Novel nomogram based on preoperative inflammatory indicators and postoperative clinicopathological features for predicting metachronous liver metastasis of colorectal cancer

Abstract

Background

The occurrence of metachronous liver metastasis (MLM) after primary resection of colorectal cancer (CRC) significantly worsens patient prognosis. Identification of patients at high risk of MLM would enable closer monitoring and more timely intervention. We therefore aimed to develop and validate a novel nomogram to predict MLM in patients with CRC, based on preoperative inflammatory indicators and postoperative clinicopathological features.

Methods

Data from 505 patients with CRC who underwent radical resection of the primary tumor at the First Affiliated Hospital of Zhengzhou University between August 2018 and August 2022 were retrospectively analyzed. The patients were divided into training (n = 289) and validation (n = 216) cohorts. Independent risk factors for MLM were identified using least absolute shrinkage and selection operator and multivariate logistic regression analyses of the training cohort and used to develop a novel nomogram. To quantify the incremental predictive value of inflammatory markers, three models were constructed using logistic regression: a pathological model (T stage, N stage, vascular invasion, mismatch repair status, and carcinoembryonic antigen), an inflammatory model (neutrophil-to-lymphocyte ratio, platelet-to-lymphocyte ratio, and lymphocyte-to-monocyte ratio), and a combined nomogram including all eight predictors. The discriminative performance of the three models was compared using area under the receiver operating characteristic curve (AUC), the DeLong test, calibration curves, decision curve analysis, and reclassification metrics (net reclassification improvement and integrated discrimination improvement). Sensitivity analyses modeling inflammatory markers as continuous variables were performed.

Results

A preoperative carcinoembryonic antigen (CEA) level > 5 ng/mL, neutrophil-to-lymphocyte ratio (NLR) > 2.35, platelet-to-lymphocyte ratio (PLR) > 127.29, and lymphocyte-to-monocyte ratio (LMR) > 3.80, and the postoperative clinicopathological features T stage, N stage, vascular invasion, and mismatch repair (MMR) proficient were identified as independent risk factors for MLM of CRC and used to develop the nomogram. In the three-model comparison, the combined nomogram achieved the highest discriminative performance (training AUC 0.937, validation AUC 0.777), significantly outperforming the pathological model (training AUC 0.911, DeLong P = 0.012; validation AUC 0.735, DeLong P = 0.037) and the inflammatory model (training AUC 0.838, DeLong P < 0.001; validation AUC 0.706, DeLong P = 0.021). Calibration curves and decision curve analysis demonstrated that the combined model had the best calibration and the highest net clinical benefit.

Conclusions

The preoperative inflammatory indicators NLR, PLR, and LMR were identified as independent risk factors for MLM. The three-model comparison demonstrated that the combined nomogram significantly outperformed both the pathological-only and inflammatory-only models in discrimination, calibration, and clinical net benefit, supporting the complementary predictive value of inflammatory markers. The novel nomogram developed and validated in this study demonstrated good discriminative ability and accuracy in predicting MLM in patients with CRC, although external validation in larger multi-center cohorts is required.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1186/s12893-026-04034-4.

Background

Colorectal cancer (CRC) is the third most common malignant tumor worldwide and has the second highest mortality rate [1]. Liver metastasis is one of the main causes of mortality in patients with CRC [2]. Synchronous liver metastases (SLM) refer to liver metastases discovered at the time or before primary CRC is definitively diagnosed, while metachronous liver metastases (MLM) refer to those occurring after the curative resection of CRC, according to Chinese guidelines [3]. SLM are typically detected by preoperative imaging and treated accordingly. MLM occurs in 15–25% of patients with CRC after radical resection of the primary tumor [3]; the five-year survival rate of these patients is less than 5%, which seriously affects the overall prognosis of patients with CRC [4, 5]. Early identification of patients at a high risk of MLM may allow more effective intervention and comprehensive treatment, which could greatly improve their prognosis [6].

At present, imaging is the main method of detecting liver metastasis in patients with CRC; however, early diagnoses cannot be made with conventional imaging techniques such as computed tomography and magnetic resonance imaging. Although positron emission tomography-computed tomography is relatively sensitive, it is not widely used owing to its high cost [7]. Therefore, it is crucial to develop a simple, economical, and effective method for the early identification of liver metastasis in patients with CRC.

