Development of a genetic algorithm for covariate analysis in population pharmacokinetic models
Roberta Bartolucci, Gennara Masciale, Elena Maria Tosca, Paolo Magni
Laboratory of Bioinformatics, mathematical modeling and synthetic Biology, Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Via Ferrata 5, Pavia, I-27100, Italy
Objectives: During the development of pharmacokinetic/pharmacodynamic (PK/PD) models, covariate analysis is a fundamental step to identify individual characteristics impacting model parameters. Stepwise is one of the most common approaches, implemented in several software tools, such as the scm function of Perl-speaks-NONMEM (PsN)[1]. However, this method applies a local search and it is based on the assumption of independent covariate effects, which could lead to erroneous solutions. An innovative technique recognized to overcome these limitations is the genetic algorithm (GA), a machine learning method inspired by the theory of natural selection [2], for which only few examples can be found in pharmacometrics [3,4]. The aim of this work was to develop a GA for covariate research as an alternative to the stepwise. It could be added as a new function tot PsN.
Methods: The GA was developed in Perl. Starting from a given base model, the algorithm initially creates a population of several NONMEM control streams by randomly adding new covariate-parameter relations. Models are executed via the execute function of PsN and results are compared in terms of fitness, a function based on the Akaike Information Criterion. Models with higher fitness have a higher probability to be selected (selection implemented as tournament selection with elitism) and combined (single point crossover and mutation) to create a new generation of models. In this way, the GA learns which covariates have a higher impact on the model and it converges to the best solution. The search is guided by a user-defined configuration file, which contains the list of covariates, parameters and type of relations to be tested, similarly to the configuration file of PsN. For categorical covariates only the linear model is available, whilst for continuous covariates there are 4 possible relationships: linear, hockey-stick, exponential and power.
A 1-compartment model for parent (V1) and metabolite (V2), with delayed linear absorption (KA and TLAG) and linear elimination (CL1 and CL2), which included the effect of weight with power model on V1 and CL1 and of race on KA was used to simulate the PK profiles of 60 subjects (true model). In a first scenario, the GA was asked to test weight and race on all the parameters using all possible relations. In a second scenario, other covariates (age, height and BMI) were considered as confounding variables. In both cases, the search was performed using populations of 30 models for a maximum of 60 generations, with probabilities of 60% for crossover and 1% for mutation. The GA performances were compared to the scm function of PsN (in "forward", "backward and "both" directions) in terms of OFV and correctness of the final model.
Results: In the first scenario, the GA was able to detect the right covariates on the right parameters, with a final OFV of -1507.84, slightly lower than the scm final models (-1505.51), which did not identify the relation weight-CL1. Interestingly, the final model of GA was also slightly better than the true model in terms of OFV (-1506.99). For the second, more complex scenario, neither the GA nor the scm were able to select the correct model. The GA and scm in "backward" direction correctly detected all the true covariate effects, adding 6 and 4 other covariate-parameter relations, respectively. The scm in "forward" and "both" directions selected only one true covariate effect and one spurious. Again, the OFV of the GA final model (-1523.33) was better than the true model and the scm models (-1509.80 in "forward" and "both", -1519.98 in "backward").
Conclusions: A genetic algorithm for covariate analysis was developed, testing its performance on two scenarios of different complexity. The GA showed good results in terms of correctness of the selected model and in term of fitness optimization. Given the number of models that the GA was asked to run, the computational time was considered an important limitation of the current version (51 hours for the first scenario and 34 days for the second, on 1 core of an ASUS PC with intel core i5 and 8GB RAM). Therefore, a further improvement is ongoing, which consists of the parallelization of the model executions exploiting a cluster for parallel computing.
References:
[1] Lindbom, Lars, Jakob Ribbing, and E. Niclas Jonsson. "Perl-speaks-NONMEM (PsN)—a Perl module for NONMEM related programming." Computer methods and programs in biomedicine 75.2 (2004): 85-94.
[2] Rothlauf, Franz. "Representations for genetic and evolutionary algorithms." Representations for Genetic and Evolutionary Algorithms. Springer, Berlin, Heidelberg, 2006. 9-32.
[3] Bies, Robert R., et al. "A genetic algorithm-based, hybrid machine learning approach to model selection." Journal of pharmacokinetics and pharmacodynamics 33.2 (2006): 195-221.
[4] Sale, Mark, and Eric A. Sherer. "A genetic algorithm based global search strategy for population pharmacokinetic/pharmacodynamic model selection." British journal of clinical pharmacology 79.1 (2015): 28-39.