# Using Explainable Machine Learning to Explore the Impact of Synoptic Reporting on Prostate Cancer
## 2 Materials and Methods
### Models  
We defined ranked patient survival as the outcome to be predicted, which is calculated based on follow-up time and event occurrence. We used two different models for this task. First, we performed a multiple CPH analysis (using scikit-survival v0.15.0 [49]), since this is one of the most common and well-known methods used in oncology. It is a semi-parametric approach that evaluates the effects of different covariates (i.e., features) on the hazard ratio (HR) of the occurrence of death. In a CPH regression, a patient's hazard is modelled as a combination of the population time-variant baseline hazard and of his/her time-invariant predictors (multiplied by their corresponding coefficients). Moreover, it \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Variable** & **Mean** & **SD** & **N** & **\%** &
\begin{tabular}{c} **Original** \\ **Completeness (\%)** \\ \end{tabular} \\ \hline Input & & & & & & \\ \hline age (in years) & 65.11 & 5.97 & - & - & 100.0 \\ \hline EAU & & & & & 84.6 \\ localized—low risk & - & - & 506 & 3.40 & \\ localized—intermediate risk & - & - & 10,930 & 73.46 & \\ localized—high risk & - & - & 3094 & 20.80 & \\ Locally advanced—high risk & - & - & 348 & 2.34 & \\ \hline incidence year & & & & & 100.0 \\
2011 & - & - & 1599 & 10.75 & \\
2012 & - & - & 1784 & 11.99 & \\
2013 & - & - & 1957 & 13.15 & \\
2014 & - & - & 1792 & 12.05 & \\
2015 & - & - & 1829 & 12.29 & \\
2016 & - & - & 1982 & 13.32 & \\
2017 & - & - & 1930 & 12.97 & \\
2018 & - & - & 2005 & 13.48 & \\ \hline academic hospital & & & & & 100.0 \\ Yes & - & - & 3485 & 23.42 & \\ No & - & - & 11,393 & 76.58 & \\ \hline SR & & & & & 100.0 \\ Yes & - & - & 7568 & 50.87 & \\ No & - & - & 7310 & 49.13 & \\ \hline \hline \end{tabular} Completeness refers to the percentage of patients with no missing values (Section 2.2). SD: standard deviation; EAU: European Association of Urology risk group; SR: synoptic reporting.  
\end{table} 
Table 2: General overview of the dataset used in this study. makes no assumptions on the underlying hazard function. We also performed a classical CPH multiple regression (using lifelines v0.25.11 [50]), which yielded HRs for each feature in the model. Additionally, we used eXtreme Gradient Boosting (XGB, using xgboost v1.3.3) as a representative ML technique for survival analysis [14]. We chose this model based on the results of our previous work, where we compared the performance of several ML algorithms for predicting ranked survival in a similar dataset and found that XGB performed the best [28]. These results are also in line with those of a few other studies in literature that have successfully used XGB for predictive modelling in oncology [29; 51; 52]. XGB poses its learning task as a numerical optimization process. It performs the gradient descent procedure by calculating the loss function and minimizes it by adding decision (regression) trees as weak learners (i.e., classifiers that perform slightly better than chance), as shown in Equation (1):  
\[\mathcal{L}^{(t)}=\sum_{i=1}^{n}l(y_{i},\hat{y}_{i}\,^{(t-1)}+f_{t}(\mathrm{x} _{i}))+\Omega(f_{t}) \tag{1}\]  
Here, \(l\) is a (differentiable) convex loss function measuring the difference between the target \(y_{i}\) and the prediction \(\hat{y}_{i}\) at the iteration \(t-1\). The tree \(f_{t}(\mathrm{x}_{i})\), is built using data \(\mathrm{x}_{i}\) that most improves the model [14]. These trees are parameterized and added one at a time until the loss reaches an acceptable value or until there is no further improvement. The final output is given by the weighted sum of the individual trees' predictions. Moreover, XGB actively tries to reduce overfitting by using subsets of the data for generating each new tree, by constraining the trees characteristics (such as number of trees or tree depth), and by weighting the updates (i.e., applying a learning rate), as given by the term \(\Omega(f_{t})\)[53]. We performed a nested cross-validation procedure.