# Using Explainable Machine Learning to Explore the Impact of Synoptic Reporting on Prostate Cancer
## 3 Results  
Table 4 shows the results of the CPH multiple regression. Based on the corresponding \(z\)- and \(p\)-values, age and EAU were the most important predictors of ranked survival for the data at hand. Additionally, SR had a significant positive effect on overall predicted survival. The features academic hospital and incidence year had no significant impact on the model's output.  
Figure 2 shows a bar plot comparing the performance of the CPH and XGB models' ranked survival predictions using the \(c\)-index. The latter is presented as a mean with its corresponding 95% confidence intervals from the tenfold cross-validation. XGB performed significantly better in predicting ranked survival predictions as compared to CPH, with \(c\)-index values of 0.67 and 0.58, respectively (\(p<0.0001\)).  
Next, we calculated SHAP values of the CPH and XGB models, which are shown in Figure 3. In short, these plots show the impact that each feature had on the model output.  
Features are ordered from top to bottom in decreasing importance, given by the mean of their absolute Shapley values. For each of them, each dot corresponds to a patient. Their location on the \(x\)-axis is determined by their SHAP value. In our case, positive SHAP values correspond to a higher chance of death, while negative values correspond to the opposite (i.e., a higher chance of survival). In other words, a patient with a higher SHAP value has a higher mortality risk relative to a patient with a lower SHAP value. The color indicates the value of the feature it represents and is depicted from low (blue) to high (pink).  
Figure 3: SHAP swarm plots of (**A**) CPH model and (**B**) XGB model. In each panel, features are arranged from top to bottom in decreasing order of importance. For each of them, each dot corresponds to a patient. Their location on the \(x\)-axis is determined by their SHAP value. Higher SHAP values correspond to a higher chance of death. The color indicates the value of the feature it represents and is depicted from low (blue) to high (pink).  
Figure 2: Mean \(c\)-index of the CPH and XGB models using tenfold cross-validation. Error bars represent the 95% confidence intervals across folds. ***** _* _* \(p\) \(<\) 0.0001.  
Afterwards, we generated dependence plots for all five features, as shown in Figure 4. In these, we also compared the CPH and XGB models (in light and dark blue, respectively). Once more, each dot corresponds to one patient. The feature's values are represented along the \(x\)-axis, while the SHAP values are shown along the \(y\)-axis (their interpretation remains unchanged: positive SHAP values correspond to a higher chance of death and viceversa).  
Since we were particularly interested in studying the effect of SR, we also studied its interaction effect with the two other most important features: age and EAU, which is shown in Figure 5. In this case, color represents the value of the interacting feature, going from low (in blue) to highest (in pink).  
Figure 4: Dependence plot for all features: (**A**) age; (**B**) EAU (encoded as 1—low risk/localised, 2—intermediate risk/localised, 3—high risk/localised, and 4—high risk/locally advanced); (**C**) SR (encoded as 0—False, 1—True); (**D**) incidence year; (**E**) academic hospital (encoded as 0—False, 1—True). Each dot corresponds to one patient. In the case of categorical features (i.e., all features except age), artificial jitter was added along the \(x\)-axis for the sake of easier representation. The \(y\)-axis scale is the same for all features in order to give a proper idea of their contributions to the model output.