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

Early integration of palliative care into oncology is endorsed by major clinical guidelines, yet the term "palliative" remains widely equated with imminent death by patients, contributing to reported refusal or delayed uptake rates in the range of roughly 30 to 68% across surveyed cohorts. This paper presents the Restorative Oncology Empowerment Framework (ROEF), a data informed, multivariate stochastic differential equation (SDE) model that reframes quality of life (QoL) management during oncology treatment as an active, dynamical restoration process toward pre morbid functioning, rather than a static end of life mitigation target. We formalise a four dimensional (physical, emotional, social, global) correlated Itô SDE with multiplicative noise and an absorbing restorative equilibrium, calibrate its scalar reduction against digitised aggregate longitudinal QoL trajectories from three published oncology cohorts, and subject the fitted model to a substantially expanded battery of quantitative checks: multi method global sensitivity analysis (Sobol/Saltelli, Morris elementary effects, and a Fourier Amplitude Sensitivity Test), Bayesian parameter inference via a self implemented adaptive Metropolis sampler, Watanabe Akaike information criterion (WAIC) comparison against two alternative structural models, Fokker Planck first passage time analysis, dynamic programming optimal control, and a probabilistic (rather than point estimate) cost effectiveness analysis. Every numerical result, table and figure in this manuscript is generated by the single self contained Python 3 engine reproduced in Appendix A, which relies only on the standard scientific Python stack (numpy, scipy, pandas); no proprietary or third party Bayesian/sensitivity analysis packages are required. We report the model's genuine, and in places unflattering, quantitative behaviour: the restoration rate parameter r dominates 24 month outcome variance (Sobol S1 approximately 0.84) with a ranking that is robust to substantial widening of the parameter ranges; but WAIC based model comparison shows that a far simpler one parameter logistic recovery model fits the same calibration data at least as well as ROEF (Delta WAIC approximately 0.1), a finding we discuss openly rather than obscure, since it directly bounds what the calibration data can currently support. We provide eight quantitative, falsifiable predictions with required sample sizes, an explicit statement of the conditions under which the framework should be considered disconfirmed, a dedicated scientific and technical risk assessment, and a staged roadmap for prospective multi centre validation.