Inflammation plays an essential role in the regulation of the tumor microenvironment, promoting tumor cell proliferation and enhancing tumor invasion, metastasis, and angiogenesis [8, 9]. Inflammatory markers can be detected using routine blood tests that are simpler, faster, and cheaper than imaging. Previous studies have shown that various preoperative inflammatory indicators, such as the neutrophil-to-lymphocyte ratio (NLR), platelet-to-lymphocyte ratio (PLR), and lymphocyte-to-monocyte ratio (LMR), have prognostic value in a variety of solid tumors including CRC [10]. In addition, the preoperative alkaline phosphatase-to-lymphocyte ratio (ALR) and gamma-glutamyl transpeptidase-to-lymphocyte ratio (GLR) can predict microvascular invasion in hepatocellular carcinoma [11, 12]. However, few studies have evaluated the ability of the preoperative NLR, PLR, LMR, ALR, and GLR to predict MLM in CRC. We therefore tested all five markers, recognizing that some may not demonstrate predictive value in this setting.

The prognosis of patients with CRC is mainly evaluated clinically using TNM staging, as developed and maintained by the Union for International Cancer Control/American Joint Committee on Cancer; however, this staging system has certain limitations [13]. Patients with CRC and liver metastases are highly diverse and complex, and even patients with the same tumor stage and pathological type can differ significantly in terms of treatment response and survival [14]. Additional postoperative clinicopathological features include vascular invasion, nerve invasion, and mismatch repair (MMR) status; however, few reports have used these features to predict MLM of CRC.

In this study, we aim to assess the predictive value of the preoperative NLR, PLR, LMR, ALR, and GLR for MLM of CRC and to combine the inflammatory indicators that demonstrate predictive value with postoperative clinicopathological features to develop a novel nomogram for predicting MLM in patients with CRC. We further compare the combined nomogram against pathological-only and inflammatory-only models to quantify the incremental predictive value of each predictor category.

Methods

Patients

The clinical data of patients who underwent radical CRC resection at the First Affiliated Hospital of Zhengzhou University between August 2018 and August 2022 were retrospectively analyzed. This study was conducted in accordance with the principles outlined in the Declaration of Helsinki and approved by the Research Ethics Committee of the First Affiliated Hospital of Zhengzhou University. Informed consent was obtained from all patients. Although different definitions of MLM exist [15–17], we defined MLM as liver metastases occurring after the curative resection of CRC, in accordance with Chinese guidelines [3]. All enrolled patients were followed up for three years, during which contrast-enhanced computed tomography or magnetic resonance imaging was performed at regular intervals to detect metastases, in compliance with the guidelines [18].

The inclusion criteria were as follows: (1) aged ≥ 18 years, (2) primary colorectal tumor with a pathological diagnosis of adenocarcinoma, (3) radical resection of the primary tumor performed, (4) only one primary malignant tumor, (5) no metastasis before resection, (6) complete postoperative pathological and follow-up data available, and (7) postoperative chemotherapy or radiotherapy administered in accordance with the guidelines of the Chinese Society of Clinical Oncology. The exclusion criteria were as follows: (1) adjuvant therapy administered before resection, (2) preoperative hematological or infectious diseases, (3) SLM, (4) multiple tumors, (5) postoperative distant metastases other than liver metastasis, and (6) histopathological results showing positive margins.

Clinical information

Clinical data collected included information on age, sex, liver metastasis, tumor site, tumor size, histological type, differentiation degree, T stage, N stage, lymph nodes examined (LNE), vascular invasion, nerve invasion, MMR status, preoperative carcinoembryonic antigen (CEA) levels, and cancer antigen (CA) 19–9 levels, as well as preoperative neutrophil, monocyte, lymphocyte, and platelet counts and gamma-glutamyl transpeptidase levels to calculate the NLR, GLR, ALR, PLR, and LMR. The NLR was calculated as neutrophils (10⁹/L)/lymphocytes (10⁹/L), GLR as gamma-glutamyl transpeptidase (U/L)/lymphocytes (10⁹/L), PLR as platelets (10⁹/L)/lymphocytes (10⁹/L), ALR as alkaline phosphatase (U/L)/lymphocytes (10⁹/L), and LMR as lymphocytes (10⁹/L)/monocytes (10⁹/L). Patients were classified into three groups based on age (≤ 60, 60–75, and > 75 years); tumor site was classified as right colon (cecum, ascending colon, hepatic flexure, and transverse colon), left colon (splenic flexure, descending colon, and sigmoid colon), or rectum; tumor size was classified as ≤ 5 or > 5 cm; histology type was classified as adenocarcinoma (not otherwise specified) or other adenocarcinoma (special histologic subtypes of adenocarcinoma); and degree of differentiation was classified as I (well differentiated), II (moderately differentiated), III (poorly differentiated), or IV (undifferentiated). The T stage, N stage, LNE, vascular invasion, nerve invasion, and MMR status were also determined according to postoperative pathological data.

Determination of preoperative inflammatory indicator cut-off values

The final blood routine and biochemical test results before surgery were used in the analysis. The optimal cut-off values for the NLR, GLR, ALR, PLR, and LMR were determined using receiver operating characteristic (ROC) curves and Youden’s index.

