Marco Virgolin1, Giuseppe Pasculli2, Daniel Roeshammar2
1InSilicoTrials Technologies B.V., 2InSilicoTrials Technologies S.p.A.
Introduction: The optimization of clinical trial design plays a crucial role in drug development, requiring a balance between statistical power, resource efficiency, and ethical considerations. Artificial intelligence (AI) represents a key opportunity in this sense [1]. Recently, Tsuchiwata & Tsuji proposed the use of genetic algorithms (GAs) to optimize blood sampling schedules in a simulated pediatric study to minimize the number of samplings without compromising the accuracy of pharmacokinetic (PK) parameters [2]. Objectives: This work extends the prior work of Tsuchiwata & Tsuji by proposing a multi-objective optimization (MOO) approach over their single-objective one, to explore the potential performance gain of MOO methods such as NSGA-II and NSGA-III (3). Methods: Blood drug concentrations at 49 timepoints for 24 subjects were generated by a Monte Carlo simulation based on the population PK model described in [2]. The PK parameters considered were C_max and AUC, calculated by non-compartmental analysis using ncappc in R [4]. The single-objective GA algorithm from (2) used a sum of errors over C_max and AUC and the square of the number of blood sampling points n_p divided by 7 (“1obj” formulation). This setting was compared with two MOO configurations: a two-objective (2obj) formulation which minimizes n_p and the sum of mean absolute percentage error (MAPE) for C_max and AUC, and a three-objective (3obj) formulation, which treats C_max MAPE, AUC MAPE, and n_p as independent objectives. To assess the quality of the solutions generated by these settings, the minimum objective obtained by discovered solutions in the Pareto set was considered, as well as the hypervolume score; the latter measuring the volume between Pareto non-dominated solutions and a predefined reference point. The reference point was set at twice the performance obtained using a conventional blood sampling schedule of 15 timepoints from [2], i.e., n_p=2×15, C_max MAPE = 2×3.01, and AUC MAPE = 2×0.68. The GA, NSGA-II, and NSGA-III were set to run with a pool of 200 candidate solutions evolving for 100 generations as in [2]. Each algorithm was executed ten times to account for stochasticity. Statistical analyses, including the Kruskal-Wallis test and post hoc Conover tests with Holm correction, were applied to determine significant differences. Results: Across ten independent runs, GA-1obj’s best-found solution had on average C_max MAPE = 3.01, AUC MAPE = 0.68, and n_p=8.2. In contrast, the MOO algorithms found multiple solutions within each run, with different trade-offs. For example, NSGA-II-2obj and NSGA-III-3obj were able to discover solutions with C_max MAPE = 0.19 and AUC MAPE <= 0.01 on average. Regarding n_p, the multi-objective algorithms were able to discover solutions with less timepoints and lower MAPEs than the GA-1obj. When compared to the conventional reference of 15 timepoints, GA-1obj found a solution that was better in all objectives in only 2 out of 10 runs, while NSGA-III-3obj and NSGA-II with either 2 or 3 objectives did so in 5 out of 10 runs. The best hypervolume score was obtained with NSGA-III-3obj (score: 183.93) and NSGA-II with either 2 (score: 180.41) or 3 (score: 180.13) objectives. Meanwhile, GA-1obj and NSGA-III-2obj performed substantially worse (scores of 151.57 and 157.40, respectively). Kruskal-Wallis tests confirmed statistically significant differences among the methods, with a p-value of less than 0.001 for all key comparisons. Post hoc analyses demonstrated that NSGA-II-2obj and NSGA-III-3obj significantly outperformed the single-objective genetic algorithm in all metrics. Conclusions: The results indicated that multi-objective optimization can provide a clear advantage over single-objective genetic algorithms in blood sampling schedule optimization. In terms of algorithm choice, NSGA-II and NSGA-III enable flexible trade-off exploration, allowing decision-makers to select optimal solutions that best balance patient burden reduction and PK accuracy and precision. Among the tested approaches, NSGA-II performed well with 2 or 3 objectives, while NSGA-III performed well only with 3 objectives. These findings highlight the promise of further exploring MOO in pharmacometrics, particularly in advanced study designs that incorporate additional complexity, such as dose selection, sample size determination, and the simultaneous optimization of efficacy and safety endpoints.
1. Janssen A, Bennis FC, Mathôt RAA. Adoption of Machine Learning in Pharmacometrics: An Overview of Recent Implementations and Their Considerations. Pharmaceutics. 2022 Aug 29;14(9):1814. 2. Tsuchiwata S, Tsuji Y. Computational design of clinical trials using a combination of simulation and the genetic algorithm. CPT Pharmacomet Syst Pharmacol. 2023 Apr;12(4):522–31. 3. Yannibelli V, Pacini E, Monge D, Mateos C, Rodriguez G. A Comparative Analysis of NSGA-II and NSGA-III for Autoscaling Parameter Sweep Experiments in the Cloud. Sci Program. 2020 Aug 28;2020:1–17. 4. Acharya C, Hooker AC, Turkyilmaz GY, Jonsson S, Karlsson MO. A diagnostic tool for population models using non-compartmental analysis: The ncappc functionality for R. Comput Methods Programs Biomed. 2016;127:83–93.
Reference: PAGE 33 (2025) Abstr 11734 [www.page-meeting.org/?abstract=11734]
Poster: Methodology – AI/Machine Learning