A total of 1,401 patients with HBV-related cirrhosis who were admitted at Capital Medical University, Beijing You’An Hospital, from January 1, 2011 to December 31, 2014 were included. Patients with cirrhosis were diagnosed through imaging and histological examination based on the etiology, medical history, clinical manifestations, and complications. According to the diagnosis time of liver cirrhosis, 1,401 patients were randomly divided into a training dataset (n = 1,017) and a validation dataset (n = 384) at a ratio of 3:1. We collected demographic and baseline clinical pathological information from all patients with cirrhosis, as shown below: age, sex, medical history, blood routine examination, liver and kidney function test, coagulation markers, alpha fetoprotein (AFP), and HBV viral DNA load as described in our previous study (11).

The standard of diagnosis for cirrhosis was based on Chinese guidelines on the management of liver cirrhosis (17), and for HCC it was based on the Chinese standard for the diagnosis and treatment of primary liver cancer (18). In order to minimize inter-etiological confounding of cirrhosis, the highest known risk of HCC development was set as etiological feature according to the standard of THRI methods (10). For the purpose of this study’s analysis, patients with cirrhosis who had both chronic hepatitis B and a history of alcohol or non-alcoholic steatohepatitis were classified as chronic hepatitis B (10, 19). The inclusion criteria and the exclusion criteria were described in detail in our previous study (11), and the screening process for all patients is shown in Figure 1 .

The enrolled patients were followed up at the outpatient clinic every 6 months, including medical examinations, laboratory tests, and ultrasound examinations (11). We calculated the follow-up since the date of cirrhosis diagnosis to the date of event occurrence (including HCC diagnosis, HBV cirrhosis-related death, and liver transplantation) or January 1, 2020, whichever occurred first. In this study, the HBV cirrhosis-related death and LT (shown by event 2) would hinder HCC (shown by event 1). Events 1 and 2 can be considered as competing events one for the other.

Missing data could increase bias and reduce the statistical power, and application of Multiple Imputation by Chained Equations (MICE) for 20 times could reduce this impact (20). Briefly, a simple imputation was first created, and each missing value was replaced with a mean value as a “place holder”. Then, the “place holder” mean imputations of the first variable were set back to missing and then replaced with predictions (imputations) from the regression model when the first variable was the dependent variable and the other variables were independent variables. Fitting models was based on the distribution of variables, logistic regression for binary variables, linear regression for continuous variables, and Poisson model for count variables. These steps of 25 iterations for each variable that had missing values would be repeated 20 times until convergence in this study. Finally, the observed values and the 20 sets of imputed values would then constitute 20 “complete” datasets. Rubin’s rules were used to pool parameter estimates, including mean deviation, regression coefficients, standard error, derive confidence intervals, and p-values. Multivariate imputation by MICE to handle missing values could reduce bias in the feature selection process.

Continuous variables were represented as mean ± standard deviation or median (interquartile range, IQR). The cutoff value of quantitative variables was selected by applying surv_cutpoint function as implemented in “survminer” package. The proportional subdistribution hazard ratios (sHR) were estimated by the Fine and Gray model (21). Univariate and multivariate competing risks regression analysis were performed to select risk factors with p-value <0.05 for constructing the final nomogram. The cumulative incidence function curve (CIF) with Fine and Gray’s test was applied to evaluate the cumulative risk of primary outcome and competing risk events between the groups. A key assumption of CIF is that only one event can occur each time, and the subsequent occurrence of other event types are precluded. The cumulative incidence function for the kth cause is defined as CIFk(t) = Pr(T ≤ t, D = k), which allowed for calculating the respective CIF of events of interest and competing risk events.

The nomogram predicted the 20, 40, 60, 80, and 100 months of HCC probability among cirrhosis patients. Discrimination and predictive accuracy were assessed using the area under the time-dependent receiver operator characteristic (ROC) curve (time-dependent AUC). The consistency was evaluated using a calibration curve with Brier scores and Harrell’s concordance index. Basing on the established model, we predicted high-risk and low-risk groups with HCC cumulative incidence rate. CIF analysis and Fine and Gray’s test were used to compare the cumulative incidence rate curves of the two groups. R (version 4.2.2) software was applied for all statistical testing and visual analysis. Extension packages, including “rms”, “cmprsk,” “riskRegression,” “pec”, and “timeROC,” were also used. A p-value <0.05 was considered statistically significant.