Statistical analysis

Continuous variables are reported as the mean ± standard deviation or median (first quartile, third quartile). Original data were analyzed using SPSS software version 26.0 (IBM Corporation, Armonk, NY, USA). Continuous variables were converted into binary variables based on the reference range or cut-off value. Least absolute shrinkage and selection operator (LASSO) regression was used to determine candidate risk factors for MLM using R software version 3.6.3 (R Foundation for Statistical Computing, Vienna, Austria). Non-zero coefficient features were selected from the LASSO regression analysis. Because MLM occurrence was treated as a dichotomous variable in our analysis, we applied multivariate logistic regression to identify independent risk factors, in conjunction with the results of the LASSO regression analysis, using a stepwise method. Events per variable (EPV) was calculated to assess the adequacy of the sample size relative to the number of model parameters. A nomogram was developed from these factors using R software version 3.6.3. The variance inflation factor was calculated to measure the multicollinearity of the regression models. The C-index with 1000 bootstrap samples was used to quantify the discrimination of the nomogram. Calibration and ROC curves were used to measure the accuracy of the nomogram. Decision curve analysis was performed to evaluate the clinical value and net benefits of the nomogram.

To further quantify the incremental predictive value of the inflammatory markers beyond the established pathological predictors and to compare the relative contributions of pathological and inflammatory predictors, three logistic regression models were constructed: (1) a pathological model including T stage, N stage, vascular invasion, MMR status, and CEA; (2) an inflammatory model including NLR, PLR, and LMR; and (3) a combined model (the nomogram) including all eight predictors. The discriminative performance of each model was assessed by ROC curves and AUCs, and pairwise comparisons of AUCs were performed using the DeLong test in both the training and validation cohorts. Calibration of each model was assessed visually using calibration curves, and clinical utility was assessed using decision curve analysis. Reclassification improvement of the nomogram over each reference model (pathological and inflammatory) was quantified using continuous net reclassification improvement (NRI) and integrated discrimination improvement (IDI), with 95% confidence intervals obtained by 1000 bootstrap resamples.

As a sensitivity analysis to assess the robustness of the data-driven cut-off values, NLR, PLR, and LMR were modeled as continuous variables using restricted cubic splines with three knots in multivariable logistic regression, and the results were compared with those of the binary cut-off model.

Results

Basic characteristics

A total of 505 patients with an average age of 67 (range, 27–85) years were ultimately included in the study. The patients were divided into two cohorts: training, which included patients who underwent resection between August 2018 and August 2020 (n = 289); and validation, which included patients who underwent resection between August 2020 and August 2022 (n = 216). The baseline characteristics of the patients in the two cohorts are presented in Table 1. In the training and validation cohorts, 69 and 57 patients developed MLM, respectively. Several baseline characteristics differed significantly between the cohorts (vascular invasion and tumor site, P < 0.001; pN stage, P = 0.006; platelets, P = 0.003; histological type, P = 0.040), which may be attributed to the temporal separation of enrollment, as the validation cohort was enrolled during a later period with gradual changes in clinical practice and patient selection.

Table 1.

