(T-017) Multi-Objective Optimization for Population Pharmacokinetic Model Selection: Evaluating Non-dominated Sorting Genetic Algorithm III Performance

Yifan Yu – University at Buffalo; Mark Sale – Ceratara USA; Alex Mazur – Certara USA; James Craig – Certara USA; Keith Nieforth – Certara USA; Gustavo Doncel – CONRAD, Eastern Virginia Medical School, Old Dominion University; Craig Hendrix – School of Medicine, Johns Hopkins University; Rachel Scott – Medstar Health, and Georgetown University School of Medicine; Robert Bies – University at Buffalo

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: 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. The model search space included the number of compartments for plasma FTC (1, 2, or 3), presence or absence of an absorption lag time, formation kinetics of FTC-TP from plasma FTC (linear or Michaelis-Menten), elimination kinetics of FTC-TP (linear or Michaelis-Menten), inclusion or exclusion of between-subject variability on V2, Q2, V3, and Q3, and the choice of residual error model (additive, proportional, or combined) for both plasma FTC and PBMC FTC-TP. NSGA-III algorithm was used to conduct multi-objective optimization with 3 optimization criteria: OFV (as a measure of goodness-of-fit), the total number of estimated parameters (representing model parsimony), and the prediction bias in steady-state PBMC FTC-TP trough concentration (a clinically relevant exposure metric). 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. 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.

Citations: [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.

Keywords: Population Pharmacokinetic Model, Multi-Objective Optimization, Non-dominated Sorting Genetic Algorithm III