Objective:To investigate the influencing factors for lung metastasis of hepato-cellular carcinoma after liver transplantation and application value of its nomogram prediction model.Methods:The retrospective cohort study was conducted. The clinicopathological data of 339 hepatocellular carcinoma patients with lung metastasis after liver transplantation who were admitted to Zhongshan Hospital of Fudan University from January 2015 to June 2019 were collected. There were 299 males and 40 females, aged from 23 to 73 years, with a median age of 54 years. According to the random numbers showed in the computer, all 339 patients were divided into training dataset consisting of 226 and validation dataset consisting of 113, with a ratio of 2:1. All patients underwent classic orthotopic liver transplantation. Observation indicators: (1) analysis of clinicopathological data of patients in the training dataset and validation dataset; (2) follow-up; (3) analysis of influencing factors for lung metastasis of hepatocellular carcinoma after liver transplanta-tion; (4) construction and evaluation of nomogram prediction model for lung metastasis of hepatocellular carcinoma after liver transplantation. Follow-up was conducted using outpatient examination and telephone interview to detect lung metastasis of patients up to November 2020. Measurement data with normal distribution were represented as Mean± SD, and comparison between groups was conducted using the paired t test. Measurement data with skewed distribution were represented as M( P25, P75) or M(range), and comparison between groups was conducted using the Mann-Whitney U test. Count data were described as absolute number or percentages, and comparison between groups was conducted using the chi-square test. The Kaplan-Meier method was used to calculate lung metastasis rate and draw lung metastasis curve. The Log-rank test was used for survival analysis. The COX proportional hazard model was used for univariate and multivariate analysis. Based on the results of multivariate analysis, the nomogram prediction model was constructed. The prediction accuracy of the nomogram model was evaluated using C-index and receiver operating characteristic (ROC) curve. The calibration curve was used to evaluate the prediction error of the model. Results:(1) Analysis of clinicopathological data of patients in the training dataset and validation dataset: there was no significant difference in general data between patients in the training dataset and validation dataset ( P>0.05). (2) Follow-up: 226 patients in training dataset and 113 patients in validation dataset were followed up. The follow-up time of training dataset was 5.2 to 69.0 months, with a median follow-up time of 29.3 months, and the follow-up time of validation dataset was 4.3 to 69.0 months, with a median follow-up time of 30.4 months. Up to the last follow-up, 48 cases of the training dataset and 22 cases of the validation dataset had lung metastasis, with the incidence and median time of lung metastasis were 21.24%(48/226), 19.47%(22/113) and 8.5 months, 7.8 months, respectively. There was no significant difference in lung metastasis between patients in the training dataset and validation dataset ( χ2=0.144, P>0.05). (3) Analysis of influencing factors for lung metastasis of hepatocellular carcinoma after liver transplantation: results of univariate analysis showed that age, alpha fetoprotein, tumor diameter, tumor differentiation degree, vascular invasion, systemic immune inflammation index and postoperative treatment were related factors for lung metastasis of hepatocellular carcinoma after liver transplantation ( hazard ratio=0.465, 3.413, 1.140, 3.791, 2.524, 2.053, 1.833, 95% confidence interval as 0.263?0.822, 1.740?6.695, 1.091?1.191, 1.763?8.154, 1.903?3.349, 1.047?4.027, 1.038?3.238, P<0.05) . Results of multivariate analysis showed that age, tumor diameter and vascular invasion were independent influencing factors for lung metastasis of hepatocellular carcinoma after liver transplantation ( hazard ratio=0.462, 1.076, 2.170, 95% confidence interval as 0.253?0.843, 1.013?1.143, 1.545?3.048, P<0.05). (4) Construction and evaluation of nomogram prediction model for lung metastasis of hepatocellular carcinoma after liver transplantation: the C-index was 0.810 (95% confidence interval as 0.758?0.863) and 0.802 (95% confidence interval as 0.723?0.881) of the nomogram prediction model for lung metastasis of hepatocellular carcinoma after liver transplanta-tion in the training dataset and validation dataset, respectively, showing good discrimination ability. The area under ROC of 0.5-, 1- and 2-year nomogram prediction model in the training dataset and the validation dataset were 0.815(95% confidence interval as 0.725?0.905), 0.863(95% confidence interval as 0.809?0.917), 0.835(95% confidence interval as 0.771?0.900)and 0.873(95% confidence interval as 0.801?0.945), 0.858(95% confidence interval as 0.760?0.956), 0.841(95% confidence interval as 0.737?0.945), respectively, which illustrated that the model had good predictive ability. The formula of nomogram prediction model=33.300 06+(?33.300 06)×age(≤50 years=0, >50 years=1)+2.857 14×tumor diameter (cm)+31.585 71×vascular invasion (M0 stage of microvascular invasion staging=0, M1 stage of microvascular invasion staging=1, M2 stage of microvascular invasion staging=2, visible tumor thrombus=3). The optimal threshold of nomogram risk score was 77.5. Patients with risk score ≥77.5 were assigned into high risk group, and patients with risk score <77.5 were assigned into low risk group. The 0.5-,1- and 2-year lung metastasis rate of patients in the high risk group and low risk group of the training dataset were 16.7%, 39.2%, 46.4% and 1.4%, 4.1%, 6.9%, respectively, showing a significant difference between the two groups ( χ2=54.86, P<0.05). The 0.5-,1- and 2-year lung metastasis rate of patients in the high risk group and low risk group of the validation dataset were 17.6%, 29.0%, 39.5% and 0, 3.1%, 4.8%, respectively, showing a significant difference between the two groups ( χ2=25.29, P<0.05). Conclusions:Age, tumor diameter and vascular invasion are independent influencing factors for lung metastasis of hepatocellular carcinoma after liver transplantation. The nomogram prediction model based on age, tumor diameter and vascular invasion can predict risk of lung metastasis for hepatocellular carcinoma patients after liver transplantation accurately.