Clinical characteristics of patients in the two cohorts

Characteristic	Training cohort	Validation cohort	P-value
	(n = 289)	(n = 216)
Age (years)	69.20 ± 13.49	67.52 ± 15.23	0.191
Sex			0.869
Male	137 (47.4%)	104 (48.1%)
Female	152 (52.6%)	112 (51.9%)
Liver metastasis			0.518
Yes	69 (23.9%)	57 (26.4%)
No	220 (76.1%)	159 (73.6%)
Tumor site			< 0.001
Left colon	76 (26.3%)	16 (7.4%)
Right colon	103 (35.6%)	102 (47.2%)
Rectum	110 (38.1%)	98 (45.4%)
Tumor size (mm)	35.00 (21.00, 54.00)	37.00 (21.00, 55.00)	0.618
Histological type			0.040
Adenocarcinoma (NOS)	188 (65.1%)	159 (73.6%)
Other adenocarcinoma	101 (34.9%)	57 (26.4%)
Differentiation degree			0.254
I	31 (10.7%)	18 (8.3%)
II	221 (76.5%)	178 (82.4%)
III	31 (10.7%)	19 (8.8%)
IV	6 (2%)	1 (0.5%)
pT			0.137
T1/T2	125 (43.2%)	108 (50%)
T3	119 (41.2%)	86 (39.8%)
T4	45 (15.6%)	22 (10.2%)
pN			0.006
N0	173 (59.9%)	102 (47.2%)
N1	87 (30.1%)	75 (34.7%)
N2	29 (10.0%)	39 (18.1%)
LNE	17 (14, 21)	13.00 (12, 20)	0.058
Vascular invasion			< 0.001
Yes	69 (23.9%)	87 (40.3%)
No	220 (76.1%)	129 (59.7%)
Nerve invasion			0.263
Yes	147 (50.9%)	99 (45.8%)
No	142 (49.1%)	117 (54.2%)
MMR status			0.578
dMMR	152 (52.6%)	119 (55.1%)
pMMR	137 (47.4%)	97 (44.9%)
CEA (ng/mL)	5.63 (1.91, 8.19)	4.16 (1.13, 6.15)	0.078
CA 19–9 (U/mL)	10.64 (6.55, 19.72)	13.22 (8.16, 20.48)	0.226
GGT (U/L)	43.00 (25.00, 87.00)	46.00 (27.00, 93.00)	0.407
ALP (U/L)	80.61 (65.00, 113.36)	71.00 (59.00, 113.30)	0.189
Platelets (× 109/L)	206.00 (156.50, 261.00)	235.00 (176.00, 301.00)	0.003
Monocytes (× 109/L)	0.46 (0.36, 0.60)	0.57 (0.32, 0.84)	0.042
Neutrophils (× 109/L)	3.59 (2.66, 4.83)	3.82 (2.63, 6.17)	0.268
Lymphocytes (× 109/L)	1.41 (1.00, 1.88)	1.35 (0.86, 1.72)	0.307
NLR	1.87 (1.42, 2.56)	1.74 (1.48, 2.82)	0.679
GLR	36.73 (26.75, 51.84)	48.50 (29.35, 60.92)	0.005
ALR	51.05 (39.92, 67.67)	58.86 (43.83, 104.60)	0.012
PLR	127.89 (99.44, 160.16)	140.39 (115.14, 182.41)	0.008
LMR	4.35 (3.23, 5.26)	4.11 (2.73, 5.57)	0.315

LNE Lymph nodes examined, MMR Mismatch repair, dMMR mismatch repair deficient, pMMR mismatch repair proficient, CEA Carcinoembryonic antigen, CA Cancer antigen, GGT Gamma-glutamyl transpeptidase, ALP Alkaline phosphatase, NLR Neutrophil-to-lymphocyte ratio, GLR Gamma-glutamyl transpeptidase-to-lymphocyte ratio, ALR Alkaline phosphatase-to-lymphocyte ratio, PLR Platelet-to-lymphocyte ratio, LMR Lymphocyte-to-monocyte ratio

Events per variable

With 69 events (MLM cases) in the training cohort and approximately 10 degrees of freedom in the final model (T stage 2 df, N stage 2 df, vascular invasion 1 df, MMR status 1 df, CEA 1 df, NLR 1 df, PLR 1 df, LMR 1 df), the EPV was 6.9, which is below the conventional threshold of 10, indicating potential overfitting and suggesting that the regression coefficient estimates may be unstable.

Optimal cut-off values of preoperative inflammatory indicators in the training cohort

The optimal cut-off values of the preoperative NLR, PLR, and LMR for predicting MLM, as determined by ROC curve analysis, were 2.35 (area under the curve [AUC] = 0.698, 95% confidence interval [CI]: 0.614–0.782, P < 0.001), 127.29 (AUC = 0.682, 95% CI: 0.604–0.760, P < 0.001), and 3.80 (AUC = 0.744, 95% CI: 0.672–0.817, P < 0.001), respectively (Fig. 1, Table 2). Among the five preoperative inflammatory indicators tested, ALR (AUC 0.519, 95% CI: 0.441–0.598, P = 0.632) and GLR (AUC 0.545, 95% CI: 0.466–0.624, P = 0.260) did not differ meaningfully from chance and were not considered for further model development, consistent with their exclusion by LASSO regression.

Fig. 1.

Receiver operating characteristic curves for the prediction of metachronous liver metastasis by inflammatory indicators. NLR, neutrophil-to-lymphocyte ratio; ALR, alkaline phosphatase-to-lymphocyte ratio; GLR, gamma-glutamyl transpeptidase-to-lymphocyte ratio; PLR, platelet-to-lymphocyte ratio; LMR, lymphocyte-to-monocyte ratio

Table 2.

