The indicators with statistical differences are based on the above analysis. Among them, the SMI was strongly correlated with gender (P = 0.03) as well as the CIN, as shown in Fig. 1. For continuous variables, it was evident that the SMI were positively corroborated with HBC (r = 0.3) and weight (r = 0.4) and negatively with age (r =  − 0.2). In contrast, there was no correlation between SMI, NLR, and PLR, so as to the albumin and globulin. In any case, no correlation was found between CIN and SMI, NLR, and ALB content.

Correlation matrix of perioperative nutritional and inflammatory indicators

A total of 256 patients with stages 1–3 esophageal squamous cell carcinoma were ultimately entered into this study according to the inclusion criteria. Among them, 63 patients (75.4%) were female, and 193 patients (24.6%) were male, with a median age of 65 years and an age quartile of 62–69 years. Patients were scanned in detail by combining the age-adjusted Charlson Comorbidity Index (ACCI) scores [16, 17]. Combining the SMI and AGS, we could enumerate 118 cases (46.1%) in G1; 107 cases (41.8%) in the G2; and 31 cases (12.1%) in the G3, and all of them were statistically different (P < 0.001). The CAS was tangentially correlated with patient age (P = 0.03, F = 3.4), gender (P = 0.04, χ2 = 6.27, V = 0.2), alcohol consumption (P = 0.04, χ2 = 6.5, V = 0.2), the mean lymphocyte count (P < 0.01, F = 6.8), NLR (P = 0.03, F = 3.7), PLR (P = 0.04, F = 5.6), and CIN (P = 0.05, F = 3.1), as shown in Table 1 and Fig. 2.

Correlation analysis and distribution of CAS indicators. A CAS and NLR. B CAS and PLR. C CAS and CIN. D CAS gender-related SMI

The AUC, accuracy, and sensitivity of each continuous variable calculated by our plotted ROC curves are detailed in Fig. 3. The optimal cut-off value of SMI for females was 32.9, with an AUC area of 0.73, sensitivity of 45.0%, and accuracy of 44.0%, while for males was 42.3, with an AUC area of 0.70, sensitivity of 22.0%, and accuracy of 25.0%. Subsequently, we proceeded to plot the area under the curve of the ROC curve pertaining to the categorical variables of the four indicators of PLR, NLR, CIN, and CAS, and the evaluation showed that the AUC value of CAS was significantly better than the NLR (AUC = 0.53), PLR (AUC = 0.55), and CIN (AUC = 0.57).

A ROC curve of each variable and corresponding AUC value. B ROC curve and value of PLR, NLR, CIN, and CAS comprehensive scoring index

The median follow-up of patients in this study was 63 months (interquartile: 60 to 68 months), of which 192 patients were kept alive at the end of follow-up. The 5-year OS and DFS rates were calculated to be 76.9% and 86.5%, respectively.

In the results of univariate analysis, detailed in Table 2, all visual variables with P < 0.2 were enrolled for final analysis by further COX regression. Among them, positive postoperative recurrence and metastasis (HR = 2.15, CI = 1.16–4.00, P = 0.02) and CAS were investigated as independent factors affecting patients’ prognosis. However, TNM stage, chemoradiotherapy, and CAS score were independent prognostic factors for DFS (P < 0.05). Moreover, CAS is as well an individual element that influences the postoperative RFS of patients. In addition, the prognosis of patients in the “2” group (HR = 4.77, CI = 2.59–8.80, P < 0.01) and the “3” group (HR = 8.36, CI = 4.19–16.67, P < 0.01) was also worse than that of patients in the “1” group, and the hazard of death was fourfold higher in the “2” group and eightfold higher in the “3” group than in the “1” group. Patients with “3” group (HR = 4.75, CI = 1.78–12.69, P < 0.01) and “2” group (HR = 1.75, CI = 1.38–1.48, P < 0.01) were estimated to have worse DFS than patients with low-risk factors. In conclusion, the K-M curves are pertaining to SMI, AGS, and CAS, as detailed in Fig. 4.

A K-M curves of correlation analysis between SMI and survival in high-risk and low-risk groups. B K-M curves of survival correlation analysis between high-risk and low-risk groups of AGS. C CAS overall survival curve. D CAS RFS rate curve

Based on the above analysis, we continued to carry out the indicators that have significant impact on postoperative survival of patients in our study, as adjustment conditions, and then constructed relevant prediction models. The results showed that, only the score of CAS, SMI combined with AGS could be independent factors affecting the survival of patients after esophageal cancer surgery. Subsequently, the relevant model visualization forest map was then plotted. Among them, model A demonstrated that the CAS had the most significant impact on the OS rate of patients, followed by postoperative tumor metastasis or recurrence, and the least of PLR, while model B showed that SMI most markedly affected patients’ postoperative survival, and AGS had the least ability to influence, respectively, as detailed in Fig. 5.

COX analysis to construct prediction model visualization forest map. A Model A. B Model B

The C-index results of model A fluctuated from 0.7 to 0.8, and model B floated from 0.8 to 0.9. After that, calibration curves showing that the model had an excellent accuracy of calibration. Figure 6 displays that the nomogram and the predicted 5-year survival of model A and model B suggested that the two models are consistent, and the accuracy of the model A calibration is favorable. Following the process of constructing clinical decision curves, the outcomes could be derived that the prediction model A had a high net benefit throughout the interval, indicating that the model has a superior clinical application merit for the prediction of prognostic survival of esophageal cancer patients. Meanwhile, the clinical impact curve visually illustrates that the model A has superior overall net return within the extent of the threshold probability and significantly affects patient prognosis, which points to the well-predicted merit of the model, as detailed in Fig. 7.

Nomogram of predicting 1-, 3-, and 5-year survival probabilities after esophagectomy. A CAS adjustment model. B SMI combined with AGS to adjust the model. C Calibration curve after 5 years of model A. D Calibration curve after 5 years of model B

Model A-related evaluation and clinical benefit analysis. A Decision curve analysis (DCA). B Clinical impact curve (CIC)