Comparison of patient baseline information according to the HGI

A total of 2605 patients with sepsis were included in the study. Table 1 presents the baseline data for the three HGI groups (Q1, Q2, Q3). Gender differences among the three groups were not statistically significant, but patients in group Q2 were significantly older than those in the other two groups. The SOFA score for patients in group Q3 was 7.14 ± 3.58, significantly higher than that of the other groups. Similarly, the SAPS II score for group Q3 was 41.89 ± 13.63, also significantly higher than those of groups Q1 and Q2. After analyzing the laboratory indicators, we found that the WBC count of group Q3 was 15.44 ± 8.52, which was significantly higher than that of group Q1 and Q2. In contrast, PLT counts, hemoglobin (HGB), and albumin levels were significantly lower in the Q3 group than in the Q1 and Q2 groups. In addition, the second group had the highest sodium concentration, while there was no significant difference in potassium levels between the three groups. Analysis of renal function indicators showed that the urea nitrogen concentration of 27.60 ± 21.87 mg/dL in group Q2 was significantly lower than that in groups Q1 and Q3, while the serum creatinine concentration of 2.04 ± 2.40 mg/dL in group Q3 was significantly higher than that in the other two groups. Finally, more patients in group Q2 had hypertension, diabetes, heart failure, and stroke compared to groups Q1 and Q3.

Table 1 Comparison of baseline information of the patients according to the HGIKaplan–Meier analysis for cumulative risk of 28-day and 365-day mortality

As illustrated in Fig. 3, a comprehensive Kaplan–Meier survival curve analysis was meticulously conducted to compare the incidence of primary outcomes among the three distinct HGI groups. The results of this detailed analysis indicated that the 28-day mortality rate in the Q1 group was significantly lower than that observed in the Q2 and Q3 groups, with these differences being statistically significant as evidenced by the log-rank test (log-rank P < 0.001; Fig. 3A). Furthermore, when examining the 365-day mortality rates, it was found that the Q3 group exhibited a markedly higher mortality rate compared to the other two groups, with these differences also being statistically significant on the log-rank test (log-rank P < 0.001; Fig. 3B).

Fig. 3

Kaplan–Meier survival analysis curve for comparing A: 28-day all-cause mortality and B: 365-day all-cause mortality between the three HGI groups

Correlation analysis of the HGI with outcome events

Using Q1 as a reference, we constructed multiple Cox proportional risk analysis models to examine the relationship between HGI and 28-day and 365-day mortality (Table 2). In the unadjusted model, the analysis showed that both Q2 and Q3 groups were significantly associated with an increased risk of 28-day mortality. The Q2 group had a hazard ratio of 1.41 (95% confidence interval: 1.10–1.82, p = 0.008), while the Q3 group had a hazard ratio of 2.55 (95% confidence interval: 1.89–3.44, p < 0.001). The Q3 group exhibited the highest risk. Subsequent analysis for 365-day mortality revealed that while the Q2 group was linked to an increased mortality risk, this association was not statistically significant. However, the Q3 group was significantly associated with higher 365-day mortality (hazard ratio = 1.59, 95% confidence interval: 1.29–1.97, p < 0.001). In Model 1 (adjusted for age and sex), both Q3 and Q2 groups were still significantly associated with an elevated risk of 28-day mortality, with Q3 having the highest risk (hazard ratio = 2.57, 95% confidence interval: 1.91–3.47, p = 0.129). Additionally, this elevated association with the risk of 28-day mortality was slightly reduced compared to that observed in the unadjusted model. In the case of the risk relationship with 365-day mortality, the analysis did not demonstrate any association with the Q2 group, while the Q3 group was significantly associated with 365-day mortality risk (hazard ratio = 1.61, 95% confidence interval: 1.31–1.99, p < 0.001). After further adjustments in model 2 (including for comorbidities such as hypertension, heart failure, and stroke), the Q2 group was found to have no associations with 28-day and 365-day mortality risk. In contrast, the Q3 group remained associated with an increased mortality risk at 28 and 365 days. However, the extent of this relationship continued to decline (28 -day mortality risk: hazard ratio = 2.34, 95% confidence interval: 1.69–3.22, p < 0.001; 365-day mortality risk: hazard ratio = 1.51, 95% confidence interval: 1.20–1.89, p < 0.001). In model 3, which was additionally adjusted for SOFA score, SAPS II score, WBC count, PLT count, and HGB, albumin, sodium, potassium, blood urea nitrogen, and serum creatinine levels, the associations of the Q3 group with 28-day and 365-day mortality risk remained stable (hazard ratio = 2.02, 95% confidence interval: 1.45–2.80, p < 0.001 and hazard ratio = 1.28, 95% confidence interval: 1.08–1.56, p = 0.033, respectively).

