## 3 Results
### Performance of Final ML Models  
#### 3.3.1 Weights  
See Table 8 for an overview of relative weight calibrations across the validation dataset (as see Supplementary File S1 for an illustration). Statistically significant differences (at the 95% level) were observed between \(\mathrm{MCO_{gs}}\) and the three alternative methods (PGAP\({}_{\mathrm{std}}\), PGAP-ML\({}_{\mathrm{reg}}\) and PGAP-ML\({}_{\mathrm{clus}}\)) for three PGs: rectum D\({}_{\mathrm{mean}}\) rectum D\({}_{\mathrm{max}}\) and PTV dose falloff. For PGAP\({}_{\mathrm{std}}\) and PGAP-ML\({}_{\mathrm{reg}}\) significant differences were also observed for bowel V\({}_{\mathrm{36.0 Gy}}\) and V\({}_{\mathrm{45.6 Gy}}\) and the higher priority P1 and P2 goals (PG\({}_{\mathrm{higher}}\)). Differences were generally small (\(<\)3.58%), with PGAP-ML\({}_{\mathrm{clus}}\) closest to \(\mathrm{MCO_{gs}}\) on average with differences \(<\)1.17%. Mean differences from \(\mathrm{MCO_{gs}}\) were also closest to zero for PGAP-ML\({}_{\mathrm{clus}}\) for six of the eight PG. PGAP-ML\({}_{\mathrm{reg}}\) was the poorest performer overall with deviations \(<\)2.49% and 3.57% for PTV conformality and PG\({}_{\mathrm{higher}}\), respectively. Figure 3 illustrates relative weight deviations from \(\mathrm{MCO_{gs}}\) at a per-patient level for all three methods. In general per-patient deviations were considered small with maximum deviations of 7.39%, 9.88% and 5.58% for PGAP\({}_{\mathrm{std}}\), PGAP-ML\({}_{\mathrm{reg}}\) and PGAP-ML\({}_{\mathrm{clus}}\) respectively. PGAP-ML\({}_{\mathrm{reg}}\) was considered the poorest performer of the three methods given the largest range and inter-quartile range differences from \(\mathrm{MCO_{gs}}\) in all cases. PGAP\({}_{\mathrm{std}}\) and PGAP-ML\({}_{\mathrm{clus}}\) were considered highly comparable. In terms of outliers, patient 25 was considered the most noteworthy patient with outlying values in six cases: bladder D\({}_{\mathrm{max}}\) (PGAP-ML\({}_{\mathrm{clus}}\) only), intra-PTV dose falloff (PGAP\({}_{\mathrm{std}}\) and PGAP-ML\({}_{\mathrm{clus}}\)) and rectum D\({}_{\mathrm{max}}\) (all methods). \(\mathrm{MCO_{gs}}\) absolute weights for rectum and bladder D\({}_{\mathrm{max}}\) and intra-PTV dose falloff were lower for patient 25 than any patient in the training dataset and this was considered the likely underlying cause. Patient 36 was also a notable outlier with outlying values in five cases: bladder D\({}_{\mathrm{mean}}\) and D\({}_{\mathrm{max}}\) (PGAP-ML\({}_{\mathrm{clus}}\)), and rectum D\({}_{\mathrm{max}}\) (all methods). Patient 36 had the largest bladder volume in the validation set with a volume 1.36 times the maximum volume in the training dataset. Patient 24 had outlying values for bladder D\({}_{\mathrm{mean}}\) and intra-PTV dose falloff for PGAP-ML\({}_{\mathrm{clus}}\) which were attributed to \(\mathrm{OV_{bladder,PTV60}}\) being the largest in the validation dataset (1.97 times the median training value) and the absolute value for PTV dose falloff being outside the range defined by the training dataset (which bound PGAP-ML\({}_{\mathrm{clus}}\) weight predictions). Finally, outlying values were observed for patient 21 in three cases: bladder D\({}_{\mathrm{mean}}\) (PGAP-ML\({}_{\mathrm{clus}}\)) and rectumD\({}_{\mathrm{mean}}\) (PGAP\({}_{\mathrm{std}}\) and PGAP-ML\({}_{\mathrm{clus}}\)). This patient had the smallest \(\mathrm{OV_{ rectum,PTV60}}\) but also had rectum and bladder D\({}_{\mathrm{mean}}\) weights outside of the training dataset range. Other patients with 1-2 outliers (patient 27, 30, 31, 38, 39 and 40) were as above, identified as being anatomically atypical or cases where the validation \(\mathrm{MCO_{gs}}\) weights were out of range of the training values.