Non-Linear Models in Metastatic Cancer Analysis

Abstract

Metastatic cancer progression is governed by complex, nonlinear biological processes, including inter-site tumor interactions, resource limitations, and heterogeneous responses to therapy. While linear models may provide reasonable approximations in early-stage or localized disease, they are generally inadequate for capturing the dynamics of metastatic spread. In this study, we propose a nonlinear state-space modeling framework to describe the evolution of latent tumor burden across multiple anatomical sites. The model incorporates nonlinear growth dynamics, metastatic seeding, and treatment effects, and relates unobserved states to clinical measurements through nonlinear observation functions. To infer the latent states from noisy and partial observations, we employ advanced sequential estimation techniques, including the Extended Kalman Filter, Unscented Kalman Filter, and Particle Filtering methods. The performance of the proposed approach is evaluated through simulation studies designed to reflect clinically relevant metastatic scenarios. Results demonstrate that nonlinear models significantly improve estimation accuracy and better capture key features of metastatic progression, such as saturation effects and treatment resistance, compared to linear approximations. These findings underscore the importance of nonlinear modeling frameworks in enhancing predictive accuracy and supporting decision-making in precision oncology.