Interpretable LASSO-Cox model: Hsp90α/albumin ratio predicts hepatocellular carcinoma prognosis

Introduction

Liver cancer is a significant global health issue, and the largest proportion of liver cancer cases is attributed to hepatocellular carcinoma (HCC). The primary causes of HCC are alcoholic hepatitis and hepatitis viruses (1). Currently, HCC ranks as the fifth most prevalent malignant tumor and the third leading cause of cancer-related fatalities. Morbidity and mortality rates have not been effectively controlled (2,3). Today, the systemic treatment of HCC has made great progress. In 2020, the Food and Drug Administration (FDA) approved the combination of atrizumab and bevacizumab as the new first-line standard treatment for unresectable HCC, and it is the first regime with a higher survival rate than sorafenib (4). According to the latest efficacy data of IMbrave150, the median overall survival (mOS) of the atrizumab plus bevacizumab group was 19.2 months [95% confidence interval (CI): 17.0–23.7], and the mOS of the sorafeab group was 13.4 months (95% CI: 11.4–16.9) (5). In addition, a prospective study by Li et al. on local treatment of HCC showed that the mOS in the hepatic arterial infusion chemotherapy (HAIC) group was 23.1 months (95% CI: 18.5–27.7), while that in the transarterial chemoembolization (TACE) group was 16.1 months (95% CI: 14.3–17.9) (6). Although there have been significant advancements in the prognosis of HCC, accurately predicting its prognosis remains a challenging task.

Prognostic evaluation plays a critical role in determining the appropriate diagnosis and treatment plan for HCC. In addition to tumor staging, the assessment of prognosis should also consider specific indicators to evaluate the severity of liver damage, as most patients with HCC have underlying liver diseases (7). Although there is evidence showing a strong association between elevated alpha-fetoprotein (AFP) levels and poor prognosis in HCC, there is a lack of reliable data to establish a definitive threshold for AFP levels as a prognostic indicator (8). As a result, there is ongoing research and efforts aimed at enhancing the diagnosis and treatment of HCC with the goal of improving overall prognosis. There is a lack of clinical evidence supporting the use of biomarkers for monitoring and diagnosing HCC, and many indicators still show low sensitivity and heterogeneity in terms of specificity. In contrast, the development of new prognostic biomarkers of HCC could potentially have a significant impact on clinical practice (8,9).

Heat shock protein (HSP) is a highly conserved protein, which is expressed at a low level under normal conditions, but its expression increases significantly in response to cellular stress. Acting as a molecular chaperone, HSP plays a critical role in maintaining protein homeostasis, regulating apoptosis, modulating cell invasion, and facilitating cell signal transduction processes (10). HSP90α, a subtype of HSP, has also been extensively studied as a potential therapeutic target and prognostic index (11,12). At the same time, the development of HCC is often associated with the autophagic consumption of the body, as evidenced by a reduction in albumin (ALB) levels (12). We conducted a novel approach by combining both markers (including HSP90α and ALB) to investigate their potential as sensitive and specific prognostic markers for HCC. To determine the feasibility of using HSP/ALB as a prognostic factor for HCC, we initiated a multicenter study. We present this article in accordance with the TRIPOD reporting checklist (available at https://tcr.amegroups.com/article/view/10.21037/tcr-2025-1391/rc).

Methods

Patients

Between July 2016 and January 2023, a total of 1,340 patients diagnosed with liver cancer were initially registered at three tertiary hospitals in China. The study adhered to the following inclusion criteria: (I) patients clinically or pathologically diagnosed with HCC; (II) no prior antineoplastic therapy received; (III) presence of measurable lesions based on solid tumor response evaluation criteria 1.1 (RECIST1.1) (13); and (IV) measurement of HSP90α and ALB levels within 1 week prior to treatment. Patients with incomplete clinical data or other malignant tumors were excluded. This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The research protocol was approved by the Clinical Trial Ethics Committee of The Affiliated Hospital of Southwest Medical University (No. KY2020254) and registered in the Chinese Clinical Trial Registry (registration number: ChiCTR2100051057). All participating hospitals/institutions were informed and agreed the study. The requirement for informed consent was waived due to the retrospective nature of the study.

Data

We obtained clinical data through medical record tracking and patient file review. Demographic information included gender and age. The etiology of interest for HCC included hepatitis B virus (HBV), hepatitis C virus (HCV), and alcoholic liver disease. Serological indicators included biochemical indexes such as Hsp90α and ALB and blood routine indexes such as leukocytes. Experienced radiologists assessed tumor load using magnetic resonance imaging (MRI) and computed tomography (CT), which included parameters such as the number of tumors, maximum tumor diameter, portal vein tumor thrombus (PVTT), extrahepatic metastasis, and lymph node metastasis. The Child-Pugh score, namely Barcelona Clinic Liver Cancer (BCLC) staging, was evaluated using the above indicators. OS is defined as the time from the first admission for treatment to death or the last follow-up.

