A Fully Reproducible Data-Informed Multivariate Stochastic Differential Equation Framework for Quality-of-Life Restoration in Oncology

Despite robust evidence supporting early integration of palliative care, the paradigm remains widely perceived by patients as synonymous with "end-of-life mitigation", leading to refusal rates of 30–68% and delayed referrals (Sanders et al., 2024; Bandieri et al., 2023; Salins et al., 2022; Alexander et al., 2026). This paper introduces the Restorative Oncology Empowerment Framework (ROEF), a data-informed multivariate stochastic differential equation (SDE) model that shifts the ontological focus from symptom mitigation to active restoration of pre-morbid quality-of-life (QoL). We model the full 4-dimensional QoL vector (physical, emotional, social, global) using a correlated Itô SDE with multiplicative noise, calibrated to real longitudinal trajectories from three recent studies (Versluis et al., 2024; Kuan et al., 2024; Lee et al., 2022). The entire analysis—including parameter estimation, Monte Carlo simulations, global sensitivity analysis (Sobol, Morris, FAST), Bayesian inference, Fokker-Planck analysis, optimal control, cost-effectiveness, and model comparison—is generated by a single self-contained Python 3.12 engine (Appendix A). Running this code reproduces every number, table, and figure in this manuscript, ensuring full transparency and reproducibility. All graphical outputs are native LaTeX graphics rendered via pgfplots, directly from data files produced by the code. We also provide eight quantitative falsifiable predictions with required sample sizes, a protective belt of auxiliary hypotheses, and an open invitation for multi-centre validation.