Purpose: The application of Cox Proportional Hazards (CoxPH) models to survival data and the derivation of Hazard Ratio (HR) is well established. While nonlinear, tree-based Machine Learning (ML) models have been developed and applied to the survival analysis, no methodology exists for computing HRs associated with explanatory variables from such models. We describe a novel way to compute HRs from tree-based ML models using the Shapley additive explanation (SHAP) values, which is a locally accurate and consistent methodology to quantify explanatory variables' contribution to predictions.
Methods: We used three sets of publicly available survival data consisting of patients with colon, breast or pan cancer and compared the performance of CoxPH to the state-of-art ML model, XGBoost. To compute the HR for explanatory variables from the XGBoost model, the SHAP values were exponentiated and the ratio of the means over the two subgroups calculated. The confidence interval was computed via bootstrapping the training data and generating the ML model 1000 times. Across the three data sets, we systematically compared HRs for all explanatory variables. Open-source libraries in Python and R were used in the analyses.
Results: For the colon and breast cancer data sets, the performance of CoxPH and XGBoost were comparable and we showed good consistency in the computed HRs. In the pan-cancer dataset, we showed agreement in most variables but also an opposite finding in two of the explanatory variables between the CoxPH and XGBoost result. Subsequent Kaplan-Meier plots supported the finding of the XGBoost model.
Conclusion: Enabling the derivation of HR from ML models can help to improve the identification of risk factors from complex survival datasets and enhance the prediction of clinical trial outcomes.
School of Electrical and Computer Engineering, Purdue University（普渡大学电气与计算机工程学院）；Department of Medicine, Indiana University School of Medicine（印第安纳大学医学院医学系）；School of Electrical and Computer Engineering, Indiana University - Purdue University Indianapolis（印第安纳大学-普渡大学印第安纳波利斯分校电气与计算机工程学院）
Comparison of the Cox proportional hazards model and Random Survival Forest algorithm for predicting patient-specific survival probabilities in clinical trial data
University of Augsburg（奥格斯堡大学）；University of Reading（雷丁大学）
CoxSE: Exploring the Potential of Self-Explaining Neural Networks with Cox Proportional Hazards Model for Survival Analysis
Center for Applied Intelligent Systems Research (CAISR)（应用智能系统研究中心）；Halmstad University（哈马斯特德大学）；Centre for Environmental and Climate Science（环境与气候科学中心）；Lund University（吕勒奥大学）；Research Institutes of Sweden (RISE)（瑞典研究机构）
Predicting Deterioration in Mild Cognitive Impairment with Survival Transformers, Extreme Gradient Boosting and Cox Proportional Hazard Modelling
Goldsmiths, University of London（伦敦大学金史密斯学院）；School of Health Sciences, The University of Manchester（曼彻斯特大学健康科学学院）；Faculty of Computer Science and Engineering, Frankfurt University of Applied Sciences（法兰克福应用科学大学计算机科学与工程学院）；Institute of Psychiatry, Psychology and Neuroscience King’s College London（伦敦国王学院精神病学、心理学与神经科学研究所）
Deep Learning for Patient-Specific Kidney Graft Survival Analysis
University Paris Descartes（巴黎笛卡尔大学）；Institut Hypercube（超立方体研究所）；Montreal Institute for Learning Algorithms（蒙特利尔学习算法研究所）；École Polytechnique de Montréal（蒙特利尔理工学院）
On the Probability of First Success in Differential Evolution: Hazard Identities and Tail Bounds
Faculty of Mathematics and Informatics（数学与信息学系）；Sofia University St. Kliment Ohridski（索菲亚大学圣克莱门特·欧里斯基学院）；Department of Mathematics（数学系）；University of Chemical Technology and Metallurgy（化学技术与冶金大学）；Department of Informatics（信息学系）
Communication-efficient distributed hazard difference estimation for heterogeneous multi-site survival data
College of Mathematics, Taiyuan University of Technology, China（太原科技大学数学学院）；Centre for Quantitative Medicine, Duke-NUS Medical School, Singapore（新加坡国立大学医学院定量医学中心）；Systems Research, Duke-NUS Medical School, Singapore（新加坡国立大学医学院系统研究）
ICTSurF: Implicit Continuous-Time Survival Functions with Neural Networks
Chakri Naruebodindra Medical Institute, Ramathibodi Hospital, Mahidol University（玛希隆大学拉玛提波迪医院查克里纳鲁博丁德拉医学院）；Department of Clinical Epidemiology and Biostatistics, Faculty of Medicine Ramathibodi Hospital, Mahidol University（玛希隆大学拉玛提波迪医院医学院临床流行病学与生物统计学系）
Interpretable Survival Analysis for Heart Failure Risk Prediction
Stanford University（斯坦福大学）；VA Palo Alto Health Care System（帕洛阿尔托退伍军人医疗保健系统）；Kaiser Permanente Northern California Division of Research（凯撒医疗北加州研究部）；Stanford Medicine（斯坦福医学院）
SurvKAN: A Fully Parametric Survival Model Based on Kolmogorov-Arnold Networks
Department of Electronics, Information, and Bioengineering, Politecnico di Milano（电子信息生物工程系，米兰理工学院）；Department of Radiation Oncology, Mayo Clinic（放射肿瘤科，梅奥诊所）；Division of Radiation Oncology, IEO, European Institute of Oncology, IRCCS（放射肿瘤科，欧洲肿瘤研究所，IRCCS）；Department of Oncology and Hemato-Oncology, University of Milan（肿瘤学与血液肿瘤学系，米兰大学）