Statistical analysis

The Chi-square test (χ²) and McNemar analysis were used for statistical analysis. The continuous variables were analyzed using the Mann-Whitney U and Wilcoxon paired symbolic sequence test. Risk factors were screened using least absolute shrinkage and selection operator (LASSO) regression analysis, followed by further elimination of risk factors using Cox regression, and then, a model was established. X-tile software (Yale University, New Haven, Connecticut, USA) was used to determine the best cut-off value for the HSP/ALB level based on OS. The ability of the model to predict curative effects was evaluated using a time-dependent subject working characteristic curve. The discrimination and consistency of the model were evaluated using the area under the curve (AUC) and calibration curve, respectively. Further, we built SurvSHAP using the global explanatory method, that is, the average SHapley Additive exPlanations (SHAP) value was calculated for each feature in all samples. The Kmurm method was used to evaluate its clinical applicability. All statistical analyses were conducted using R Software (version 4.2.2) and SPSS (version 26.0). The difference was statistically significant, which means the bilateral P<0.05.

Results

Patient characteristics

A total of 1,340 patients with HCC were included in our retrospective study. Among them, males accounted for 0.84, Child-Pugh A accounted for 0.73, multiple tumors accounted for 0.54, and BCLC stage ≥ B accounted for 0.86. Table 1 shows the baseline characteristics of the patients.

Factors associated with the OS

We will divide the training set and the validation set at 7:3 into the training set and the validation set. The training set is used to build the model, and the validation set is used for model validation. The features were screened using LASSO regression, and the changing characteristics of the coefficients of these variables are shown in Figure 1A. We chose the variable corresponding to lambda.1se as the characteristic prognostic variable. The cross-validation method was used in the subsequent iterative analysis. The final selected variables included BCLC stage, Child-Pugh grade, tumor diameter, lymphocyte ratio (Lym-r), AST, ALP, and HSP/ALB (Figure 1B). A LASSO-Cox regression model was developed by applying cox regression on the basis of LASSO regression (Figure 2).

Figure 1 Variable screening based on LASSO regression. (A) The change of variable coefficient; (B) determining the best index in LASSO regression model by cross-validation. LASSO, least absolute shrinkage and selection operator.

Figure 2 Cox regression, which is based on LASSO regression. *, P<0.0; **, P<0.01; ***, P<0.001. AIC, Akaike information criterion; ALB, albumin; ALP, alkaline phosphatase; AST, aspartate transferase; BCLC, Barcelona Clinic Liver Cancer; HSP, heat shock protein; LASSO, least absolute shrinkage and selection operator; Lym-r, lymphocyte ratio.

The ROC curve for HSP/ALB alone showed that the AUC values for predicting 1-, 2-, and 3-year OS were 0.757, 0.731, and 0.713, respectively; after introducing HSP/ALB into the prediction model based on LASSO-Cox regression, the AUC values for predicting 1-, 2-, and 3-year OS were 0.850, 0.842, and 0.810, respectively (Figure 3A,3B).

Figure 3 Time series ROC curve. (A) Time series ROC curve of single HSP/ALB; (B) time series ROC curve of single LASSO-Cox prediction model. ALB, albumin; AUC, area under the curve; HSP, heat shock protein; LASSO, least absolute shrinkage and selection operator; ROC, receiver operating characteristic.

Efficacy

The mOS for the entire cohort was 18.8 months. After determining the cut-off value in training set, it was found that the mOS of patients with HSP/ALB ≥3.77 (high) (8.3 months, 95% CI: 7.6–9.3) was significantly lower than that of patients with HSP/ALB <3.77 (low) (38.7 months, 95% CI: 35.8–45) (Figure 4A). In the training cohort, the mOS of patients with HSP/ALB ≥3.77 was 7.3 months (95% CI: 5.8–8.9), and that of patients with HSP/ALB <3.77 was 36.1 months (95% CI: 28.4–39.8) (Figure 4B). In the validation cohort, the mOS of patients with HSP/ALB ≥3.77 was 7.1 months (95% CI: 4.9–9.0), and that of patients with HSP/ALB <3.77 was 36.2 months (95% CI: 31.6–43.7) (Figure 4C).

Figure 4 Survival curves for different subgroups based on risk stratification, pooled set. (A), training set (B) and valid set (C) according to the cut-off value. Kaplan-Meier curve of TACE group (D), TACE combined operation group (E) and RT group (F). ALB, albumin; H, high; HSP, heat shock protein; L, low; RT, radiotherapy; TACE, transarterial chemoembolization.

