Machine Learning Augmented Tumor Growth and Survival Models: Insights from Hepatocellular Carcinoma Data

Background:
Traditional pharmacometrics (PMX) tumor growth dynamics and overall survival (TGD-OS) modeling help understand patient characteristics, treatments, tumor progression, and outcomes. However, they often rely on predefined assumptions and may not fully capture tumor biology and patient heterogeneity. Machine learning (ML) offers opportunities to enhance TGD-OS modeling by identifying complex patterns with minimal assumptions. This study evaluates two ML approaches in TGD-OS modeling and compares their predictive performance and computational efficiency to traditional PMX TGD-OS models.

Methods:
Two ML approaches for enhancing TGD-OS modeling with hepatocellular carcinoma (HCC) data were demonstrated. The first is a universal differential equation (UDE) approach, integrating model-predicted longitudinal TGD and demographic covariates with a neural network (NN) to learn the hazard function of overall survival (OS). Implemented using the SciML ecosystem and Lux.jl in Julia [1,2].
The second approach is neural network for overall survival (NN-OS), using a NN to predict OS by learning the relationship between derived tumor metrics and the location and scale parameters of a parametric survival time distribution. Implemented using TensorFlow and Keras in R [3,4]. Model comparisons were based on concordance scores that measured the agreement between predicted and observed data.

Results:
The UDE model's predictive ability improved with better predictors. More informative NN inputs led to higher concordance, with c-index values of 0.544 for demographic covariates alone, 0.657 for TGD alone, and 0.664 for TGD combined with demographic covariates. The NN-OS approach effectively captured the average trend in the data. Predictive covariates identified using SHapley Additive exPlanations (SHAP) matched clinical expectations. TGD-related covariates were more informative than demographic covariates but using both resulted in the highest concordance. Model concordance reached 0.742 for the TGD-OS model, 0.738 for the NN-OS model, and 0.683 for the UDE model against external validation data (N = 312).

Conclusions:
The TGD-OS, NN-OS, and UDE approaches achieved comparable predictive performance, demonstrating that ML-based extensions can perform on par with traditional PMX modeling. ML models simplify the covariate selection process by eliminating stepwise selection, allowing for the inclusion of all covariates and accommodating complex data types like images and sequencing data. Integrating ML techniques into TGD-OS modeling can enhance clinical utility, contributing to more personalized and effective treatment strategies. Further research is needed to explore incorporating additional features and complex data types into these models, with applicability extending beyond HCC.