Table 2 Association between the HGI and posterior survival in patients with sepsis

Furthermore, Fig. 4 presents the association between HGI and mortality rates using restricted cubic splines to model the potential nonlinear relationships.Fig. 4A (28-day mortality): interpretation of HR curve: The green line represents the estimated HR as a function of HGI, with the dashed lines showing the 95% confidence interval (CI). The overall p-value indicates that the relationship between HGI and 28-day mortality is statistically significant. Additionally, the p-value for nonlinearity suggests that the relationship does not significantly deviate from linearity. Hazard ratio trend: The curve shows a positive association, implying that as HGI increases, the hazard of mortality at 28 days also increases. Specifically, higher HGI values are associated with increased 28-day mortality risk, as the hazard ratio exceeds 1 for positive HGI values.Fig. 4B (365-day mortality): interpretation of HR curve: Similar to Fig. 4A, the green line represents the estimated HR with the dashed lines indicating the 95% CI. The overall p-value confirms a significant association between HGI and 365-day mortality. The p-value for nonlinearity suggests a borderline nonlinear relationship. Hazard ratio trend: This curve also indicates a positive association, where increased HGI values are linked to higher mortality risk at 365 days. The hazard ratio rises above 1 for higher HGI values, signifying an elevated risk of mortality with higher HGI over a longer duration.

Fig. 4

Restricted cubic spline curve displaying the HGI hazard ratios of A: the 28-day mortality rate and B: 365-day mortality rate of the patients with sepsis

Analysis of mediating factors for the effect of HGI on 28-day and 365-day mortality rates

The impact of the HGI on mortality among patients with sepsis was further investigated by conducting a mediation analysis, as depicted in Fig. 5. The findings showed that the HGI potentially influenced mortality risk in patients with sepsis through its interaction with the SOFA and SAPS II scores. In particular, the SOFA score mediated 20.7% of the association between the HGI and 28-day mortality (IE = 0.004, 95% CI: 0.003–0.010; DE = 0.017, 95% CI: 0.008–0.030, Fig. 5A) and 31.9% of the relationship with 365-day mortality (IE = 0.005, 95% CI: 0.003–0.010; DE = 0.010, 95% CI: 0.008–0.020, Fig. 5C). Moreover, mediation by the SAPS II score accounted for 24.5% of the correlation between the HGI and 28-day mortality (IE = 0.005, 95% CI: 0.003–0.010; DE = 0.016, 95% CI: 0.007–0.030, Fig. 5B) and 50.5% of the association with 365-day mortality (IE = 0.007, 95% CI: 0.005–0.010; DE = 0.007, 95% CI: 0.006–0.020, Fig. 5D). Thus, the SOFA and SAPS II scores are comprehensive indicators with metrics for evaluating the circulatory, respiratory, urinary, and hematological systems. Although initial analyses of contrasting indicators such as WBC and PLT counts demonstrated no significant differences, significant disparities were evident in the comprehensive assessments provided by the SOFA and SAPS II scores. Consequently, we propose that the influence of the HGI on sepsis extends beyond a single metric, underlining the necessity of a multifaceted systemic intervention.

Fig. 5

Analysis of the mediation effects of the SOFA and SAPS II scores on the interaction between the HGI and survival in patients with sepsis. The effects of A the SOFA score and B the SAPS II score on 28-day mortality in patients with sepsis. The effects of C the SOFA score and D the SAPS II score on 365-day mortality in patients with sepsis

Subgroup analysis

Additionally, we assessed patient outcomes by conducting subgroup analyses of mortality risk based on comorbidities such as hypertension, diabetes, heart failure, acute kidney injury, and stroke. In the subgroup analysis with 28-day mortality as the end point (Fig. 6), the mortality risk of the patients with sepsis accompanied by chronic conditions including hypertension and diabetes exhibited a close association with the Q2 and Q3 groups, indicating that higher HGI values in these subgroups were correlated with increased mortality risk.

Fig. 6

Subgroup analysis of chronic conditions with 28-day mortality as the outcome event

In the case of patients with sepsis but no other chronic diseases, our analysis indicated an elevated mortality risk in the Q3 group, consistent with the previously mentioned results. In the subgroup analysis with 365-day mortality as the end point (Fig. 7), the mortality risk of patients with sepsis and chronic conditions such as hypertension and diabetes was strongly associated with group Q3, but not with group Q2. In the patients with sepsis but no additional chronic diseases, the mortality risk was similarly increased in the Q3 group, aligning with the findings discussed above.

Fig. 7

Subgroup analysis of chronic conditions with 365-day mortality as the outcome event