A total of 1,401 liver cirrhosis patients, from January 1, 2011 to December 31, 2014, who met the eligibility criteria were retrospectively enrolled. We assessed the demographic, laboratory, and clinical characteristics between the original database and the 20-times-imputation datasets ( Table 1 ). The most missing data in clinical parameters (PT, PTA, INR, fibrinogen, and thrombin time) were 130 (9.3%). The rest of the variables had a missing proportion of less than 1.57%. The negligible difference between the original database and the 20 imputed datasets allowed for the usage of the latter for predicative research of cirrhosis patients’ outcome.

The median follow-up time was 69.9 months (IQR: 43.8–86.6). By the end of the follow-up, 80 cirrhosis patients died and 58 received LT; therefore, 138 cases were set as competitive risk events (event 2). A total of 442 patients developed HCC and were set as event of interest (event 1). The cumulative HCC incidences of 1, 3, 5, and 7 years were 1.6% (95%CI, 1.1%–2.3%), 13.3% (95%CI, 11.6%–15.2%), 22.9 (95%CI, 20.8%–25.2%), and 32.2% (95%CI, 29.6%–35.0%), respectively. The cumulative incidences of death and LT at 1, 3, 5, and 7 years were 0.3% (95%CI, 0.1%–0.7%), 2.6% (95%CI, 1.9%–3.6%), 5.0 (95%CI, 4.0%–6.3%), and 9.1% (95%CI, 7.5%–10.8%), respectively ( Figure 2 ). The characteristics of HCC diagnosed at the end of the follow-up are summarized in Supplementary Table S1 . In the HCC stage, above 60% of patients had single or small tumors or BCLC stage A, and in about 83.2% of patients metastasis did not occur.

The univariate and multivariate competing risk regression analyses in 20 training imputed datasets were performed to select the predicting factors of HCC and estimate the respective sHRs ( Table 2 ). Univariate analysis showed that nine variables including age, sex, antiviral therapy, alcohol drinking, family history of CHB, alanine transaminase, hepatitis B e antigen (HBeAg), hepatitis B surface antigen (HBsAg), and alpha fetoprotein (AFP) were associated with the risk of HCC. After multivariate competing risk regression analysis, six independent risk factors including age, sex, antiviral therapy history, alcohol drinking history, HBeAg, and AFP were finally identified and incorporated into the model. Cumulative incidence curve analyses of the six prognostic factors were plotted based on Fine–Gray test ( Figure 3 ). It could be seen that the HCC risk had a statistical increase in the male group, older age (≥51 years) group, positive of HBeAg group, unacceptance of antiviral therapy group, alcohol drinking group, and high AFP level [log₁₀ (AFP) ≥ 0.57) group (all Fine–Gray test, p < 0.05). The sHR of the prognostic factors are outlined in Table 2 .

The HCC competing risk nomogram was established in 20 imputed training datasets based on the following six independent predictive factors: age, sex (female or male), antiviral therapy history (yes or no), HBeAg (positive or negative), alcohol drinking history (yes or no), and log₁₀ (AFP). The coefficients of competing risk nomogram are shown in Supplementary Table S2 . This model could be used to calculate the probability of HCC occurrence for each cirrhosis patient—for example, a 46.36-year-old and alcohol-drinking male cirrhosis patient with 2.56 ng/mL of AFP, accepting antiviral therapy and HBeAg negative at diagnosis of cirrhosis, had a total score of about 273, and the respective 20-, 40-,60-,80-, and 100-month HCC incidences were about 4.1%, 10.5%, 16.9%, 24.1%, and 32.4% ( Figure 4A ).

