Abstract: 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
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
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.