Figure 2 shows the restricted cubic spline curve depicting the association between the ROX index and all-cause mortality in COPD patients. An L-shaped relationship was observed between the ROX index and mortality, both during hospitalization and throughout the follow-up period. To quantify this association, a simple piecewise linear model was fitted. When the ROX index was below 9.72, each unit increase in the ROX index was associated with a significant reduction in 28-day mortality risk (HR per SD, 0.84 [95% CI 0.78–0.90], P<0.001). Above a ROX index of 9.72, the risk curve plateaued, and no significant association was found between the ROX index and 28-day mortality (HR per SD, 1.01 [95% CI 0.96–1.07], P =0.628). To assess the robustness of the identified inflection point, we performed a bootstrap sensitivity analysis with 1,000 resamples, which yielded a 95% confidence interval of 8.74 to 10.35 for the threshold value (Figure S1 and Figure S2), confirming the stability of the 9.72 cutoff. Furthermore, similar associations were observed in Cox proportional hazards analyses for 3-month mortality, 1-year mortality, in-ICU mortality, and in-hospital mortality.

Figure 2 shows the restricted cubic spline curve depicting the association between the ROX index and all-cause mortality in COPD patients. An L-shaped relationship was observed between the ROX index and mortality, both during hospitalization and throughout the follow-up period. To quantify this association, a simple piecewise linear model was fitted. When the ROX index was below 9.72, each unit increase in the ROX index was associated with a significant reduction in 28-day mortality risk (HR per SD, 0.84 [95% CI 0.78–0.90], P<0.001). Above a ROX index of 9.72, the risk curve plateaued, and no significant association was found between the ROX index and 28-day mortality (HR per SD, 1.01 [95% CI 0.96–1.07], P =0.628). To assess the robustness of the identified inflection point, we performed a bootstrap sensitivity analysis with 1,000 resamples, which yielded a 95% confidence interval of 8.74 to 10.35 for the threshold value (Figure S1 and Figure S2), confirming the stability of the 9.72 cutoff. Furthermore, similar associations were observed in Cox proportional hazards analyses for 3-month mortality, 1-year mortality, in-ICU mortality, and in-hospital mortality.