Prediction of metachronous liver metastasis by preoperative inflammatory indicators

Indicator	AUC	95% CI	Sensitivity	Specificity	Cut-off value	P-value
NLR	0.698	0.614–0.782	0.638	0.782	2.35	< 0.001
ALR	0.519	0.441–0.598	/	/	/	0.632
PLR	0.682	0.604–0.760	0.783	0.573	127.29	< 0.001
GLR	0.545	0.466–0.624	/	/	/	0.260
LMR	0.744	0.672–0.817	0.727	0.681	3.80	< 0.001

AUC Area under the curve, CI Confidence interval, NLR Neutrophil-to-lymphocyte ratio, ALR Alkaline phosphatase-to-lymphocyte ratio, PLR Platelet-to-lymphocyte ratio, GLR Gamma-glutamyl transpeptidase-to-lymphocyte ratio, LMR Lymphocyte-to-monocyte ratio

Independent risk factors for MLM in the training cohort

Among the 17 candidate parameters, LASSO regression analysis identified preoperative CEA level, NLR, PLR, LMR, T stage, N stage, MMR status, and vascular invasion as risk factors for MLM (Fig. 2). Multivariate logistic regression identified T stages 3 and 4, N stages 1 and 2, vascular invasion, MMR proficient (pMMR), preoperative CEA level > 5.0 ng/mL, NLR > 2.35, PLR > 127.29, and LMR > 3.80 as independent risk factors for MLM in patients with CRC (Table 3). The variance inflation factor of all risk factors was < 2.5; therefore, there was no multicollinearity in the regression model. Of note, several odds ratios had wide confidence intervals (e.g., N2: OR 21.26, 95% CI 3.57–126.51; T4: OR 13.63, 95% CI 3.40–54.56), which reflects the limited number of events and reinforces the overfitting concern.

Fig. 2.

Candidate risk factors of metachronous liver metastasis analyzed using LASSO regression. A LASSO coefficient profile. Screening included 17 clinical variables; a coefficient profile plot was created against the log(lambda) sequence. B The optimal penalty parameter (λ) in the LASSO model determined by tenfold cross-validation and the minimum criteria in the training cohort. To make the model more concise and user-friendly, we chose lambda.1se over lambda.min. When λ = lambda.1se (0.036), LASSO regression retains eight non-zero coefficient independent variables. LASSO, least absolute shrinkage and selection operator

Table 3.

Multivariate regression analysis of metachronous liver metastasis in the training cohort

Variable	OR (95% CI)	P-value
pT
T1/T2	Reference
T3	5.163 (1.903–14.004)	0.001
T4	13.625 (3.403–54.560)	< 0.001
pN
N0	Reference
N1	2.758 (1.140–6.676)	0.024
N2	21.259 (3.573–126.508)	0.001
Vascular invasion
No	Reference
Yes	2.794 (1.042–7.494)	0.041
MMR status
dMMR	Reference
pMMR	2.668 (1.035–6.876)	0.042
CEA (ng/mL)
≤ 5	Reference
> 5	9.359 (2.585–33.881)	0.001
NLR
≤ 2.35	Reference
> 2.35	4.772 (1.825–12.477)	0.001
PLR
≤ 127.29	Reference
> 127.29	4.091 (1.617–10.349)	0.003
LMR
≤ 3.80	Reference
> 3.80	3.785 (1.232–11.629)	0.020

OR Odds ratio, CI Confidence interval, MMR Mismatch repair, dMMR mismatch repair deficient, pMMR mismatch repair proficient, CEA Carcinoembryonic antigen, NLR Neutrophil-to-lymphocyte ratio, PLR Platelet-to-lymphocyte ratio, LMR Lymphocyte-to-monocyte ratio

Development of a novel nomogram and three-model comparison: pathological, inflammatory, and combined models (nomogram)

Based on the results of the multivariate logistic regression analysis, T stage, N stage, vascular invasion, pMMR, CEA level, NLR, PLR, and LMR were used to develop a nomogram for predicting the risk of MLM in patients with CRC (Fig. 3). The apparent C-index of the training cohort was 0.934 (0.902–0.966) and that of the validation cohort was 0.777 (0.703–0.850). We performed 1000 iterations bootstrap validation on the training cohort to further quantify and correct for overfitting-induced optimism. Bootstrap correction revealed a modest optimism of 0.014 for the C-index, yielding a bias-corrected C-index of 0.919. The bootstrap-corrected calibration slope was 0.857, which is below 1, indicating that the regression coefficients are somewhat overfit and the linear predictor may be too extreme. This finding is consistent with the EPV of 6.9 and warrants a cautious interpretation of the coefficient magnitudes. Detailed bootstrap performance metrics are shown in Supplementary Table S1.

Fig. 3.

