental analysis uses techniques derived from statistical moment theory to... 

Kakutani, T., Yamaoka, K., Hashida, M. and Sezaki, H. (1985) A new method for assessment of drug disposition in muscle application of statistical moment theory to local perfusion systems. J. Pharmacokin. Biopharm., 13, 609-631. 

An important limitation of compartment analysis is that it cannot be applied universally to any drug. A simpler approach that is useful in the case of bioequivalency testing is the model independent method. It is based on statistical-moment theory. This approach uses the mean residence time (MRT) as a measure of a statistical half-life of the drug in the body. The MRT can be calculated by dividing the area under the first-moment curve (AUMC) by the area under the plasma curve (AUC). ... 

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 ... 

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. 

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. 

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. 

---