Data-Driven Modelling and Statistical Learning in Cancer Dynamics : Nonlinear Bayesian Filtering and Learning Approach in Cancer Dynamics

Sammanfattning

Prediction of tumor dynamics in Non-Small Cell Lung Cancer is stochastic due to biological variability and noisy clinical measurements. This study presents an integrated framework combining stochastic modelling, Bayesian filtering, and deep learning for patient-specific tumor size tracking. A three-compartment Ordinary differential equation model describing high-antigen tumor cells, low-antigen tumor cells, and cytotoxic T lymphocytes was fitted to the TCGA lung cancer with non-linear least squares. An extension to a stochastic differential equation with additive noise. Three Bayesian filters Extended Kalman, Unscented Kalman, and Particle filter, were applied to assimilate noisy tumor size measurements into the model, with mean absolute error from 4 mm to 0.7 mm, 0.5 mm, and 0.2mm, respectively. The Particle filter achieved the highest accuracy and best uncertainty calibration across all disease stages. A convolutional neural network provided a complementary data-driven prediction approach. Together, these results demonstrate that stochastic modelling combined with Bayesian filtering provides an accurate and clinically interpretable framework for patient-specific tumor size estimation in Lung cancer.