Davide Ronchi(1), Elena Maria Tosca(1), Isaia Ravasi(1), Roberta Bartolucci(1), Paolo Magni(1)
1) Laboratory of Bioinformatics, Mathematical modelling, and Synthetic Biology, Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Via Ferrata 5, Pavia, I-27100, Italy
Objectives:
Covariate identification is an important step in the development of a pharmacokinetic/pharmacodynamic (PK/PD) population model [1]. Among the different approaches available for covariate selections, stepwise (SCM) is the most used. However, scm is based on a local search and on the assumption of independent covariate effects [2]. Moreover, it is manly designed to test a few covariate-parameter relationships, often chosen ad hoc or based on prior knowledge [3].
The application of genetic algorithm (GA) for selecting covariate overcoming these limitations has recently raised interest [4,5]. However, the extremely high computational costs and its convergence in dependence from the population size limit its actual use during the model building process.
Here, our previously developed GA [6] has been improved to address these issues.
Methods:
The GA is implemented in Perl. Pop-up models coded in MN-trans are run through PsN, and results are compared in terms of a fitness function. Models with higher fitness have a higher probability to be selected (tournament selection with elitism) and combined (single point crossover and mutation) to create a new generation of models. The search is guided by a user-defined configuration file containing the list of covariates, parameters, and type of relations to be tested. For categorical covariates the linear model is available, whilst for continuous covariates 4 relationships are possible: linear, hockey-stick, exponential, and power.
An initialization strategy of the chromosome population has been proposed based on hierarchical clustering to reduce the probability of falling in a local minimum while maintaining limited the size of the chromosome population.
Further, the fitness function, previously defined based on AIC, has been improved to limit the introduction of highly correlated covariates on the same model parameter.
Finally, the GA was integrated in an R workflow for an easier manipulation.
The updated GA was tested in one simulated scenario and in one real case-study. In the first one, 8 highly correlated covariates (7 continuous, 1 categorical) were tested on parameters of a 1-compartment model using a simulated 200-individual dataset. The “true-model” includes BMI and CRCL on CL and BSA and SEX on V. The GA was, then, applied on the Remifentanil case study where 6 possible covariates (5 continuous, 1 categorical) were tested on parameters of a 3-compartment model using a real 65-individual dataset [7].
GA and scm implemented in Perl-speaks-NONMEM (PsN) [8] were compared in terms of AIC and covariance selected.
Results:
For the simulated scenario, both GA and scm introduced BSA, CRCL on CL and SEX on V. Although the 2 algorithms identified the same covariates, the final GA model had a lower AIC than the scm one (AIC = -6523.31 vs -6519.86), due to a different covariate-parameter relationship. Because BSA was not included on V, it was manually added to the model selected by GA providing a non-significant improvement in the AIC (-6523.78). To evaluate the robustness of results and computational costs, GA was run several times, starting from a population of models initialised by hierarchical clustering or randomly selected. The not-random initialised GA always converged to the same optimal solution with a computational-time gain, respect to the random-initialised one, higher than 46.2% in average.
For the real case-study, GA selected AGE and WT on CL, LBM on V1, AGE on Q2, AGE and SEX on V2, AGE on Q3, AGE and HT on V3 (AIC = 4032.67), while scm AGE and BSA on CL, LBM on V1, AGE on Q2, AGE on V2, AGE and SEX on Q3, AGE and LBM on V3 (AIC = 4033.74). Again, AIC of the GA final model was slightly lower. Results were also compared with the ones obtained with the GA without including penalty for the inclusion of correlated covariates; a significant improvement was observed.
It is important to underline that covariate selected by scm depended on the order in which they were tested and that in both scenarios the best model, selected by scm for different runs, was used for comparison.
Conclusions:
The updated GA showed good results both in terms of correctness of the selected model and fitness optimization. The initialization strategy reduced convergence times and allowed to obtain replicable results using a reduced population size. In addition, the new fitness function, accounting for covariate correlations, helped to limit the number of selected covariates
References:
[1] Joerger M. Covariate pharmacokinetic model building in oncology and its potential clinical relevance. AAPS J. 2012;14(1):119-132. doi:10.1208/s12248-012-9320-2
[2] Ribbing J, Jonsson EN. Power, selection bias and predictive performance of the Population Pharmacokinetic Covariate Model. J Pharmacokinet Pharmacodyn. 2004 Apr;31(2):109-34. doi: 10.1023/b: jopa.0000034404.86036.72. PMID: 15379381.
[3] Hartung N., Wahl M., Rastogi A., Husinga W. Nonparametric goodness‐of‐fit testing for parametric covariate models in pharmacometric analyses. CPT Pharmacometrics Syst Pharmacol. 2021 Jun; 10(6): 564-576. doi: 10.1002/psp4.12614
[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.
[5] Ismail, M., Sale, M., Yu, Y. et al. Development of a genetic algorithm and NONMEM workbench for automating and improving population pharmacokinetic/pharmacodynamic model selection. J Pharmacokinet Pharmacodyn 49, 243–256 (2022). https://doi.org/10.1007/s10928-021-09782-9
[6] Development of a genetic algorithm for covariate analysis in population pharmacokinetic models. PAGE 29 (2021) Abstr 9861 [www.page-meeting.org/?abstract=9861]
[7] Charles F. Minto, Thomas W. Schnider, Steven L. Shafer; Pharmacokinetics and Pharmacodynamics of Remifentanil: II. Model Application. Anesthesiology 1997; 86:24–33 doi: https://doi.org/10.1097/00000542-199701000-00005
[8] 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
Reference: PAGE 30 (2022) Abstr 10098 [www.page-meeting.org/?abstract=10098]
Poster: Methodology – AI/Machine Learning