P-PHARM: A Population Pharmacokinetic-Pharmacodynamic Data Modeling Software
R.Gomeni
SIMED, 9-11 rue G.Enesco 94008 Creteil, France.
P-Pharm is a computer program designed for fitting a general nonlinear regression model to data. The data analyzed is typically collected from pre-clinical and clinical studies involving the administration of a drug to individuals and the subsequent measurement of drug samples in different biological fluids.
The appropriate modeling of this data involves accounting for both unexplainable inter and intra-subject effects (random effect) as well as measured concomitant effects (fixed effects). P-Pharm has been designed to interactively allow the user to define such mixed effect modeling on Microsoft-Windows environment. This approach is particularly useful when only a few measurements are available for each individual sampled within a population. The program computes the mean population parameters values together with their variance in a population of individuals by using a Non-Linear-Mixed-Effect modeling approach.
An EM-type algorithm is used in the program: this is an iterative process suitable to compute the Maximum Likelihood estimates in complex problems of missing and incomplete data. The algorithm operates in two iterated steps:
- E: Conditional Expectation where the individual parameters in the model are estimated assuming that they have a known prior distribution (mean + error variance)
- M: Likelihood maximization where the ML posterior population mean and variance are computed
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:
- I: the EM algorithm is used without any covariable in order to estimate the individual population parameters.
- II: the possible optimal relationships between individual parameters and the available covariables are investigated by using a stepwise multiple linear regression algorithm or user-defined non-linear models.
- III: the population parameters are re-estimated taking into account the dependency of the covariables retained in the phase II.
P-Pharm includes procedures to validate the Pk-Pd model and the estimated population parameters together with a procedure to identify the outliers subjects and/or measurements.