Yifan Yu1, Mark Sale2, Alex Mazur2, James Craig2, Keith Nieforth2, Gustavo Doncel3, Craig Hendrix4, Rachel Scott5,6, Robert Bies1
1University at Buffalo, 2Certara, 3Eastern Virginia Medical School, Old Dominion University, 4School of Medicine, Johns Hopkins University, 5Medstar Health, 6Georgetown University School of Medicine
Objectives: Non-dominated sorting genetic algorithm III (NSGA-III) is an evolutionary algorithm intended to solve multi-objective optimization (MOO) problems, particularly those with 3 or more objectives, by applying a reference point based non-dominated sorting approach [1]. This study aims to evaluate the performance of NSGA-III in the context of PopPK model selection, assessing its ability to optimize multiple competing objectives. Methods: In pharmacometric model selection, there is typically a trade-off between model fit and parsimony. In addition, the model fit metrics (e.g. -2ll) may be insensitive to clinically relevant parameters, such as Cmax or Cmin. Commonly, the selection of the “best” model among competing objectives is subjective, given these trade-offs and the need to consider non-numerical criteria. We use MOO to select this set of non-dominated solutions and present that set of solutions to the user for final model selection. We compare that set to the results of a traditional PopPK model selection. Emtricitabine (FTC) and emtricitabine triphosphate (FTC-TP) PK data from the CONRAD 137 study [2] were used in this analysis. 2114 observed concentrations (1126 plasma FTC concentrations and 988 PBMC FTC-TP concentrations) from 120 female subjects were included. PK data from the single dose phase and multiple dose phase were merged. In this analysis, the search space was defined as follows. •Number of compartments for plasma FTC (1|2|3) •With or without an absorption lag time •The formation kinetics of PBMC FTC-TP from plasma FTC (Linear|Michaelis-Menten) •The elimination kinetics of PBMC FTC-TP (Linear|Michaelis-Menten) •With or without between subject variability on V2, Q2, V3, and Q3 •Residual error model of plasma FTC (additive|proportional|combined additive and proportional) •Residual error model of PBMC FTC-TP (additive|proportional|combined additive and proportional) NSGA3 algorithm was used to conduct multi-objective optimization with 3 optimization criteria: •Objective function values (-2LL, OFV) •Number of total estimated parameters •Bias in steady-state PBMC FTC-TP trough concentration prediction The OFV measured goodness-of-fit, ensuring the model adequately describes the dataset. The number of estimated parameters served as a parsimony criterion for model simplicity. The prediction bias in steady-state PBMC FTC-TP concentration ensured the model captured clinically relevant exposure. Inequality constraints removed crashed NONMEM runs. We ran NSGA-III with 12 partitions for 15 generations, using a population size of 92 in each generation. The final Pareto fronts from NSGA-III were compared with the model developed using the traditional stepwise method. Results: The traditional stepwise method final model has 3 compartments for plasma FTC, with saturable formation kinetics of PBMC FTC-TP using Michaelis-Menten equation and a linear elimination from PBMC. The OFV of the final traditional selection model is 3543.015, with 18 parameters estimated. There is a 9.03% bias in steady-state PBMC FTC-TP tough concentration prediction. The NSGA-III algorithm identified a Pareto front consisting of 30 models from the search space, with the OFV ranging from 3520.126 to 10134.822 and the total number of estimated parameters varying between 12 and 24. Among the identified Pareto fronts, the bias in steady-state PBMC FTC-TP trough concentration ranged from 0.24% to 98.09%. This Pareto front illustrates a trade-off between model complexity and predictive performance. Conclusions: The Pareto front identified by NSGA-III provides a broader view of the optimal solution space and offers insights into the trade-offs between the competing objectives. The NSGA-III algorithm with one of the optimization criteria as bias in PBMC FTC-TP concentration was able to identify a set of models in which some of the models had less bias than traditional methods, other models had better fit, and still other models were more parsimonious. The selection of the final model(s) from among these non-dominated models is left to the pharmacometrician as a subjective decision based on the objectives of the analysis, biological plausibility, and examination of diagnostic graphics.
[1] K. Deb and H. Jain, “An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints,” in IEEE Transactions on Evolutionary Computation, vol. 18, no. 4, pp. 577-601, Aug. 2014. [2] Thurman AR, Schwartz JL, Cottrell ML, Brache V, Chen BA, Cochón L, Ju S, McGowan I, Rooney JF, McCallister S, Doncel GF. Safety and Pharmacokinetics of a Tenofovir Alafenamide Fumarate-Emtricitabine based Oral Antiretroviral Regimen for Prevention of HIV Acquisition in Women: A Randomized Controlled Trial. EClinicalMedicine. 2021 May 23;36:100893.
Reference: PAGE 33 (2025) Abstr 11347 [www.page-meeting.org/?abstract=11347]
Poster: Methodology - New Modelling Approaches