Masato Fukae1,2, Joga Gobburu2
1Daiichi Sankyo Co., Ltd., 2University of Maryland Baltimore
Objectives: An advantage of the nonlinear mixed effects model (NLME) is that mechanistic knowledge (e.g. clearance concept) can be incorporated in a statistic model. A developed model, often called a pharmacometric model, is integral to predict outcomes in future clinical trials in model-informed drug development. A deep nonlinear mixed effects model (DeepNLME) is a novel approach that includes small neural networks (NNs) in the function of population parameters and/or the ordinal differential equations, allowing to benefit partially from a completely data-driven approach in the framework of pharmacometrics even with less understanding of underlying mechanisms. Since this is an emerging methodology [1], the predictive performance is still unclear. The present work investigated the performance of DeepNLME in a typical population pharmacokinetics using both simulated data and an actual dataset from a first-in-human study. Methods: Using simulated datasets for a typical population pharmacokinetics, the ability of DeepNLME to characterize covariate effects was compared with the conventional NLME. The scenarios included estimating the effect of (1) a binary covariate (e.g. sex), (2) a continuous covariate (the power function, e.g. weight), and (3) a continuous covariate (the hockey-stick type function, e.g. renal function). In each scenario, 200 datasets were generated, and then each dataset was analyzed by both the conventional NLME and DeepNLME. Finally, the results were summarized by appropriate measurements such as mean error (ME) and absolute mean error (MAE). For scenarios 1 and 2, the true functions were given to the conventional NLME while a slightly different function, power model, was used for scenario 3. As an actual dataset, PK data from single ascending dose (SAD) and multiple ascending dose (MAD) cohorts in a first-in-human study of DS-8500 were used. Dose ranges in the SAD and MAD cohorts were from 1 to 600 mg and from 10 to 300 mg, respectively. The SAD data was used as the training set while the MAD was used as the test set. The training set was given to both the conventional NLME and DeepNLME to estimate parameters including a NN describing absorption rate. The absorption phase was replaced by the NN because an absorption process is generally less understood and the modeling is time-consuming and influences the accuracy for the prediction of Cmax, an important exposure metric for an exposure-response analysis. The prediction performance of the conventional NLME and DeepNLME was compared using the test set. The conventional approach employed a simple first-order absorption model for a comparison purpose while DeepNLME embedded a small NN containing three input variables, two hidden layers, and a single output. The input variables were dose level, time after dosing, and a random effect for the neural network. Results: For the simulated datasets, scenario 1 (a binary covariate like sex) showed exactly the same results from the conventional NLME and DeepNLME, which was as expected because no room for flexibility was available under this scenario. In scenario 2 (a continuous covariate like weight), the conventional NLME performed slightly better than DeepNLME. This was also as expected because the conventional NLME was given the true model of power function. In scenario 3, on the other hand, DeepNLME outperformed over the conventional NLME, suggesting the potential advantage of DeepNLME because the true function is always unknown in an actual drug development setting. For the actual dataset, DeepNLME predicted the unseen PK data from the test set better than the conventional NLME, with little systematic deviations in the standard goodness-of-fit plots. In particular, the prediction performance in the absorption phase improved within the entire PK profile. Conclusions: The present work showed the potential advantages of the novel modeling approach, DeepNLME. Further assessment is necessary as this work just compared the performance under limited conditions.
[1] Rackauckas et al. 2021, Universal Differential Equations for Scientific Machine Learning, arXiv:2001.04385
Reference: PAGE 33 (2025) Abstr 11435 [www.page-meeting.org/?abstract=11435]
Poster: Methodology – AI/Machine Learning