Nomogram for predicting the risk of MLM in the training cohort. MLM, metachronous liver metastasis; MMR, mismatch repair; dMMR, mismatch repair deficient; pMMR, mismatch repair proficient; CEA, carcinoembryonic antigen; NLR, neutrophil-to-lymphocyte ratio; PLR, platelet-to-lymphocyte ratio; LMR, lymphocyte-to-monocyte ratio

The discriminative performance of the three models is shown in Fig. 4 and Supplementary Table S2. In the training cohort, the combined model (nomogram) achieved the highest AUC (0.937, 95% CI: 0.907–0.968), followed by the pathological model (0.911, 95% CI: 0.873–0.948) and the inflammatory model (0.838, 95% CI: 0.787–0.889). The DeLong test showed that the combined model significantly outperformed both the pathological model (P = 0.012) and the inflammatory model (P < 0.001). In the validation cohort, the combined model maintained the highest AUC (0.777, 95% CI: 0.703–0.850), significantly better than the pathological model (0.735, 95% CI: 0.661–0.809; DeLong P = 0.037) and the inflammatory model (0.706, 95% CI: 0.633–0.779; DeLong P = 0.021).

Fig. 4.

Comparison of receiver operating characteristic curves for the pathological model, inflammatory model, and combined nomogram in the training and validation cohorts

Calibration curves for all three models are shown in Fig. 5. In both cohorts, the combined model demonstrated good agreement between predicted and observed probabilities across the range of predicted risk. Decision curve analysis (Fig. 6) showed that the combined model provided the greatest net benefit across a clinically relevant range of threshold probabilities (approximately 0–30% in the training cohort and 0–25% in the validation cohort), surpassing both the pathological model and the inflammatory model. This demonstrates the superior clinical utility of the combined nomogram.

Fig. 5.

Comparison of calibration curves for the pathological model, inflammatory model, and combined nomogram in the training and validation cohorts

Fig. 6.

Comparison of decision curve analysis for the pathological model, inflammatory model, and combined nomogram in the training and validation cohorts

Reclassification metrics quantifying the added value of the nomogram over each reference model are presented in Supplementary Table S3. Compared with the pathological model, the continuous NRI was 0.836 (95% CI: 0.593–1.061, P < 0.001) in the training cohort and 0.353 (95% CI: 0.145–0.553, P < 0.001) in the validation cohort. The corresponding IDI was 0.087 (95% CI: 0.048–0.122, P < 0.001) and 0.126 (95% CI: 0.079–0.179, P < 0.001). Compared with the inflammatory model, the nomogram yielded even greater reclassification improvement: continuous NRI of 1.141 (95% CI: 0.917–1.347, P < 0.001) and IDI of 0.251 (95% CI: 0.188–0.313, P < 0.001) in the training cohort, and NRI of 0.357 (95% CI: 0.099–0.637, P = 0.013) and IDI of 0.095 (95% CI: 0.007–0.183, P = 0.034) in the validation cohort. These results indicate that the nomogram provides statistically significant but modest reclassification improvement over both reference models in both cohorts.

Sensitivity analysis using continuous inflammatory markers

In the sensitivity analysis modeling NLR, PLR, and LMR as continuous variables using restricted cubic splines with three knots, the model C-index was 0.935 versus 0.937 for the binary cut-off model. The likelihood ratio test comparing the continuous RCS model with the binary model yielded P = 0.772, suggesting that the binary cut-off model provides adequate fit. NLR showed significant non-linearity when modeled continuously (chi2 = 10.52, df = 2, P = 0.005), while PLR (chi2 = 2.49, df = 2, P = 0.288) and LMR (chi2 = 7.36, df = 2, P = 0.025) did not consistently show strong evidence of non-linearity. Detailed results are provided in Supplementary Table S4.

Discussion

The occurrence of MLM is a major cause of poor prognosis in patients with CRC; therefore, its early prediction is beneficial for guiding clinical diagnosis and treatment decisions. In this study, we used retrospective data to identify independent risk factors for MLM and established a convenient nomogram that integrates preoperative inflammatory indicators and postoperative clinicopathological features.

