## 4 Discussion
The largest variances in difference from \(\mathrm{MCO_{gs}}\) for both input parameters (weights) and outputs metrics (dose distribution) was observed for PGAP-MLreg. This is thought to be related to the size and composition of the training dataset not adequately representing the patient population. PGAPstd and PGAP-MLclus were more robust to the limited dataset size, with small deviations from \(\mathrm{MCO_{gs}}\) observed for outlier patients. Given regression allows predictions to be extrapolated beyond the bounds defined by the training dataset, increased robustness of PGAPstd and PGAP-MLclus compared to PGAP-MLreg is thought to be due to PGAPstd and PGAP-MLclus prediction weights being bounded by the training data. For outlier patients PGAP-MLreg could therefore lead to inconsistent or spurious predictions. As generating the ground truth training data is time consuming, curation of a suitably large dataset for accurate regression modelling may be challenging, especially for busy radiotherapy clinics. Therefore, these results indicate PGAP-MLreg may not be the best suited ML approach for routine clinical application. Across the three methods, PGAP-MLclus was considered the most comparable to \(\mathrm{MCO_{gs}}\) based on the number of significant differences observed following Wilcoxon testing, the magnitude of dose differences and the fact fewer outliers were observed. However, the superiority of PGAP-MLclus over PGAPstd was considered marginal. As PGAPstd is equivalent to PGAP-MLclus when K = 1, these results indicate that for the majority of patients individualisation via clustering may not be necessary if a simple site-specific protocol based on an average weight is implemented. However, marginal improvements may be gained when using PGAP-MLclus for patients who are anatomical outliers, most likely for ROIs where large anatomical variances are common, such as for bladder and patient outline ROIs. A key strength of this study was that training and evaluation was performed with plans generated using a posteriori multicriteria optimisation methodology (\(\mathrm{MCO_{gs}}\)), which we consider to be a gold standard in patient-specific plan generation [22]. This contrasts with the majority of KBP training approaches and AP comparative studies in the literature, which use manual plans generated with TAE [29; 58; 59]. Our ML models and study results are therefore not confounded by unwarranted variation or sub-optimality of plans within the training and validation datasets, which are known issues associated with TAE manual planning [53]. Across all three methodologies at a population level there was excellent correspondence with \(\mathrm{MCO_{gs}}\), with all volume and dose metrics within \(\pm\)0.66% and \(\pm\)0.34 Gy, respectively. In terms of trade-off balancing, PGAP-MLreg and PGAPstd led to a marginal reduction in PTV48 D98% (0.17 and 0.28 Gy, respectively), resulting in a corresponding minor reduction in rectum V40.5 Gy and V48.6 Gy (0.3-0.4%). This was considered a clinically insignificant difference. No other trade-off differences were observed. In terms of individual patients PGAP-MLclus and PGAPstd, yielded plans with high correlation to the gold standard MCO generated comparator (\(\mathrm{MCO_{gs}}\)). The correlation was weaker for PGAP-MLreg, which as discussed was attributed to the small training dataset size. Results provide strong evidence that PGAPstd, (built on a PBAIO AP framework),generates individualised plans, even when a site-specific protocol is utilised. This is an important finding, not only in validating the use of PGAPstd for prostate cancer, but also providing evidence that a posteriori multicriteria optimisation yields minimal benefits over AP in terms of the individuation of patient plans. In terms of the utility of patient-specific protocols, whilst PGAP-MLclus and PGAP-MLreg did not yield marked improvements, anatomical variances were shown to be an important factor in the prediction of weights during training.