Population PK/PD analysis

The non-linear mixed effects model is the most widely used method and has proven to be very useful for continuous measures of drug effect, categorical response data, and survival-type data. The nonlinear mixed-effects modeling software (NONMEM) introduced by Sheiner and Beal is one of the most commonly used programs for population analysis. A detailed review of software for performing population PK/PD analysis is available. ... 

The graphs and examples are geared toward NONMEM simply because NONMEM is the most widely used computer program for population PK/PD analysis. The principles, on the other hand, are quite general and should be easily adoptable for use with other software employing the same methodological strategy as NONMEM does. 

Exploratory data analysis in the field of population PK/PD analysis has received considerable attention in the literature over the years and the basic graphical tools for this exercise (e.g., histograms, scatterplot matrices, and QQ plots) have been described elsewhere (5-9) and will therefore not be detailed here. 

Categorical data is becoming increasingly common in population PK/PD analysis, especially ordered categorical data. Examples of such data are adverse events and efficacy measurements such as pain scales (16) or sedation scores (17). This section focuses on graphical methods for categorical type data. 

The population PK/PD analysis, rather than individual PK/PD analysis, allows for rehable data analysis following sparse sampling, correctly accounts for sources of variabihty, allows for pooling of data across individuals and studies, and provides for an integrated model for PK/PD data (even across species). However, data analysis should be driven by the question of interest, rather than the method of analysis. It is not always necessary to use complicated methods of analysis. Sometimes a simpler individual PK/PD model approach can be used if the PK/PD data collected are relatively rich in a quite homogeneous population (especially in Phases 1 and Ha settings). 

Piotrovsky, V. Drug efficacy analysis as an exercise in dynamic (indirect-response) population PK-PD modelling. Population Approach Group... 

Objective The objective of this analysis was to develop a population PK/PD model based on the data after intravenous administration that allows to explore in silico which absorption characteristics would be required for other administration routes and/or which receptor binding properties are crucial for backup compounds. 

The Trial Simulator (Pharsight Corp., http //www.pharsight.com) is a comprehensive and powerful tool for the simulation of clinical trials. Population PK/PD models developed with tools mentioned in Section 17.10.3 can be implemented in a Trial Simulator. In addition, treatment protocols, inclusion criteria, and observations can be specified. Also covariate distribution models, compliance models, and drop-out models can be specified. All of these models can be implemented via a graphical user interface. For the analysis of simulation results a special version of S-Plus is implemented and results can also be exported in different formats, like SAS. 

Lunn, D.J. Best, N. Thomas, A. Wakefield, L Spiegelhalter, D. Bayesian analysis of population PK/ PD models general concepts and software. J. Pharmaco-kinet. Pharmacodyn. 2002, 29 (3), 271-307. 

L. Zhang, S. L. Beal, and L. B. Sheiner, Simultaneous vs. sequential analysis for population PK/PD data I best-case performance. J Pharmacokinet Pharmacodyn 30 387-404 (2003). 

One criticism against the use of informative priors is their subjective nature, which may be perceived to introduce bias into the upcoming analysis. The choice of priors and assigning an appropriate level of informativeness is therefore of considerable importance. For population PK/PD studies, there may well be explicit, quantitative data that describes the parameter values in populations that are similar to the population in the current study. In this case it is possible to pool the available information in a meta-analytic technique to provide an appropriate level of prior information. Some care must be taken to assess for heterogeneity between studies and for applicability of studies to the current population under consideration. A brief summary of an approach is shown below. It would be impossible to include an exhaustive treatment of elicitation processes within the confines of this chapter. 

D. J. Lunn, N. Best, A. Thomas, J. Wakefield, and D. Spiegelhalter, Bayesian analysis of population PK/PD models general concepts and software. I Pharmacokinet Pharmacodyn 29 271-307 (2002). 

Population PK/PD data is multidimensional. In an analysis of PK data, the most obvious predictor we have is time. In an analysis of PD data, we have time and drug exposure as the fundamental independent variables. What should not be forgotten, however, is that there may be other potential predictors that can explain the observed variability (e.g., body weight, sex, age, and other covariates), some of which also vary with time. Again, we must use graphical methods that can accommodate this situation. 

Incorporating covariates in a population PK/PD model is often an important part of the model building process and is often also an overall aim of the analysis. 

Graphs are useful in all phases of population PK/PD modeling. Before the analysis, the importance lies in data set checkout as well as exploratory analysis. During the analysis, graphical analysis is the mainstay in model diagnostics and guides model development. After the analysis, when the results need to be communicated, graphics can be used to transparently convey quite involved information. 

TIMING AND EFFICIENCY IN POPULATION PK/PD DATA ANALYSIS PROJECTS... 

A population PK and PK/PD analysis was performed to develop a model for the time course of theophyUine concentrations and for the time course and exposure-response of apneic episodes to treatment with theophylline (3). Results of the population pharmacokinetics of theophylline will not be presented. 

Utilization of the Poisson and ZIP in population PK/PD modeling requires coding the appropriate distribution into the software selected for analysis. Example code will be given as appropriate for NONMEM implementation however, the fundamentals are applicable to other software programs. 

This chapter endeavors to show that a population PK/PD approach to the analysis of count data can be a valuable addition to the pharmacometrician s toolkit. Nonlinear mixed effects modeling does not need to be relegated to the analysis of continuously valued variables only. The opportunity to integrate disease progression, subject level covariates, and exposure-response models in the analysis of count data provides an important foundation for understanding and quantifying drug effect. Such parametric models are invaluable as input into clinical trial and development path simulation projects. 

Gibiansky, L., Gibiansky, E., Yu, R.Z., and Geary, R.S. ISIS 2302 Validation of the population pharmacokinetic model and PK/PD analysis. Presented at American Association of Pharmaceutical Scientists Annual Meeting, Boston MA, 2001. 

The NONMEM package continues to be the most widely used software for population-based PK/PD analysis. Its limitations lie mostly with its user interface, which, despite the numerous modifications to the code including the NM-TRAN preprocessor, remains a warehouse of FORTRAN 77 subroutines. Several alternatives to NONMEM are currently available and others are still under development. It is beyond the scope of this chapter to compare the details of the software itself, nor is it practical given short lifetime of each release. Aarons - has recently reviewed and critiqued the currently available software for population pharmacokinetic analysis. 

Tables 15.5 and 15.6 provide an updated summary of the currently available software for population-based PK/PD analysis. Most of the software listed in Tables 15.5 and 15.6 can be installed and run from a variety of platforms. All can be run from a PCAVindows environment, although some require other programs to operate (i.e., FORTRAN or Visual Basic compiler, SAS, SPLITS, etc.). The most current information can be obtained directly from the manufacturer or parties responsible for code distribution. In any event, software development of population-based PK/PD algorithms appears to be very active relative to the previous 20h- years and the available tools will, hopefully, be superior and more user-friendly than the original NONMEM source code.

Lunn, D.J., Best, N., Thomas, A., Wakefield, J., and SpiegeUialter, D. 2002. Bayesian analysis of population PK/PD models general concepts and software. /. Pharmacokinet. Pharmacodynam. 29 271-307. Magni, R, BeUazzi, R., Nauti, A., Patrini, C., and Rindi, G. 2001. Compartmental model identification based on an empirical Bayesian approach the case of thiamine kinetics in rats. Med. Biol Eng. Comput. 39 700-706. 

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