R. Gomeni
SIMED, 9-11 rue G. Enesco 94008 Créteil Cedex
Introduction: P-Pharm is a comprehensive software package for population pharmacokinetic-pharmacodynamic data modeling. P-Pharm has been developed alongside the latest technology resulting in the present version which runs under the Microsoft-Windows environment. The program has been organized in a manner which allows the user to simultaneously open several working windows, thus permitting the experimental data to be analyzed independently using various computational options. Different methodologies and models can therefore be evaluated immediately and the optimal approach visually selected.
Data Management: The experimental data is organized using a relational database management system such as ORACLE, INGRESS, etc… The SQL retrieval language allows the user to select data from specific sub-populations of individuals in order to perform the appropriate data modeling. Finally a powerful report generator allows the user to paint sophisticated forms, which display the experimental data and/or the estimated parameters.
Population PK-PD modeling: The program computes the mean population parameter values, together with their variance, in. a population of individuals. In addition the program identifies which covariable, if any, may affect the variability on the computed population parameters. For each individual one or more drug concentration samples must be supplied together with a set of measurements of the concomitant variables (Covariates) such as: age, weight. creatinine clearance, etc. Our data modeling approach includes:
- The definition of a kinetic/dynamic model for generating predicted drug concentrations as a function of individual kinetic/dynamic parameters
- A measurement error model
- A statistical model for the estimation of the mean and magnitude of the variability of the kinetic/dynamic parameters
- A second stage regression model to relate the structural model parameters to eventual covariables
Computational algorithm: An EM-type algorithm is used in P-Pharm; this is an iterative process suitable of computing the Maximum Likelihood estimates in complex problems of missing and incomplete data. The algorithm operates in two iterated steps :
- Step E – Conditional Expectation (Bayes), where the individual parameters in the model are estimated assuming that they have a known prior distribution (mean + error variance)
- Step M – Likelihood maximization where the ML posterior population mean and variance are computed
Covariable handling: The program supplies a generalized procedure to identify and quantify the possible sources of variability in the Pk-Pd parameters using the available covariates. This procedure works in three computational phases:
- Phase I -the EM algorithm is used without any covariable in order to estimate the individual and the population parameters.
- Phase II -in this phase the relation between individual parameters and the available covariable are investigated by using:
- an appropriate data display (individual Pk-Pd parameters .vs. selected covariables) with the definition of the more appropriate model using the interactive interpreter
- multidimensional search (stepwise multiple regression) to identify the possible optimal linear relationship between the model parameters and the available covariable
- Phase III -the EM algorithm is used with the inclusion of the covariable retained in Phase II. Each covariable is entered in the analysis in sequential order and the final decision to retain covariables is taken on the basis of a chi2 test.
Models: The program includes a procedural language interpreter which can be used to interactively define mathematical equations suitable to model the experimental data and/or the relationship between kinetic parameters and covariables. In addition, a pre-defined library of the most usual models is included concerning a single or a multiple dose administration.
Reference: PAGE 2 () Abstr 902 [www.page-meeting.org/?abstract=902]
Poster: oral presentation