## 4 Discussion  
The proposed automated prediction approach for CTRs showed high PCCs of 0.953 (IN) and 0.926 (EX) and high ICCs of 0.943 (IN) and 0.904 (EX) for the prediction of CTRs on both internal test dataset B and the external test dataset, respectively. Further to this, the predicted CTRs showed the prognostic power of both datasets in stratifying SBRT patients into low-risk and high-risk patients, as shown in Figure 13.  
As shown in Figure 9, the two worst cases (Figure 9c,d) showed lower DSCs of 0.747 and 0.771 than the best case (Figure 9b) (DSC: 0.895). These lower DSCs affected the difference between reference and predicted contours and caused the larger differences in CTRs. The solid component contours are similar to each other between the predicted and reference ones. Since the whole tumor contour varied, this variability of whole tumor contours could cause the larger CTR differences. The other best case (Figure 9a) shows a lower DSC of 0.729 and low \(\Delta\)CTR because of the small sizes of the solid component and large whole tumor regions. On the other hand, the two best cases (Figure 9a,b) showed higher DSCs of 0.889 and 0.748 than the worst case (Figure 9d) (DSC: 0.559) as shown in Figure 12. The worst case (Figure 12c) shows a DSC of 0.785, however, the tumor edge is  
Figure 12: Four cases that indicated the lowest (**a,b**) and highest (**c,d**) differences in CTR (\(\Delta\)CTR) between reference and predicted CTRs by the proposed model for the external test dataset. \(\Delta\)CTR = 1 Reference CTR–Predicted CTR\(\mid\). Green line: whole tumor contour, sky blue line: solid component contour, orange line: overlapping contour. Figure 13: Kaplan–Meier survival curves for time to progression between low-risk and high-risk patients who were stratified with the medians of reference CTRs (**left**) and predicted CTRs (**right**) for internal test dataset B and the external test dataset. erroneously involved in a tumor region and leads to the lower accuracy. This issue could be solved by combining other DLS models [39] with our approach. DL-based prediction approaches for CTRs have been investigated for lung cancer patients treated with surgical resection [15; 16; 17]. [PERSON] et al. [15] reported an area under receiver operating characteristic curve (AUC) of 0.803 (validation test) for the prediction of tumor invasiveness for lung adenocarcinoma. [PERSON] et al. [16] demonstrated the prediction power of tumor invasiveness with an AUC of 0.826 (validation test). [PERSON] et al. [17] showed ICCs of 0.838 and 0.832 for DL-based measurements of maximum whole tumor size and maximum solid component size, respectively. In this study, the proposed prediction model exhibited ICCs of 0.980 and 0.801 for both sizes of the external test dataset as shown in Figures S7 and S9. _The AJCC Cancer Staging Manual (8 th edition)_ suggested to the radiologists to estimate the tumor sizes in all different projections if it is technically possible [31]. [PERSON] et al. [39] proposed a method that can measure the diameters of lung cancer regions on the three orthogonal views (axial, coronal and sagittal views). [PERSON] et al. [40] measured the diameters of breast cancers by dividing the cancer into serval slices in one dimension, whereas the proposed approach measured the maximum diameters of whole tumor regions and solid components with the Feret method for all projections. Thus, the proposed approach in this study followed the guidelines rather than past studies. [PERSON] et al. [41] measured the lung tumor diameters by a semi-automatic method based on the contours delineated by two radiologists. On the other hand, the authors developed the DLS model to automatically predict the contours, which could reduce the labors of radiologists, for the prediction of CTRs. CT image quality (e.g., motion artifacts or image blurring) degraded by respiratory motion could affect the segmentation accuracy of lung tumors [42].