## 2 Materials and Methods
### Modelling  
#### 2.6.1 Predictive Features  
Geometric anatomical variables relating to ROIs were chosen as predictive factors in-line with previous work [5; 6; 41; 42]. Features included volumes of ROIs, distances between ROIs and other variables such as volume ratios. A summary of the selection can be found in Table 5. Over 100 features were initially extracted and data cleaning performed to ensure: robustness during modelling [43], better modelling performance (reduction in type I and II errors) [44] and computational efficiency [45]. Data cleaning involved eliminating incomplete features, removing zero-variance features (e.g., all zeros) and removing those with low variance. No features were removed for missing data as the data were fully homogeneous and no variables were considered low variance. Only variables with zero variance were removed and all remaining variables did not differ from a standard normal distribution.  
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt} p{142.3 pt} p{142.3 pt}} \hline
**Type of Feature** & **Feature** & **Variant** & **Example** & **Example** \\ \hline \multirow{6}{*}{Volumetric} & Volume & individual OARs and total OARs & \multirow{2}{*}{volume of rectum (cm\({}^{3}\))} \\  & Overlap of OAR with PTV & None & & \\ \cline{2-3}  & Volume-in-field of PTV: OAR volume within the superior-inferior slices of a PTV & None & & bladder VIF\({}_{\text{PTV60}}\): volume of the bladder within the superior-inferior slices of PTV60 (cm\({}^{3}\)) \\ \cline{2-3}  & Volume-out-of-field of PTV: OAR volume above the superior slices and below the inferior slice of a PTV & None & & rectum VFF\({}_{\text{PTV48}}\): volume of the rectum above superior slice and below the inferior slices of PTV48 (cm\({}^{3}\)) \\ \cline{2-3}  & Volume defined by nested PTVs (i.e., PTV annulus) & None & & volume of PTV48 minus PTV60 (cm\({}^{3}\)) \\ \hline \multirow{2}{*}{Spatial} & Distance between ROIs & minimum, maximum and average surface-to-surface distance and distance between centres-of-mass & minimum distance between rectum and bladder (cm) \\ \hline \multirow{6}{*}{Derived} & Overlap volume with expanded PTV & 0.2 cm increments of isotropic expansion up to 2.4 cm & \multirow{2}{*}{OV\({}_{\text{recum,PTV60},\text{km}}\): volume of rectum in PTV60\({}_{\text{L4.cm}}\) (cm\({}^{3}\))} \\  & Rate of change (slope) between overlap volumes of adjacent expanded PTVs with OARs & None & & slope between OV\({}_{\text{recum,PTV60},\text{km}}\) and OV\({}_{\text{recum,PTV60},\text{km}}\) (cm\({}^{3}\)) \\ \cline{1-1} \cline{2-3}  & Ratio of two ROI volumes & None & & ratio of volume of rectum to volume of PTV48 \\ \hline \end{tabular}
\end{table}
Table 5: Summary of variables considered for FeatureDS1 and FeatureDS2. Features fall into three categories: volume related (volumetric), distance related (spatial) and derivations of volumetric and/or spatial (derived). Variants are denoted where multiple features of their kind are generated.  
Collinearity between variables can leading to modelling bias [46], so associations between features were also explored. A subset of the master set of features was therefore defined. For any two features with a Pearson correlation coefficient of 0.85 or higher, one of the two features was randomly removed. A value of 0.85 was considered a reasonable cut-off and is in-line with other ML studies in the general ML literature [47; 48; 49]. Two feature datasets are therefore defined: the full set of cleaned features (FeatureDS1) and a subset of FeatureDS1 containing uncorrelated features (FeatureDS2).