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.尽管已有充分证据支持早期姑息治疗的整合应用，但该范式仍被患者广泛等同于“临终缓解”，由此造成30%~68%的治疗拒绝率与转诊延迟（Sanders等，2024；Bandieri等，2023；Salins等，2022；Alexander等，2026）。本文提出康复肿瘤学赋能框架（Restorative Oncology Empowerment Framework, ROEF），这是一种基于数据构建的多变量随机微分方程（stochastic differential equation, SDE）模型，将本体论视角从症状缓解转向主动恢复患者患病前的生活质量（quality-of-life, QoL）。 我们采用带乘性噪声的关联伊藤随机微分方程（Itô SDE），对完整的四维生活质量向量（躯体、情绪、社会、整体维度）进行建模，并基于三项近期研究的真实纵向轨迹完成校准（Versluis等，2024；Kuan等，2024；Lee等，2022）。整套分析流程——涵盖参数估计、蒙特卡洛模拟、全局敏感性分析（Sobol法、Morris法、FAST法）、贝叶斯推断、福克-普朗克分析、最优控制、成本效益分析与模型比较——均由单一自包含的Python 3.12引擎实现（附录A）。运行该代码即可复现本文手稿中的所有数值、表格与图表，确保研究的完全透明性与可复现性。所有图形输出均为通过pgfplots渲染的原生LaTeX图形，直接基于代码生成的数据文件完成。我们还提出八项可量化证伪的预测及所需样本量，构建了辅助假说保护带，并公开邀请开展多中心验证。