The overall incidence of MLM in this study was 25.0% (126/505), which is higher than the 15–25% reported previously [19], which may be attributed to the inclusion of a higher proportion of patients with advanced-stage disease in our cohort, as patients with stage IV CRC at initial diagnosis were excluded but those with high-risk stage II-III disease were retained. Of the five preoperative inflammatory indicators assessed, only NLR, PLR, and LMR demonstrated predictive value for MLM of CRC, whereas ALR and GLR showed no discriminative ability. These findings are consistent with the established roles of NLR, PLR, and LMR in CRC prognosis [10]. With the fact that ALR and GLR showed no discriminative value (both P > 0.05), we excluded them and focused on NLR, PLR, and LMR. The elevated preoperative NLR, PLR, and LMR in patients with MLM may be related to the following aspects: first, neutrophils are involved in all stages of tumor development [20] and can increase tumor cell attachment to endothelial monolayers [21], suppress intraluminal natural killer cell-mediated tumor cell clearance, and enhance the extravasation of disseminated carcinoma cells [22]. The liver is the first site of colorectal venous drainage, and the hepatic sinusoids, acting as blood filters, are generally considered the organs most susceptible and earliest invaded by CRC. Gordon-Weeks et al. [23] found that neutrophils can promote hepatic metastasis growth through fibroblast growth factor 2-dependent angiogenesis in mice. Second, lymphocytes play an important role in the immune response to the tumor by promoting the death of cytotoxic cells and inhibiting the proliferation and migration of tumor cells [24]; thus, lymphocyte counts can reflect the extent of the anti-tumor response. Decreased lymphocyte numbers indicate decline in the immune system, which makes it easier for tumor cells to metastasize. Third, tumor metastasis involves separation from the primary tumor, vascular invasion, transport through blood, adhesion to the capillary walls of distant organs, extravascular migration, and proliferation at new sites; platelets are involved in almost every step of this process [25]. Fourth, monocytes can inhibit the immune response to the tumor, enabling cancer cells to evade immunosurveillance and thus promote tumor growth [26]. Wilcox et al. [27] found that inflammatory cytokines in the tumor microenvironment can promote monocyte proliferation, which can drive the suppression of host anti-tumor immunity and promote tumor angiogenesis. Hu et al. [28] identified an association between preoperative peripheral blood monocyte counts and liver metastasis in patients with CRC. Increases in the NLR, PLR, and LMR of patients with CRC before surgery may indicate rapid tumor development, increased invasiveness, and decreased immune response, thereby increasing the probability of postoperative liver metastasis. The higher LMR identified as an independent risk factor for MLM in this study may appear counterintuitive compared with some previous prognostic studies, which associated higher LMR with better overall survival [29, 30]; however, some studies showed contrary clinical outcomes [31, 32]. We believe that the role of LMR may be highly context-dependent, and the inconsistent directionality with previous reports can be attributed to three key factors: our study’s focus on preoperative MLM occurrence as the predictive endpoint, distinct from most previous LMR studies that investigated post-treatment survival outcomes; our cohort’s enrolment of early-stage patients for initial MLM risk stratification, while most existing reports focused on advanced or metastatic disease; and finally, the substantial variations in optimal LMR cut-off values across studies due to heterogeneous cohort characteristics and statistical methods.

The three-model comparison provided quantitative evidence for the incremental predictive value of inflammatory markers beyond pathological features. The combined nomogram significantly outperformed the pathological model in both cohorts (DeLong P = 0.012 training; P = 0.037 validation), and the positive NRI and IDI values confirmed that the addition of NLR, PLR, and LMR improved risk reclassification. Notably, the inflammatory model alone (AUC 0.838 training, 0.706 validation) was substantially inferior to the pathological model (AUC 0.911 training, 0.735 validation), indicating that inflammatory markers alone cannot substitute for established pathological risk factors. However, the combination of both sets of predictors in the nomogram achieved the best performance across all metrics (discrimination, calibration, and net clinical benefit), demonstrating that pathological and inflammatory markers capture complementary prognostic information. This pattern is consistent with the understanding that tumor biology is jointly determined by intrinsic tumor characteristics (reflected in pathological features) and the host systemic inflammatory response (reflected in inflammatory markers). The non-significant categorical NRI observed in the validation cohort likely reflects the limited number of events and the coarse risk categories used, rather than a lack of incremental value, as the continuous NRI and IDI were both statistically significant.

In this study, the training cohort demonstrated significantly better performance metrics than the validation cohort (C-index 0.934 vs. 0.777, AUC 0.937 vs. 0.777). We attribute this gap to several factors. First, overfitting is likely a major contributor, as indicated by the EPV of 6.9 (below the recommended threshold of 10), the bootstrap-corrected calibration slope of 0.857, and the wide confidence intervals for several odds ratios in Table 3. These findings suggest that the model may have captured noise specific to the training data rather than generalizable signal. Second, the validation cohort had a more adverse prognostic profile: vascular invasion was higher (40.3% vs. 23.9%, P < 0.001), node-positivity was higher (N1 + N2: approximately 53% vs 40%, P = 0.006), and the mean age was lower (67.52 vs 69.20 years, P = 0.191). These differences indicate that the validation cohort contained a more heterogeneous and clinically challenging patient population, which partially attenuated the model's performance. Additionally, we cannot exclude the potential impact of temporal changes in clinical practice: patients in the validation cohort were enrolled in a later period, during which the diagnostic criteria and therapeutic management for MLM may have been gradually updated, thus introducing minor variations in outcome assessment. Nevertheless, the C-index in the validation cohort indicates the favorable discriminative ability of our nomogram, which supports its potential clinical utility for individualized MLM risk prediction. Several studies have used nomograms to predict LM [33–35] and demonstrated their good predictive value; however, few studies have included both inflammatory indicators and pathological features, especially for MLM prediction. The nomogram developed in the present study was aimed at facilitating perioperative clinical decision-making: the pathological variables can be obtained postoperatively, thus allowing clinicians to finalize the risk assessment after surgery to guide subsequent surveillance and treatment. We hope that it can facilitate risk-stratified postoperative surveillance; for instance, patients identified as high-risk for MLM could be assigned to more intensive imaging follow-up (e.g., quarterly contrast-enhanced abdominal imaging) rather than adhering to the conventional semi-annual schedule, while low-risk patients could be spared unnecessary intensive testing to reduce clinical burden. Additionally, high-risk patients may be considered for tailored adjuvant therapy to reduce the risk of MLM.

