3.1 General Patient Information
We collected data on 372 hospitalized patients with LF who were observed within 30 days of hospitalization period. This cohort included 6 patients with malignant tumors outside the liver, 27 patients who were admitted to hospital in a state of shock, and 7 patients with renal parenchymal injury. In addition to these patients, 35 patients with ≥ 20% missing clinical data, totaling 75 patients were excluded from the study (resulting in a 20.2% missing rate). The final analyzed patient population consisted of 297 LF patients, and only 30 of them developed HRS within 30 days of admission. The inclusion criteria encompassed demographic characteristics, relevant medical history, and admission-related examination results (Table 1).
Table 1
General information of the included patients.
Categorical variables | N (%) / Mean ± SD / Median (P25,P75) | Continuous variables | N (%) / Mean ± SD / Median (P25,P75) |
Hepatorenal syndrome | | WBC | 6.10[4.05;9.45] |
No | 267 (89.9%) | NEUT | 4.10[2.43;7.5] |
Yes | 30(10.1%) | LYM | 0.97[0.61;1.36] |
Sex | | RBC | 3.16[2.48;3.87] |
Male | 241(81.1%) | HGB | 96[77;118.5] |
Female | 56(18.9%) | MCV | 95[85.55;103.9] |
Age (years) | | MCH | 32.10[27.75;34.9] |
<55years old | 152(51.2%) | MCHC | 336[324;344] |
≥ 55years old | 145(48.8%) | PLT | 56[23.05;103.5] |
History of alcohol consumption | | K | 3.87[3.44;4.3] |
No | 248(83.5%) | Na | 135[132;138] |
Yes | 49(16.5%) | PT | 20.8[17.7;24.4] |
History of smoking | | PTA | 44[35;57] |
No | 253(85.2%) | INR | 1.78[1.46;2.21] |
Yes | 44(14.8%) | APTT | 49.6[43.75;56.4] |
Ascites | | ALB | 29.1[24.55;33.5] |
No | 248(83.5%) | GLB | 32.1[26.225;37.95] |
Yes | 49(16.5%) | TBil | 115.3[65.1;252.05] |
Gastrointestinal bleeding | | AKP | 141.5[100;202] |
No | 274(92.3%) | GGT | 67[32;156] |
Yes | 23(7.7%) | ALT | 42[27.25;95.5] |
Infection | | AST | 85[49;167] |
No | 288(97.0%) | BUN | 4.9[3.4;8.78] |
Yes | 9(3.0%) | SCr | 71[57;102] |
Spontaneous bacterial peritonitis | | UA | 227[140;349] |
No | 230(77.4%) | CysC | 1.23[0.93;1.8] |
Yes | 67(22.6%) | | |
3.2 Comparison between the Training and Validation Sets
The 297 LF patients included in the study were randomly allocated into a training set (n = 208, 70%) and a validation set (n = 89, 30%). The training set was used for developing the risk-prediction model, whereas the validation set was employed to assess the predictive efficacy of the model. In the training and validation sets, 24 and 6 cases had HRS, respectively, accounting for 11.5% and 6.7% of the corresponding sets, respectively. Statistical analyses regarding general information, clinical characteristics, and laboratory indices revealed no significant differences between the two sets, except for MCH and MCHC (P > 0.05). These results indicate that the clinical study variables were evenly distributed between the training and validation sets following group randomization .
3.3 Comparison between the HRS and Non-HRS Groups
Among the 297 LF patients, 30 (10.1%) developed HRS within 30 days of admission. Significant differences were observed between the HRS and non-HRS groups in terms of HRS, WBC, NEUT, PLT, Na, AKP, GGT, ALT, AST, SCr, BUN, UA, CysC, ascites, and SBP (P < 0.05).
