Fig 2: Directed acyclic graphs and covariate balance diagnostics for IPTW modelsCausal structures and balance assessments for SOS1 are presented in (A–C), AFP (D–F), and FIB-4 (G–I). (A, D, and G) Directed acyclic graphs (DAGs) outlining hypothesized confounding relationships between biomarker exposure and clinical outcomes, adjusted using inverse probability of treatment weighting (IPTW). (B, E, and H) Covariate balance (“love”) plots showing standardized mean differences (SMDs) for baseline variables before and after weighting. Vertical dashed line denotes absolute SMD = 0.1 threshold for acceptable balance. (C, F, and I) Distributions of stabilized IPTW weights and corresponding effective sample sizes (ESS) indicating the quality of weight estimation for each biomarker model.

Fig 3: Restricted cubic spline models for time-updated associations between biomarkers and progression riskSpline curves depict adjusted hazard ratios (solid orange lines) with 95% confidence intervals (shaded areas) for SOS1 (A, D, and G), AFP (B, E, and H), and FIB-4 (C, F, and I) at baseline, 12 and 24 months, respectively. Models were fitted using Cox proportional hazards regression with restricted cubic splines (four knots) adjusted for age, sex, diabetes status, MELD score, and etiology. The horizontal dashed line indicates a hazard ratio of 1.0 (reference). Tick marks along the x axes represent individual participant biomarker values used in spline estimation. All biomarker levels were modeled on their original continuous scales without transformation.

Fig 4: Competing-risk cumulative incidence of hepatocellular carcinoma and death across biomarkers and landmarksCumulative incidence functions are shown for SOS1 (A–C), AFP (D–F), and FIB-4 (G–I) stratified by biomarker tertiles at baseline (0 m), 12 months, and 24 months landmarks. Curves represent mutually exclusive outcomes for hepatocellular carcinoma (solid) and death (dashed) within each biomarker tertile (low, mid, and high). The y axis indicates cumulative incidence from the specified landmark, and the x axis denotes months since landmark. Models were estimated using fine-gray subdistribution hazards with non-hepatic death treated as a competing risk. All participants alive and event-free at the landmark were included in subsequent risk estimation.

Fig 5: External validation of SOS1 in the TCGA-LIHC dataset(A–I) Boxplots showing expression of candidate biomarkers in tumor versus adjacent normal liver tissues. SOS1 was significantly upregulated in tumors (p < 0.001), whereas AFP showed no discriminatory power; other ECM and inflammatory mediators (COL1A1, FN1, MMP9, IL1B) were variably increased. p values indicate two tailed t tests.(J) Spearman correlation heatmap demonstrating that SOS1 clustered most strongly with fibronectin (FN1) and COL1A1, consistent with its role in matrix remodeling.(K) Receiver operating characteristic (ROC) curves revealed that SOS1 (AUC = 0.78) outperformed AFP (AUC = 0.46) and other comparators for distinguishing tumors from normal tissues.(L) Multivariate Cox regression analysis confirmed that high SOS1 expression independently predicted worse overall survival after adjustment for age and sex (HR = 1.50, 95% CI 1.05–2.14, p = 0.024).