Mohamed Ismail (1), Mark Sale (2), Robert Bies (1)
(1) University at Buffalo, Buffalo, NY, USA; (2) Nuventra Pharma Sciences, Durham, NC, USA
Objectives:
The current approach to population PKPD model selection is formally known as downhill search and is a local search method. Out of necessity, the approach greatly reduces the sample space of possible models by proceeding in a stepwise manner, first finding the best structural model, then searching for significant covariate relationships and statistical models. Not only is the approach inefficient, it is also not guaranteed to find the optimal solution due to interaction between model components [1]. Further, this method involves many repetitive (i.e. testing various covariate forms) and predictable processes that lend themselves to automation.
Genetic algorithms (GA) are a class of global search methods inspired by the mathematics of evolution. They can be used to find global optimal solutions for difficult problems even in the presence of non-differentiable functions, as is the case in the discrete nature of including/excluding model components in search of the best performing mixed-effects PKPD model [2, 3].
The objectives of this work were to harness the capabilities of GA for automated PKPD modeling, and create an open source software application to implement these algorithms for widespread use and continued community development.
Methods:
Software
The program is built in R [4], and includes a Shiny GUI. It has been integrated with PsN and xpose4.
The Control Stream Template
To implement the GA, the construction of the NMTRAN control stream is altered slightly to allow for programmatic editing of the text. A control stream template resembles a typical NMTRAN control stream but includes model placeholders. The placeholders are then replaced by the program to construct syntactically correct control streams.
The Chromosome
A model is represented by a “chromosome”, which is made up of a collection of model characteristics, or genes.
Fitness
The fitness of a model is determined by the value of the objective function with penalty terms.
Fitness= -2LL+5×NParam+10×UnsuccessfulCovariance+20×UnsuccessfulMinimization
In this context, a smaller value indicates a more fit model.
Initializing the GA
The GA begins with randomly selecting an initial population of models. The models are run in parallel by calling PsN’s execute. Upon completion, the program calculates the fitness of each model and continues to the selection phase to determine the next generation of models.
Selection
Tournament selection was implemented. It is a ranked selection method and is ideal in instances when fitness values are close in magnitude.
More fit models have a higher likelihood to proceed to be “parents” in the next generation, and can be included more than once.
Crossover
The crossover genetic operator mimics biological reproduction, swapping genes of parent models to produce new, potentially more fit models. To implement crossover, the algorithm randomly selects two points along the parent chromosomes, and swaps all genes between those points.
Number of compartments, Age on CL, Weight on V, SexM on CL, Absorption, Residual error
1, None, Linear, Additive shift, First-order, Proportional
2, Linear, Power, None, Zero-order, Proportional
^ ^
^ = Crossover points
Children models:
1, None, Power, None, First-order, Proportional
2, Linear, Linear, Additive shift, Zero-order, Proportional
Mutation
The mutation operator is implemented on the child models produced by crossover. Each gene of each model has a small probability to be mutated. Mutation randomly changes the phenotype of a gene. Mutation promotes diversity in models and introduces new genetic material.
Results:
The application performs automated model selection of the globally optimal population PKPD model. It not only returns a single best model, but ranks all models that were run in a tabular interface, allowing the modeler to select from among the best models based on diagnostic plots or other criteria.
In addition to the GA implementation, the application serves as a convenient workbench for NONMEM. Features include
• Organizes and displays models in tabular format, allowing the user to sort, filter, edit, create, and delete models
• Displays run results and parameter estimates
• Integrated with xpose4 and PsN to create diagnostic plots and run PsN scripts
Conclusions:
An automated solution for population PK/PD modeling will allow modelers to focus on hypothesis generation and model evaluation rather than text processing and model execution.
References:
[1] Wade, J.R., Beal, S.L. & Sambol, N.C. Journal of Pharmacokinetics and Biopharmaceutics (1994) 22: 165. https://doi.org/10.1007/BF02353542
[2] Bies, R.R., Muldoon, M.F., Pollock, B.G. et al. J Pharmacokinet Pharmacodyn (2006) 33: 195. https://doi.org/10.1007/s10928-006-9004-6
[3] Sale M, Sherer EA. A genetic algorithm based global search strategy for population pharmacokinetic/pharmacodynamic model selection. British Journal of Clinical Pharmacology. 2015;79(1):28-39. doi:10.1111/bcp.12179.
[4] R Core Team (2017). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
Reference: PAGE 27 (2018) Abstr 8526 [www.page-meeting.org/?abstract=8526]
Poster: Methodology - New Modelling Approaches