Population pharmacokinetics estimation methods

Ette El, Williams PJ. Population pharmacokinetics II. Estimation methods. Ann Pharmacother. 2004 38(11) 1907-1915. 

All the objective functions shown in Table 15.1 are derived from a least-squares regression approach as previously described, whereas the estimation method more commonly used in population pharmacokinetics and nonlinear mixed effect modeling in general is based on a maximum likelihood (ML) approach. ML is an alternative to the least-squares objective function it seeks to maximize the likelihood or log-likelihood function (or to minimize the negative log-likelihood function). In general terms, the likelihood function is defined as... 

Sheiner LB, Beal SL. Evaluation of methods for estimating population pharmacokinetic parameters. II. Biexponential model and experimental pharmacokinetic data. / Pharmacokinet Biopharm 1981 9 635-51. 

Various methods are available to estimate population parameters, but today the nonlinear mixed effects modeling approach is the most common one employed. Population analyses have been performed for mAbs such as basiliximab, daclizu-mab and trastuzumab, as well as several others in development, including clenolixi-mab and sibrotuzumab. Population pharmacokinetic models comprise three submodels the structural the statistical and covariate submodels (Fig. 3.13). Their development and impact for mAbs will be discussed in the following section. 

Parametric population methods also obtain estimates of the standard error of the coefficients, providing consistent significance tests for all proposed models. A hierarchy of successive joint runs, improving an objective criterion, leads to a final covariate model for the pharmacokinetic parameters. The latter step reduces the unexplained interindividual randomness in the parameters, achieving an extension of the deterministic component of the pharmacokinetic model at the expense of the random effects. Recently used individual empirical Bayes estimations exhibit more success in targeting a specific individual concentration after the same dose. 

Although population pharmacokinetic parameters have been estimated either by fitting all individuals data together as if there were no kinetic differences, or by fitting each individual s data separately and then combining the individual parameter estimates, these methods have certain theoretical problems that can only be aggravated when the deficiencies of typical clinical data are present. The nonlinear mixed-effect analysis avoids many of these deficiencies and... 

Sheiner, L.B. Beal, S.L. Evaluation of methods for estimating population pharmacokinetic parameters I. michaelis-menten model routine clinical data. J. Pharmacokinet. Biopharm. 1980, 8 (6), 553-571. 

Standard Two-Stage Method. Population characteristics of each parameter are estimated as the empirical mean (arithmetic or geometric) and variance of the individual estimates pharmacokinetic parameters derived from experimental pharmacokinetic studies. ° The advantage of the STS approach is its simplicity, but the validity of its results should not be overemphasized. It has been shown from simulation studies that the STS approach tends to overestimate parameter dispersion. ... 

The definitions and statistical theory of PPK, advantages, and disadvantages of PPK have been discussed in this chapter. Models, data type, methods, and software programs for estimating population pharmacokinetic parameters, design, and analysis of population pharmacokinetic studies have been reviewed, as well as its application in biopharmaceutics. The use of population methods continues to increase while there is a shortage of those who can implement the approach. 

Furthermore, when alternative approaches are applied in computing parameter estimates, the question to be addressed here is Do these other approaches yield similar parameter and random effects estimates and conclusions An example of addressing this second point would be estimating the parameters of a population pharmacokinetic (PPK) model by the standard maximum likelihood approach and then confirming the estimates by either constructing the profile likelihood plot (i.e., mapping the objective function), using the bootstrap (4, 9) to estimate 95% confidence intervals, or the jackknife method (7, 26, 27) and bootstrap to estimate standard errors of the estimate (4, 9). When the relative standard errors are small and alternative approaches produce similar results, then we conclude the model is reliable. 

Over the past 25 years a variety of methods have been proposed for the characterization of the population pharmacokinetics of drugs. In this chapter, the statistical framework for estimating population pharmacokinetics in terms of individual and population models is discussed as a prelude to discussing some of the methods used in estimating population pharmacokinetics. In doing so we have adopted a user-friendly approach described previously (14). The goals of a PPK analysis and the data type (1) will determine the method selected for the analysis. 

---