## 3 Results  
Table 1 presents the characteristics of the 785 patients diagnosed with high-risk PCa included in the analysis. The median age of the patients (interquartile range [IQR]) was 69.0 (IQR, 64.0-73.0) years. The median PSA level was 14.4 (IQR, 7.7-26.4) ng/mL. The cT stage was cT1 in 131 (16.7%) patients, cT2 in 298 (38.0%) patients, cT3a in 278 (35.4%) patients, and cT3b in 78 (9.9%) patients. The GS was 6 in 39 (5.0%) patients, 7 in 245 (31.2%) patients, 8 in 187 (23.8%) patients, 9 in 311 (39.6%) patients, and 10 in 3 (0.4%) patients. The median %PC was 40.0% (IQR, 25.0-58.3%) after using multivariate imputation by chained equations for the missing values. The median follow-up interval was 87.0 (IQR, 57.4-129.2) months, and the median duration of ADT was 25.0 (IQR, 23.7-27.9) months. The 5- and 7-year BCR-free survival rates were 92.1% and 89.3%, respectively. The Kaplan-Meier curves in Figure 1 show BCR-free survival according to each clinical variable evaluated. Age, PSA level, cT stage, biopsy GS, and %PC were significantly associated with BCR-free survival. The dose of CIRT was not identified as a significant predictor of BCR-free survival in the Kaplan-Meier analysis. The LASSO regression multivariate model was used to construct the nomograms shown in Figure 2a,b (5- and 7-year BCR-free survival rates, respectively). The LASSO coefficient solution path graphically represents how each variable's coefficient changed as the penalty term (lambda) was varied. Based on the LASSO coefficient solution path (Figure S1), age, PSA level, cT stage, and biopsy GS were input into the 5-year BCR-free survival nomogram. These same predictors plus %PC were input into the 7-year BCR-free survival nomogram. Points were assigned to each category and then summed to calculate the overall probability of each outcome. The points in each category were summed to calculate the overall probability of each outcome, as described previously [28]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variables** & **N = 785** \\ \hline Age (year) Median (IQR) & 69.0 (64.0, 73.0) \\ PSA (ng/mL) Median (IQR) & 14.4 (7.7, 26.4) \\ cT stage & cT1: 131(16.7\%), cT2: 298 (38.0\%), \\  & cT3a: 278 (35.4\%), cT3b: 78 (9.9\%) \\  & GS6: 39 (5.0\%), GS7: 245 (31.2\%), \\ Gleason Score & GS8: 187 (23.8\%), GS9: 311 (39.6\%), \\  & GS10: 3 (0.4\%) \\ Positive core (\%) Median (IQR) & 40.0 (25.0, 58.3) \\ Duration of ADT (Months) Median (IQR) & 25.0 (23.7, 27.9) \\  & 66.0 Gy (RBE)/20 fractions: 91 (11.6\%), \\ Dose of CIRT & 63.0 Gy (RBE)/20 fractions: 98 (12.5\%), \\  & 57.6 Gy (RBE)/16 fractions: 301 (38.3\%), \\  & 51.6 Gy (RBE)/12 fractions: 295 (37.6\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Patients’ characteristics in the present study. Figure 1: Kaplan–Meier curves for BCR-free survival according to each clinical variable. BCR: biochemical recurrence, PSA: prostate-specific antigen, %PC: percentage of biopsy positive cores. Figure 2: Nomograms predicting BCR-free survival after CIRT with ADT. Directions: A line was drawn upwards to the number of points in each category. The points were summed, and then a line of total points was drawn downwards to determine the probability on the bottom line. ADT: androgen deprivation therapy, BCR: biochemical recurrence, CIRT: carbon-ion radiotherapy, PSA: prostate-specific antigen. To determine the predictive accuracy of the nomograms, training, validation, and entire datasets were used. Based on the training, validation, and entire datasets, the AUC values for the 5-year BCR-free survival rate were 0.71, 0.60, and 0.66, respectively, and those for the 7-year BCR-free survival rate were 0.73, 0.62, and 0.68, respectively. The AUC values indicated suboptimal-to-good performance. The median likelihoods of achieving BCR-free survival at 5 and 7 years were 0.93 and 0.90, respectively. The entire dataset was divided into two distinct categories: patients exhibiting a high probability of BCR-free survival, and patients with a low probability, based on the aforementioned cut-off values.