Pharmacokinetics model dependent analysis

A few programs are now available that allow the efficient simultaneous data analysis from a population of subjects. This approach has the significant advantage that the number of data points per subject can be small. However, using data from many subjects, it is possible to complete the analyses and obtain both between- and within-subject variance information. These programs include NONMEM and WinNON-MIX for parametric (model dependent) analyses and NPEM when non-parametric (model independent) analyses are required. This approach nicely complements the Bayesian approach. Once the population values for the pharmacokinetic parameters are obtained, it is possible to use the Bayesian estimation approach to obtain estimates of the individual patient s pharmacokinetics and optimize their drug therapy. 

As discussed above, all ADMET aspects are dependent on each other and should all be considered when making predictions. Integrated analysis of different aspects of drug pharmacokinetic profiles is yet another future trend. Ultimately, drug ADMET properties should be predicted based on an integration of a compilation of in silico models reflecting different aspects of the process. 

From previous chapters it is clear that the evaluation. of pharmacokinetic parameters is an essential part of understanding how drugs function in the body. To estimate these parameters studies are undertaken in which transient data are collected. These studies can be conducted in animals at the preclinical level, through all stages of clinical trials, and can be data rich or sparse. No matter what the situation, there must be some common means by which to communicate the results of the experiments. Pharmacokinetic parameters serve this purpose. Thus, in the field of pharmacokinetics, the definitions and formulas for the parameters must be agreed upon, and the methods used to calculate them understood. This understanding includes assumptions and domains of validity, for the utility of the parameter values depends upon them. This chapter focuses on the assumptions and domains of validity for the two commonly used methods — noncompartmental and compartmental analysis. Compartmental models have been presented in earlier chapters. This chapter expands upon this, and presents a comparison of the two methods. 

Logarithmically transformed, concentration-dependent pharmacokinetic parameters should be analysed using analysis of variance (ANOVA). Usually the ANOVA model includes the formulation, period, sequence or carry-over and subject factors. 

FIGURE 3.6 Compartmental analysis for different terms of volume of distribution. (Adapted from Kwon, Y., Handbook of Essential Pharmacokinetics, Pharmacodynamics and Drug Metabolism for Industrial Scientists, Kluwer Academic/Plenum Publishers, New York, 2001. With permission.) (a) Schematic diagram of two-compartment model for compound disposition. Compound is administrated and eliminated from central compartment (compartment 1) and distributes between central compartment and peripheral compartment (compartment 2). Vj and V2 are the apparent volumes of the central and peripheral compartments, respectively. kI0 is the elimination rate constant, and k12 and k21 are the intercompartmental distribution rate constants, (b) Concentration versus time profiles of plasma (—) and peripheral tissue (—) for two-compartmental disposition after IV bolus injection. C0 is the extrapolated concentration at time zero, used for estimation of V, The time of distributional equilibrium is fss. Ydss is a volume distribution value at fss only. Vj, is the volume of distribution value at and after postdistribution equilibrium, which is influenced by relative rates of distribution and elimination, (c) Time-dependent volume of distribution for the corresponding two-compart-mental disposition. Vt is the starting distribution space and has the smallest value. Volume of distribution increases to Vdss at t,s. Volume of distribution further increases with time to Vp at and after postdistribution equilibrium. Vp is influenced by relative rates of distribution and elimination and is not a pure term for volume of distribution. 

Once the study is completed and the plasma or serum samples are analyzed for drug concentrations and AUC and Cmax are determined for each subject. AUC and Cmax are treated as the dependent variables (Y) in the analysis. At this point, there are a number of ways to assess for dose proportionality. The Statisticians in the Pharmaceutical Industry/Pharmacokinetics UK Joint Working Party (SPI/PUK JWP) have reviewed the statistical methods used to assess dose proportionality and have published a summary of their findings (Gough et ah, 1995). These methods will now be summarized. In the untransformed regression approach, the simple linear model is fit to the data... 

AUC(0—oo) and Cmax are presented in Table 6.5. Two subjects did not return to the clinic and did not complete the study. Hence, these subjects had only data from Period 1. Natural-log transformed AUC(0—oo) and Cmax were used as the dependent variables. The analysis of variance consisted of sequence, treatment, and period as fixed effects. Subjects nested within sequence were treated as a random effect using a random intercept model. The model was fit using REML. Table 6.6 presents the results. The 90% Cl for the ratio of treatment means for both AUC(0—oo) and Cmax were entirely contained within the interval 80-125%. Hence, it was concluded that food had no effect on the pharmacokinetics of the drug. 

Alternatively, instead of using the EBE of the parameter of interest as the dependent variable, an estimate of the random effect (t ) can be used as the dependent variable, similar to how partial residuals are used in stepwise linear regression. Early population pharmacokinetic methodology advocated multiple linear regression using either forward, backwards, or stepwise models. A modification of this is to use multiple simple linear models, one for each covariate. For categorical covariates, analysis of variance is used instead. If the p-value for the omnibus F-test or p-value for the T-test is less than some cut-off value, usually 0.05, the covariate is moved forward for further examination. Many reports in the literature use this approach. 

---