## 3 Results  
Figures 3-5 show the density plots (a) and boxplots (b) of _OED_, _EAR_, and _LAR_ for both treatment schemes. Table 1 reports the minimum, maximum, and mean values for each of these metrics. Since treatment plans were recalculated by altering only the fractionation schedule (SF vs. HF), the observed risk variations for the same patient are primarily attributable to changes in total dose (_D_) and dose per fraction (_dj_). The _OED_ distribution shows a rightward shift for the 3D-CRT SF treatment compared to HF (Figure 3). As _OED_ directly influences _EAR_ and _LAR_ (Equations (4) and (6)), similar trends are observed in Figures 4 and 5. Figure 2: EclipseTM plug-in script workflow. To assess whether one treatment approach results in a significantly higher risk of radiation-induced lung cancer, a one-tailed paired Student's \(t\)-test was performed on **OED**, _EAR_, and _LAR_ values for SF and HF plans. The test assumed that paired differences are normally distributed, the data are continuous, each pair is dependent, and the pairs are mutually independent. The results indicate that the two datasets belong to distinct populations (\(p\)-value < 0.01), due to a consistent increase in **OED** for SF compared to HF (mean **OED** ratio = 1.137 \(\pm\) 0.002). _LAR_ depends on **OED** and the time interval between age\({}_{\text{e}}\) and age\({}_{\text{a}}\), weighted by survival probability. Figure 6 illustrates the variation in _LAR_ between SF and HF as a function of age\({}_{\text{e}}\). For the same patient, _LAR_ is systematically lower with HF due to the reduced _OED_ associated with its lower prescription dose. The figure also highlights the inverse correlation between  
Figure 4: Excess Absolute Risk (_EAR_) for 3D conformal radiotherapy (3D-CRT) treatment plans using standard fractionation (SF) and hypof fractionation (HF). (**a**) Density curves illustrate the distribution of _EAR_ values for patients in each fractionation group. (**b**) Boxplots show group medians (center line), interquartile ranges (boxes), and data spread (whiskers). The reported \(p\)-value from a one-tailed paired Student’s \(t\)-test compares SF and HF groups. Figure 3: Organ Equivalent Dose (_OED_, in Gy) for 3D conformal radiotherapy (3D-CRT) treatment plans using standard fractionation (SF) and hypofractionation (HF). (**a**) Density curves illustrate the distribution of _OED_ values for patients in each fractionation group. (**b**) Boxplots show group medians (center line), interquartile ranges (boxes), and data spread (whiskers). The reported \(p\)-value from a one-tailed paired Student’s \(t\)-test compares SF and HF groups. _LAR_ and _age\({}_{e}\):_ younger patients face a higher risk, given their longer life expectancy and greater time window for secondary cancer development. Data dispersion reflects inter-patient variability in _OAR_ morphology, which affects _LAR_ computation. Finally, _RR_ values were calculated for each patient using age- and region-specific _LIR_ data for lung cancer in Sicilian women. The _RR_ ranged from 1.26 to 1.86 (mean value 1.80) for SF, and from 1.23 to 1.76 (mean value 1.70) for HF. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Treatment** & **V5** & **V20** & **OED** & **EAR** & **LAR** & **Treatment** \\
**Type** & **(\%)** & **(\%)** & **(Gy)** & **(1/10,000 PY)** & **(1/10,000 P)** & **Type** \\ \hline
3D-CRT SF & 24.7 & 11.3 & 2.9 & 32 & 274 & 1.80 \\  & (12.3–35.3) & (2.1–19.2) & (2.0–3.6) & (23–42) & (31–455) & (1.26–1.86) \\
3D-CRT HF & 22.0 & 11.3 & 2.5 & 28 & 241 & 1.70 \\  & (9.4–32.1) & (1.9–17.9) & (1.7–3.2) & (20–37) & (27–400) & (1.23–1.76) \\ \hline \end{tabular}
\end{table} 
Table 1: \(\text{V}_{5}\), \(\text{V}_{20}\), Organ Equivalent Dose (_OED_), Excess Absolute Risk (_EAR_), Lifetime Attributable Risk (_LAR_), and Relative Risk (_RR_) for 3D-CRT standard fractionated (SF) and hypofracationation (HF) approaches. Figure 5: Standard fractionation (SF) and hypofracationation (HF).