Statistical moment analysis

Fig. 39.16. Paradigm for the fitting of sums of exponentials from a compartmental model (c) to observed concentration data (o) as contrasted by the results of statistical moment analysis (s). (After Thom [13].)...

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. 

Level B utilizes the principles of statistical moment analysis. The mean in vitro dissolution time is compared to either the mean residence time or the mean in vivo dissolution time. Like correlation Level A, Level B utilizes all of the in vitro and in vivo data, but unlike Level A it is not a point-to-point correlation because it does not reflect the actual in vivo plasma level curve. It should also be kept in mind that there are a number of different in vivo curves that will produce similar mean residence time values, so a unique correlation is not guaranteed. 

In these equations kei is the elimination rate constant and AUMC is the area under the first moment curve. A treatment of the statistical moment analysis is of course beyond the scope of this chapter and those concepts may not be very intuitive, but AUMC could be thought of, in a simplified way, as a measure of the concentration-time average of the time-concentration profile and AUC as a measure of the concentration average of the profile. Their ratio would yield MRT, a measure of the time average of the profile termed in fact mean residence time. Or, in other words, the time-concentration profile can be considered a statistical distribution curve and the AUC and MRT represent the zero and first moment with the latter being calculated from the ratio of AUMC and AUC. 

Nishida, K., Tonegawa, C., Kakutani, T., Hashida, M. and Sezaki, H. (1989) Statistical moment analysis of hepatobiliary transport of phenol red in the perfused rat liver. Pharm. Res., 6,140-146. 

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

A level B correlation is based on comparisons between MDT in vitro and MDT in vivo, or MAT. MDT and MAT are average rate characteristics, which take into account all data points. They are determined by statistical moment analysis, as described in the sections In Vitro Dissolution and Bioavailability Studies for in vitro and in vivo data, respectively. 

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. 

One of the most useful properties of statistical moment analysis is that it permits estimation of the apparent volume of distribution that is independent of drug elimination (i.e. regardless of the model chosen to describe the concentration time data). 

When a drug is administered by an extravascular route, statistical moment analysis theory also can be employed for estimating the rate of absorption. This approach, however, requires the calculation of MRT for intravascular as well as extravascular routes, because the method is based on the differences in MRT for different modes of administration. In general,... 

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. 

The absorption rate constant obtained by the feathering, or residual, method could be erroneous under the conditions stated above. Should that be the case, it is advisable to employ some other methods (Wagner and Nelson method, statistical moment analysis, Loo-Rigelman method for a two-compartment model, just to mention a few) of determining the absorption rate constant. Though these methods tend to be highly... 

Xitag for statistical moment analysis, the mass of drug remaining in the intravenous infusion bag at time t... 

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