Background

Since the 90's, the importance of evaluating and optimising population designs has been highlighted. Indeed, pharmacologists and statisticians must specify a population design before running a study and performing estimation. This choice is crucial for an unbiased and efficient estimation of the parameters of the nonlinear mixed effects model used to analysed the data. Population designs consist of a set of elementary designs to be performed in group(s) of patients. Simulation studies confirmed that the balance between the number of groups, the number of subjects per group and the number and the allocation of the sampling times in each group strongly influence the precision of the parameter estimates, leading sometimes to unreliable results datasets.
The classical approach to evaluate a design was based on clinical trial simulation; however, this approach is very time consuming and does not allow testing several designs in a reasonable delay. **PFIM** was the first software tool proposed in 2001 to circumvent this problem [1-3]. PFIM is a set of R functions that evaluates and/or optimises population designs based on the expression of the Fisher information matrix (FIM) in nonlinear mixed effects models [4-9]. Now several software tools are available, and a recent comparison showed that they provide the same results when using the same approximation of the FIM [10]. This study also shows that the simpler block diagonal form is the best one when First Order approximation is used to compute the FIM, which is the default in most software [10].
Since 2008, two main versions are implemented in parallel in PFIM: a graphical user interface (GUI) package using the R software (PFIM Interface) and an R script version (PFIM).
The GUI version, **PFIM Interface 3**, implements most features of the R script version of PFIM 3 dedicated to design evaluation and optimisation for multiple response models.
A new R script version, **PFIM 4**, is now available as an extension of the version PFIM 3. This new version kept the improvements of PFIM 3 for models with inter-occasion variability (IOV) [9] and models including fixed effects for the influence of discrete covariates on the parameters [6]. Several new features for outputs of for optimization fixing some times or some parameters are added. One important new feature is Bayesian design for prediction of standard errors and shrinkage of individual parameter using Maximum A Posteriori estimation [11]. Another new feature is the ability to save the Fisher matrix and to perform design evaluation and/or optimisation given a previous FIM, obtained from fitted data or from a previous evaluated design. This feature is needed for model based adaptive design [12].
More details on additional options available in PFIM Interface 3 and PFIM 4 are given in the news section. The documentations for both these new versions are available in the relevant section and include detailed explanations and examples as to how to use these versions of PFIM.

Main references

[1] Retout S, Duffull S, Mentré F. Development and implementation of the population Fisher information matrix for evaluation of population pharmacokinetic designs, *Computer Methods and Programs in Biomedicine*, 2001, 65: 141-151.

[2] Retout S, Mentré F. Optimisation of individual and population designs using Splus, *Journal of Pharmacokinetic and Pharmacodynamics,* 2003, 30: 417-443.

[3] Bazzoli C, Retout S, Mentré F. Design evaluation and optimisation in multiple response nonlinear mixed effect models: PFIM 3.0, *Computer Methods and Programs in Biomedicine, *2010, 98 : 55-65.

[4] Mentré F, Mallet A, Baccar D. Optimal design in random-effects regression models, *Biometrika,* 1997, 84: 429-442.

[5] Retout S, Mentré F, Bruno R. Fisher information matrix for nonlinear mixed-effects models: evaluation and application for optimal design of enoxaparin population, *Statistics in Medicine,* 2002, 21: 2623-2639.

[6] Retout S, Mentré F. Further developments of the Fisher information matrix in nonlinear mixed-effects models with evaluation in population pharmacokinetics, *Journal of Biopharmaceutical Statistics,* 2003, 13: 209-227.

[7] Retout S, Comets E, Samson A, Mentré F . Design in nonlinear mixed effects models: optimization using the Fedorov-Wynn algorithm and power of the Wald test for binary covariates, *Statistics in Medicine,* 2007, 26: 5162-5179.

[8] Bazzoli C, Retout S, Mentré F. Fisher information matrix for nonlinear mixed effects multiple response models: evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model, *Statistics in Medicine, 2009, *28 :1940-1956.

[9] Nguyen TT, Bazzoli C, Mentré F. Design evaluation and optimisation in crossover pharmacokinetic studies analysed by nonlinear mixed effects models, *Statistics in Medecine*, 2012, 31: 1043-1058.

[10] Nyberg J, Bazzoli C, Ogungbenro K, Aliev A, Leonov S, Duffull S, Hooker AC, Mentré F. Methods and software tools for design evaluation for population pharmacokinetics-pharmacodynamics studies. *British Journal of Clinical Pharmacology*, 2014 Feb 18. doi: 10.1111/bcp.12352.

[11] Combes FP, Retout S, Frey N, Mentré F. Power of the likelihood ratio test and of the correlation test using empirical Bayes estimates for various shrinkages in population pharmacokinetics. *CPT: Pharmacometrics & Systems Pharmacology*, 2014, 3: e109.

[12] Mentré F, Chenel M, Comets E, Grevel J, Hooker A, Karlsson MO, Lavielle M, Gueorguieva I. Current use and developments needed for optimal design in pharmacometrics: a study performed amongst DDMoRe’s European Federation of Pharmaceutical Industries and Associations (EFPIA) members. *CPT: Pharmacometrics & Systems Pharmacology*, 2013, 2:e46.

Contact information

Pr France Mentré (Chair)

Caroline Bazzoli (active member)

Julie Bertrand

Emmanuelle Comets (active member)

Anne Dubois

Cyrielle Dumont (active member)

Hervé Le Nagard (active member)

Giulia Lestini (active member)

Thu Thuy Nguyen (active member)

Sylvie Retout

Citations

When using **PFIM** in a scientific publication, please use the following citation to reference the software:

When using **the Federov-Wynn algorythm **with **PFIM** in a scientific publication, please use the following citation to reference the algorithm:

When using **PFIM for Bayesian design of individual parameters and prediction of shrinkage** in a scientific publication, please use the following citation:

©2014 UMR 1137, INSERM & University Paris Diderot