A DeepNLME-based Tumor Growth Dynamics and Overall Survival Model for Non Small Cell Lung Cancer
Authors: Tarek Mohamed , Contento Lorenzo , Roy Amit , Gauthier Kiran , Kondic Anna , Shen Jun 
Published: February 2025

Objective: To develop a deep nonlinear mixed effects (DeepNLME) tumor growth dynamics and overall survival (TGD-OS) model to identify and characterize patterns of non-small cell lung cancer (NSCLC) tumor response and the relationship to OS.Methods: DeepNLME [1] is an implementation of scientific machine learning [2] inside a mixed-effects framework. It is especially valuable in cases where a part (or all) of the structural model is unknown and there is between-subject variability, such as in the case of TGD-OS models. The TGD component of the model developed in this work was a structurally positive neural ODE, shared between all the subjects, with subject-specific input random effects to individualize the dynamics to each subject. The OS component of the model used a structural log logistic hazard function whose parameters were neural network functions of the TGD model output and various covariates (baseline and time-varying). The TGD-OS model was fitted in a stepwise way, incrementally adding complexity to the model. A previously developed NSCLC TGD-OS mixture model was used as a reference model in this study to compare the models’ OS prediction accuracy. The data used for the training and validation of the DeepNLME model was from 6285 patients in 9 studies, receiving immuno-oncology agents or chemotherapies. When fitting the DeepNLME model, 8 studies were used for the training and 1 study was used for validation using unseen data. Some early data analysis was also performed on each subject’s model using its random effects’ empirical Bayes estimates (EBEs) to make long-term individual predictions (ipreds) of the sum of longest diameters (SLD) given a few observations per subject.Results: The developed TGD model was able to fit most of the SLD data which had high variability including some of the patterns that cannot be easily described with traditional models. The long-term ipreds for each subject were found to be good when many observations are present for each subject but limited when only early data is available. For the OS data, the log likelihood of the DeepNLME model using the TGD model's EBEs was higher than the reference model by 868.3 points on the training data and by 88.5 points on the validation data, highlighting the potential of DeepNLME TGD-OS models in comparison to more traditional pharmacometrics (PMx) models.Conclusions: The DeepNLME-based model has some advantages over traditional PMx models in describing the unusual TGD profiles. Using neural networks and neural ODEs as components of TGD-OS models appear to also improve the OS log likelihood on both the training and validation data, compared to more traditional PMx models. More work is needed to explore the value of DeepNLME TGD-OS models in decision-making given early data and to improve the models’ prediction performance with such data.Citations: [1] Rackauckas C, Ivaturi V. 2019, "Neural-embedded nonlinear mixed effects models (NENLME) in Pumas.jl." ACoP[2] Rackauckas et al. 2020, “Universal Differential Equations for Scientific Machine Learning.” arXiv