Subgroup analysis of different treatment modalities

Based on the determined cut-off value and the treatment received by the patients, a subgroup analysis was conducted, which included three groups: TACE alone, TACE combined with operation, and radiotherapy (RT) group (external RT was used during the treatment). In all subgroups analyzed, the mOS of patients with HSP/ALB ≥3.77 was worse than that of patients with HSP/ALB <3.77. Specifically, in the TACE group, the mOS was 9.05 months (95% CI: 7.9–10.5) for HSP/ALB ≥3.77 versus 23.4 months (95% CI: 19.2–28) for HSP/ALB <3.77 (Figure 4D). In the TACE combined with operation group, the mOS was 30.9 months (95% CI: 16.3–NA) for HSP/ALB ≥3.77 versus NA for HSP/ALB <3.77 (Figure 4E). In the RT group, the mOS was 46.9 months (95% CI: 14.7–NA) for HSP/ALB <3.77 versus 8.75 months (95% CI: 5.3–NA) for HSP/ALB ≥3.77 (Figure 4F). Additionally, we supplemented the analysis with survival differences between high- and low-risk groups in the RFA cohort undergoing combined TACE and systemic therapy. Results consistently indicate that the low-risk group (risk score <3.77) demonstrated significantly better prognosis than the high-risk group (risk score ≥3.77) (Figure S1A,S1B).

LASSO-Cox regression prediction model

A nomogram was developed using LASSO-Cox regression to screen variables and create a clinically applicable model (Figure 5A). Through the dangerous features screened by LASSO-Cox, we show the relationship between the features in terms of confusion matrix (Figure 5B). We ranked the importance of variables according to the SHAP value, in the following order: BCLC staging and HSP/ALB, AST, Lym-r, ALP, Child-Pugh grading (Figure 6).

Figure 5 Nomogram and correlation matrix. (A) Nomogram for predicting 3-year survival rate in patients with HCC. (B) Confusion matrix between features. *, P<0.05; **, P<0.01; ***, P<0.001. ALB, albumin; ALP, alkaline phosphatase; AST, aspartate transferase; BCLC, Barcelona Clinic Liver Cancer; HCC, hepatocellular carcinoma; HSP, heat shock protein; Lym-r, lymphocyte ratio; OS, overall survival.

Figure 6 SurvSHAP was used to calculate feature importance and rank the features selected by LASSO-Cox. ALB, albumin; ALP, alkaline phosphatase; AST, aspartate transferase; BCLC, Barcelona Clinic Liver Cancer; HSP, heat shock protein; LASSO, least absolute shrinkage and selection operator; Lym-r, lymphocyte ratio.

The DCA curve (Figure S2A) and calibration curve (Figure S2B) of the model based on LASSO-Cox regression to predict the 1-, 2-, and 3-year survival time showed that the prediction model has good prediction performance, and the prediction results were in good agreement with the observed results in the validation set.

Risk stratification

To calculate the risk score for each sample, we employ the risk factors obtained from the nomogram post-Cox regression. Using the optimal risk cutoff value determined by X-tile software, patients are then categorized into low-risk, medium-risk, and high-risk groups. Finally, survival analysis was employed to visualize and validate the risk stratification (Figure 7). It was observed that the mOS of the low-risk group significantly outperformed that of the medium-risk and high-risk groups.

Figure 7 Survival curve under risk stratification corresponding to overall cohort. H, high; L, low; M, medium.

Discussion

The clinical prognosis of HCC is poor, and its incidence is difficult to control. Although some prognostic markers are commonly used in clinical practice, there is still a need for the development of prognostic markers that can further improve the predictive efficiency (14,15). The HSP90α and ALB included in this study are closely related to the development of HCC. Clinical observation has revealed that the ratio of these markers has sufficient predictive value for the prognosis of HCC (16,17). In our study, HSP/ALB as an independent prognostic indicator was screened using the LASSO-Cox model. Through screening of the cut-off value and conducting survival analysis, it was confirmed that patients with HSP/ALB <3.77 had higher mOS compared to patients with HSP/ALB ≥3.77. Finally, survival analysis was employed to visualize and validate the risk stratification. It was observed that the OS of the low-risk group significantly outperformed that of the medium-risk and high-risk groups. Furthermore, HSP/ALB was included in the prediction model established by LASSO-Cox regression, and it was found to contribute to stable and accurate prediction efficiency.

