Life Expectancies (LE)* (years) Used in the Decision Model**.

*For the deceased group, we determined the LEs by calculating the area under the curve (AUC) at 18 months normalized by the percent of the deceased population [(total AUC- percent of survival at 18 months X 18 months)/percent of deceased at 18 months]. We used the Declining Exponential Approximation of Life Expectancy (DEALE) method to approximate the overall LEs of each treatment group based on survival rates at 18 months. The DEALE model is a good approximation for our study since these patients have high mortality rates which are shown to be more accurate when using the declining exponential function. [16], [17]. The subtraction of the weighted average of the LEs of the deceased group from the overall survival at 18 months gives the weighted average of the LE of the surviving group. From there, we derived the LEs of the surviving group by dividing by proportion surviving post 18 months.**We used the DEALE method to derive the overall life expectancies of the two subgroups differentiated by BPI score. We then extrapolated the life expectancies of the patients who died before 18 months and those remaining alive assuming a perfect declining exponential curve. Since median survival by baseline pain was only reported for abiraterone but not for the mitoxantrone or cabazitaxel groups, we assumed that all the treating groups had the same difference in their median survival between their individual subgroups with and without baseline pain (4.1 months). This was chosen as a more conservative estimate across all treatments than if we had used the abiraterone reported difference by baseline pain presence. With the overall survival derived from the each treatment groups median survival using the DEALE method, and the same difference of 4.1 months between the subgroups with baseline pain and no baseline pain for all treatments, we were able to derive the respective life expectancies of the subgroups with baseline pain and no baseline pain for each treatment group. From there, we further calculated the life expectancies of the patients who died before 18 months and who lived beyond that point for each subgroup as described previously. We then used these new life expectancies differentiated by baseline pain in our secondary decision tree analysis (results not shown).针对死亡队列，我们通过计算18个月时的曲线下面积（Area Under the Curve, AUC）并按死亡人群占比进行归一化，得到其预期寿命（Life Expectancy, LE），计算公式为：(总AUC - 18个月时生存率×18个月)/18个月时死亡率。我们采用下降指数近似预期寿命法（Declining Exponential Approximation of Life Expectancy, DEALE），基于18个月时的生存率估算各治疗组的总体预期寿命。由于本研究纳入的患者死亡率较高，而下降指数函数在这类人群中估算更为准确，因此DEALE模型非常适配本研究场景[16, 17]。将18个月总体生存率减去死亡队列预期寿命的加权平均值，即可得到存活队列预期寿命的加权平均值；后续再通过18个月后的存活比例进行除法运算，即可推导出存活队列的预期寿命。 我们采用DEALE法推导了以简明疼痛量表（Brief Pain Inventory, BPI）评分分层的两个亚组的总体预期寿命。随后我们假设死亡发生在18个月前及18个月后存活的患者均遵循完美的下降指数曲线，对其预期寿命进行外推。由于仅阿比特龙（abiraterone）组报告了按基线疼痛分层的中位生存期，而米托蒽醌（mitoxantrone）组与卡巴他赛（cabazitaxel）组均未报告该数据，因此我们假设所有治疗组中，伴基线疼痛与不伴基线疼痛的亚组间中位生存期差异均为4.1个月。相较于直接采用阿比特龙组报告的基线疼痛相关生存期差异，该假设为所有治疗组提供了更为保守的估算结果。结合通过DEALE法由各治疗组中位生存期推导得到的总体生存率，以及所有治疗组伴/不伴基线痛亚组间4.1个月的固定生存期差异，我们可推导出每个治疗组中伴基线疼痛与不伴基线疼痛亚组的各自预期寿命。随后我们按照前述方法，进一步计算了每个亚组中18个月前死亡及18个月后存活患者的预期寿命。最终我们将这些按基线疼痛分层的新预期寿命应用于次级决策树分析（结果未展示）。