Objectives: A new method for population PK/PD, based on statistical theory, has been developed and implemented in two different programs (PDx-MC-PEM and S-ADAPT).  It is based on the exact EM algorithm combined with important sampling. It accurately evaluates point estimates of population parameters from pharmacokinetic (PK)/Pharmacodynamic (PD) data without linearizing the expectation step. We call this algorithm the Monte Carlo Parametric Expectation Maximization (MC-PEM) method. 

Method: In our implementation of this method, the PK/PD parameters are modeled to be multivariate normally or log-normally distributed among subjects, and observed data are modeled to have measurement error that is normally or log-normally distributed about the predicted value for each subject, similar to the manner in which NONMEM models population data.  In addition, population parameters may be modeled to subject characteristics (covariates), and intra-subject error coefficients may also be determined.  

Results: The MC-PEM method was first tested on simulated sparse data (one datum per subject) generated from a simple one-compartment model and was found to accurately estimate the population parameter estimates in all cases.  The MC-PEM method was also tested on simulated data generated from a two compartment PK/sigmoidal Emax PD model with a total of 8 PK/PD population parameters and 36 inter-subject variance-covariance parameters.  The MC-PEM method yielded population parameters and variance-covariance parameters that were similar to the simulated values. MCPEM performance was compared to NONMEM (FOCE with interaction). MCPEM was more stable, less sensitive to initial estimates and with equal accuracy and precision, at least for all successful NONMEM runs. Since then, the MC-PEM method has been successfully used to analyze very complex PK/PD/efficacy models containing up to six differential equations and 16 parameters.

The implementation of the MCPEM methodology into a PK/PD environment resulted in the generation of two programs, the PDx-MC-PEM and S-ADAPT programs. PDx-MC-PEM is a population PK/PD fitting and simulation program. Serge Guzy, President POP-PHARM developed the engine part of the program while Globomax developed the corresponding interface. It is characterized by a user-friendly interface and a large built-in PK/PD library. The library contains 1,2,3 compartment models, linear, non linear and parallel linear-non linear kinetics, multiple dosage regimen capability, IV infusion, oral and IV Bolus route of administration. All the models can be combined with a large series of PD models. All PK models can also be linked to an effect compartment and then to one of the PD models. Indirect response models, disease progression models and Dose response models are also available. The user does not have to code anything, does not need any programming skills but only understanding of basic pharmacokinetics as well as basic understanding of the algorithm. A second program S-ADAPT (scriptable ADAPT) has been developed by Bob Bauer and allows the user to build his own model. This powerful program requires basic knowledge in FORTRAN and general programming skills.  The program is very flexible with respect to the structural model, the covariate model, the intra-individual error structure and the type of PK/PD parameter distributions.  In addition, the program allows one to perform model and statistically based simulations, non compartmental analysis, evaluation of PK/PD parameter standard errors and post-hoc analysis.  The S-ADAPT program can be completely controlled by a run-time scripting language, and interactive and batch analysis can be performed with continuity. Both programs have been extensively tested and validated and are available.

Conclusion: The MCPEM methodolody appears to be extremely robust, not sensitive to initial estimates. Due to its robustness, covariance components are never  forced to be zero as it often occurs in NONMEM even though some covariance could be no identifiable. Stochastic  concepts to analyze Population PK/PD data appear to be not only valid but also, in many instances, superior to deterministic algorithms.