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Purpose: The application of Cox Proportional Hazards (CoxPH) models tosurvival data and the derivation of Hazard Ratio (HR) is well established.While nonlinear, tree-based Machine Learning (ML) models have been developedand applied to the survival analysis, no methodology exists for computing HRsassociated with explanatory variables from such models. We describe a novel wayto compute HRs from tree-based ML models using the Shapley additive explanation(SHAP) values, which is a locally accurate and consistent methodology toquantify explanatory variables' contribution to predictions.  Methods: We used three sets of publicly available survival data consisting ofpatients with colon, breast or pan cancer and compared the performance of CoxPHto the state-of-art ML model, XGBoost. To compute the HR for explanatoryvariables from the XGBoost model, the SHAP values were exponentiated and theratio of the means over the two subgroups calculated. The confidence intervalwas computed via bootstrapping the training data and generating the ML model1000 times. Across the three data sets, we systematically compared HRs for allexplanatory variables. Open-source libraries in Python and R were used in theanalyses.  Results: For the colon and breast cancer data sets, the performance of CoxPHand 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 anopposite finding in two of the explanatory variables between the CoxPH andXGBoost result. Subsequent Kaplan-Meier plots supported the finding of theXGBoost model.  Conclusion: Enabling the derivation of HR from ML models can help to improvethe identification of risk factors from complex survival datasets and enhancethe prediction of clinical trial outcomes.

Computing the Hazard Ratios Associated with Explanatory Variables Using Machine Learning Models of Survival Data