Evaluating model overfitting was performed through bootstrap internal validation method. After 1,000 bootstrap cross-validation iterations, the adjusted C-index of the model was 0.75 (95%CI, 0.71–0.79). The time-dependent AUC was used to validate the discriminative ability of the nomogram. The time-dependent AUC values for the prediction of HCC at 12, 24, 36, 60, and 96 months in the training cohort were 0.68 (95%CI, 0.60–0.76), 0.74 (95%CI, 0.69–0.78), 0.70 (95%CI, 0.66–0.75), 0.75 (95%CI, 0.71–0.78), and 0.75 (95%CI, 0.70–0.80), respectively ( Figure 4B ). The adjusted Brier scores of the calibration curve for the model at 12, 24, 36, 60, and 96 months were 0.34 (95%CI, 0.31–0.36), 0.29 (95%CI, 0.27–0.32), 0.26 (95%CI, 0.24–0.28), 0.22 (95%CI, 0.20–0.23), and 0.20 (95%CI, 0.19–0.21) ( Figure 4C ), respectively. Similarly, the time-dependent AUC values were assessed in the validation cohort at 12, 24, 36, 60, and 96 months, which were 0.68 (95%CI, 0.52–0.83), 0.69 (95%CI, 0.60–0.78), 0.70 (95%CI, 0.62–0.78), 0.68 (95%CI, 0.60–0.75), and 0.80 (95%CI, 0.73–0.87), respectively ( Figure 4D ), and the adjusted Brier scores were 0.30 (95%CI, 0.25–0.34), 0.25 (95%CI, 0.22–0.29), 0.23 (95%CI, 0.20–0.26), 0.21 (95%CI, 0.18–0.24), and 0.20 (95%CI, 0.19–0.22) ( Figure 4E ).

In order to further evaluate the discriminative ability of the HCC competitive risk prediction nomogram, the risk score of each cirrhosis patient was calculated. The low-risk group (score <1.67) and high-risk group (score ≥1.67) were created based on the cutoff value of the risk score, which was selected by applying surv_cutpoint function implemented in “survminer” software. Patients in the training and validation cohorts were stratified based on their risk scores of HCC in the presence of competing events. The cumulative incidence curves of HCC and competitive risk event in the two groups were drawn ( Figure 5 ). The respective incidences had significant differences in the low-risk and high-risk groups both in the two cohorts (p < 0.001). For the training cohort, the cumulative 20-, 40- 60-, 80-, and 100-month incidences of HCC were 11.2 (95%CI, 8.2–13.6), 26.0 (95%CI, 21.6–30.6), 42.1 (95%CI, 36.9–47.1), 53.0 (95%CI, 47.2–58.5), and 63.2 (95%CI, 55.7–69.8) in the high-risk group and 2.4 (95%CI, 1.4–3.8), 7.7 (95%CI, 5.8–10.0), 13.0 (95%CI, 10.5–15.8), 19.4 (95%CI, 16.2–22.90), and 26.3 (95%CI, 22.0–30.8) in the low-risk group (p < 0.001) ( Figure 5A ). The cumulative 20-, 40- 60-, 80-, and 100-month incidences of HCC were 8.6 (95%CI, 4.8–13.7), 23.2 (95%CI, 16.7–30.62), 32.7 (95%CI, 25.3–40.3), 43.3 (95%CI, 34.5–51.9), and 60.6 (95%CI, 45.0–73.1) in the high-risk group and 2.2 (95%CI, 0.8–4.8), 8.4 (95%CI, 5.3–12.5), 13.8 (95%CI, 9.7–18.7), 20.8 (95%CI, 15.5–26.8), and 26.0 (95%CI, 19.4–33.2) in the validation cohort ( Figure 5B ). In addition, patients with a higher HCC risk did not have a higher risk of death and LT.

Meanwhile, we compare our model with four other existing risk scores whose parameters all included HBV infection and cirrhosis. Toronto HCC risk index (THRI) scoring system, our previous You’an model (11), the AASL (age, albumin, sex and liver cirrhosis)-HCC scoring system, and real-world risk score for hepatocellular carcinoma (RWS-HCC) were allowed to apply our data. The result of time-dependent AUC of our model and other four models showed that our model has best discriminatory power ( Figure 6 ).