An amortized approach to non-linear mixed-effects modeling based on neural posterior estimation

Non-linear mixed-effects models are a powerful tool for studying heterogeneous populations in various fields, including biology, medicine, economics, and engineering. However, fitting these models to data is computationally challenging if the description of individuals is complex and the population is large. To address this issue, we propose a novel machine learning-based approach: We exploit neural density estimation based on normalizing flows to approximate individual-specific posterior distributions in an amortized fashion, thereby allowing for an efficient inference of population parameters. Applying this approach to problems from cell biology and pharmacology, we demonstrate its scalability to large data sets in an unprecedented manner. Moreover, we show that it enables accurate uncertainty quantification and extends to stochastic models, which established methods, such as SAEM and FOCEI are unable to handle. Thus, our approach outperforms state-of-the-art methods and improves the analysis capabilities for heterogeneous populations.