3.4 Single-Factor and Multifactor Logistic Regression Analyses of the Training Set
To identify factors influencing the occurrence of HRS in LF patients, one-way logistic regression analysis was performed with the occurrence of HRS as the dependent variable, controlling for confounding factors. The results showed that the following 11 variables were influencing factors (P < 0.05): ascites, SBP, PLT, K, Na, APTT, GGT, BUN, SCr, UA, and CysC (Table 2). Multifactorial logistic stepwise regression analysis revealed ascites (P = 0.024), SBP (P = 0.048), GGT (P = 0.014), UA (P = 0.044), and CysC (P < 0.01) as independent risk factors affecting the development of HRS in LF patients.
Table 2
Results of Multifactor Logistic Regression Analysis.
Variables | β | S.E | Z | P | OR(95%CI) |
Intercept | -6.159 | 0.919 | -6.704 | < .001 | 0.002(0.000 ~ 0.013) |
Ascites | | | | | |
No | | | | | |
Yes | 1.212 | 0.538 | 2.252 | 0.024 | 3.361(1.170 ~ 9.653) |
Spontaneous bacterial peritonitis | | | | | |
No | | | | | |
Yes | 1.052 | 0.532 | 1.978 | 0.048 | 2.865(1.010 ~ 8.127) |
GGT | 0.003 | 0.001 | 2.463 | 0.014 | 1.003(1.001 ~ 1.005) |
UA | 0.003 | 0.001 | 2.010 | 0.044 | 1.003(1.001 ~ 1.006) |
CysC | 1.042 | 0.316 | 3.302 | < .001 | 2.836(1.527 ~ 5.266) |
3.5 Establishment of a Risk-Prediction Model for HRS in LF Patients
A prediction model was established based on the results of the logistic regression analysis, yielding the following formula (with GGT in u/L, UA in µmol/L, and CysC in mg/L):
Logit (P) = − 6.159 + 1.212 × ascites + 1.052 × SBP + 0.003 × GGT + 0.003 × UA + 1.042 × CysC
3.6 Visualization of the Model
A nomogram model was established using these five variables to generate a visual chart suitable for clinical application. Each indicator, such as GGT, was aligned with corresponding endpoints, and a vertical line was drawn upward to the scoring axis to determine the individual scoring value. These values were then summed to obtain the total score, which corresponded to the risk for HRS occurrence in LF patients. In this model, a high total score indicates a high HRS risk. For example (Fig. 1), consider an LF patient with ascites (26.5 points), SBP (22.5 points), 150 u/L GGT (10 points), 670 µmol/L UA (40 points), and 2 mg/L CysC (45 points). The total score of this patient would be 144 points, indicating a high risk for HRS occurrence, with a probability of > 0.6. Accordingly, medical staff should implement preventive measures against HRS in this patient.
3.7 Evaluation and Validation of the Model
3.7.1 Distinguishing ability of the model
The distinguishing ability of the model was evaluated using the ROC curve analysis. The model had an AUC of 0.877 (95% CI: 0.822–0.933) in the training set (Fig. 2A). At the optimal cutoff point of 0.077, it demonstrated high specificity (61.7%) and sensitivity (87.5%). In the validation set, its AUC was 0.828 (95% CI: 0.706–0.950) (Fig. 2B), and at the optimal cutoff point of 0.235, it showed high specificity (70.1%) and sensitivity (95.8%). These results indicate the good distinguishing ability of the model.
3.7.2 Calibration of the model
The bootstrap resampling method was employed to repeatedly sample the training and validation sets 1000 times each. Subsequently, calibration curves were plotted after validation (Fig. 3A and Fig. 3B). The fitted logistic curves of both sets closely overlapped with the standard curves, suggesting a strong agreement between the predicted and actual risks and indicating minimal prediction error. Additionally, the goodness-of-fit Hosmer-Lemeshow test yielded the following results: χ2 = 4.4172, P = 0.8177 (for the training set) and χ2 = 4.8204, P = 0.6819 (for the validation set). These results indicate that there is no significant difference between the predicted and actual observed values in both groups, demonstrating good goodness of fit.
3.7.3 DCA
DCA was employed to analyze the net benefit of the model for clinical applications. The curves for both the training and validation sets were observed to be far from the two extreme curves (Fig. 4A and Fig. 4B), namely, all the patients treated and none treated. This observation indicates that the model holds significant clinical value.