The present study has several limitations. First, the relatively short 3-year follow-up period of this study may have resulted in the exclusion of a small number of late-onset MLM events, and longer follow-up in future independent studies would help to further confirm the true incidence of MLM. Second, most patients in this study received standardized adjuvant treatment, compliant with clinical guidelines. Differences in chemotherapy regimens or responses are not included in this study, which may have potentially affected our estimation of the MLM risk. We hope to further explore the relationship between MLM risk and differences in chemotherapy regimens or responses in future studies. Third, although the nomogram prediction model developed in this study included eight indicators, Cox regression, which was not applied in this study, may identify more risk factors. Indeed, many biomarkers including inflammation- and nutrition-related indicators [36–38] have good predictive value and clinical applicability for the prognosis of CRC. This study did not include all these indicators, necessitating further research. Fourth, the determination of cut-off values for NLR, PLR, and LMR using ROC/Youden-based, data-driven thresholds in our cohort may limit the nomogram's generalizability to external patient populations; further studies are needed to validate these thresholds in large, independent multi-center cohorts. Moreover, the in-sample threshold selection likely contributes to the apparent optimism in discrimination observed in the training cohort. Fifth, competing events such as non-hepatic recurrence or cancer-related mortality may potentially impact MLM assessment. Sixth, the EPV of 6.9 and the bootstrap-corrected calibration slope of 0.857 suggest that the regression coefficients may be overfitted; future studies with larger sample sizes should consider applying shrinkage or penalized estimation techniques to obtain more stable coefficient estimates. As the present study was a single-center retrospective study, the results need to be validated and the applicability of the developed nomogram should be confirmed through a multi-center study with a larger sample size.

Conclusion

This study established a novel nomogram, comprising preoperative inflammatory indicators and postoperative clinicopathological features, to predict the risk of MLM in patients with CRC. Of the five inflammatory markers screened, only NLR, PLR, and LMR demonstrated predictive value, while ALR and GLR showed no discriminative ability. The nomogram included eight indicators: preoperative CEA level; the preoperative inflammatory indicators NLR, PLR, and LMR; and the postoperative pathological features T stage, N stage, vascular invasion, and MMR status. The three-model comparison demonstrated that the combined nomogram significantly outperformed both the pathological-only and inflammatory-only models in terms of discrimination (AUC, DeLong test), calibration, and net clinical benefit (decision curve analysis), with statistically significant reclassification improvements (NRI and IDI). The nomogram has good accuracy and clinical application value and may help clinicians to identify patients with CRC at high risk of MLM early, to enable close monitoring and timely intervention. However, the model's overfitting concerns (EPV of 6.9, calibration slope of 0.857) and the gap between training and validation performance indicate that external validation in larger, multi-center cohorts is necessary before clinical implementation.

Abbreviations

ALR

Alkaline phosphatase-to-lymphocyte ratio

AUC

Area under the curve

CA

Cancer antigen

CEA

Carcinoembryonic antigen

CI

Confidence interval

CRC

Colorectal cancer

GLR

Gamma-glutamyl transpeptidase-to-lymphocyte ratio

LASSO

Least absolute shrinkage and selection operator

LMR

Lymphocyte-to-monocyte ratio

LNE

Lymph nodes examined

MLM

Metachronous liver metastasis

MMR

Mismatch repair

pMMR

Mismatch repair proficient

NLR

Neutrophil-to-lymphocyte ratio

OR

Odds ratio

PLR

Platelet-to-lymphocyte ratio

ROC

Receiver operating characteristic curve

SLM

Synchronous liver metastasis

Authors’ contributions

YG and XW planned and conceived the study. XF and FZ collected the data. YG, FZ, JD, YZ, ZS, HY, LY, and ZC analyzed the data. YG and XW wrote and critically revised the manuscript. All authors read and approved the final manuscript.

Funding

This study did not receive any specific grants from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability

The datasets used in this study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

The study was conducted in accordance with the principles outlined in the Declaration of Helsinki and was approved by the Research Ethics Committee of the First Affiliated Hospital of Zhengzhou University. Informed consent was obtained from all patients.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.