Clinical decision-makers have been actively searching for a non-invasive and simple biomarker that can accurately predict the efficacy of HCC. At present, AFP is the most widely used indicator, but it is acknowledged that its prognostic value in HCC is relatively limited (18). There are two main limitations to using AFP as a prognostic marker for HCC. First, its elevation in other benign liver diseases has raised concerns about its accuracy for monitoring HCC. Second, Giannini et al. have highlighted that AFP may not have significant prognostic value in well-compensated cirrhosis and certain patients with HCC (19,20). HSP has the potential to overcome the limitations of previous biomarkers. Previous studies have elucidated the diagnostic and prognostic value of HSP family members in HCC, as well as their relationship with immune cell infiltration, immune biomarkers, and immune checkpoints. The overexpression of HSP is strongly linked to the cancer stage and the level of AFP in HCC, and individuals with high HSP expression are likely to have a worse prognosis (10,21,22). HSP90 is a chaperone protein highly expressed in all eukaryotic cells, which is another important member of the HSP family. It is an adenosine triphosphate-dependent chaperone protein that has multiple isomers, with the most significant members being HSP90α and HSP90β isomers in humans. These isomers are encoded by independent but highly conserved genes and have different roles. HSP90 is commonly overexpressed in cancer cells as it plays a crucial role in supporting the survival and proliferation of cancer cells (23,24). As HCC progresses, there is often a concurrent decrease in ALB levels, which is attributed to the consumptive nature of the disease. Based on clinical observation and research findings, there is a compelling rationale to believe that HSP/ALB may serve as a meaningful predictor for HCC prognosis. Our study provides evidence that HCC patients with HSP/ALB <3.77 exhibit a favorable prognosis, thereby supporting the use of this ratio in constructing a stable predictive model.

The approval of lenvatinib by the FDA and its high efficacy marks a new level in the research and development of targeted drugs for the treatment of HCC. Furthermore, the introduction of the second-line therapy drug Ragfini and the development of programmed cell death protein 1 (PD-1) inhibitors such as Navuliu have brought about a new era in targeted immunotherapy for HCC (25,26). Various combination therapies, such as the combination of antiangiogenic drugs with PD-1 inhibitors, PD-1 inhibitors combined with targeted drugs, or the combination of surgery or other local regional therapies with these drugs, have been extensively researched and shown promising prospects (27-31). The TACTICS trial showed that the median PFS (mPFS) of the TACE plus sorafenib group reached 25.2 months (32). The phase III randomized clinical trial also showed that the mOS of the lenvatinib combined with TACE group reached 17.8 months (33). Elisabeth’s research also showed that transarterial radioactive embolization (TARE) of yttrium 90 (90Y) has also made great progress. The mOS of the TARE group and TACE group was 30.2 and 15.6 months, respectively (34). The meta-analysis conducted on different treatment modalities provides robust evidence supporting the effectiveness of current therapies (35,36). For this reason, we conducted a subgroup analysis on different treatment approaches using a limited dataset from retrospective data. We utilized LASSO-Cox regression to evaluate the TACE group, TACE plus operation group, and RT group, we found that HSP/ALB ≥3.77 was identified as an independent risk factor for mOS.

Our study is an innovative, multicenter investigation based on the HSP/ALB. We used LASSO-Cox regression to ensure that the most valuable predictive variables are screened and a prediction model is established. We used X-tile and RCS methods to ensure that the best cutoff value is determined. Further survival analysis, including subgroups, fully confirms the value of predictors and models. However, there are still some limitations in this study. First of all, because it is a retrospective study, the selection bias cannot be eliminated. Second, considering the accuracy and limitations of the available data, we conducted a limited number of subgroup analyses, which may potentially reduce the level of evidence in our study. In view of this, it is imperative to conduct additional prospective studies to corroborate our findings. Furthermore, robust treatment groups should be employed to validate the predictive efficacy of HSP/ALB in diverse treatment approaches.

Conclusions

The integration of HSP/ALB into the LASSO-Cox prediction model improves its predictive performance, indicating that HSP/ALB can serve as a reliable prognostic predictor.

Acknowledgments

The authors would like to thank all the reviewers who participated in the review and MJEditor (www.mjeditor.com) for its linguistic assistance during the preparation of this manuscript.

Footnote

Reporting Checklist: The authors have completed the TRIPOD reporting checklist. Available at https://tcr.amegroups.com/article/view/10.21037/tcr-2025-1391/rc

Data Sharing Statement: Available at https://tcr.amegroups.com/article/view/10.21037/tcr-2025-1391/dss

Peer Review File: Available at https://tcr.amegroups.com/article/view/10.21037/tcr-2025-1391/prf

Funding: This work was supported by the Demonstration Project for Tumor Radiotherapy Application Based on Domestic Innovative Radiotherapy Equipment (No. 2023YFC2413906).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://tcr.amegroups.com/article/view/10.21037/tcr-2025-1391/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The research protocol was approved by the Clinical Trial Ethics Committee of the Affiliated Hospital of Southwest Medical University (No. KY2020254) and registered in the Chinese Clinical Trial Registry (registration number: ChiCTR2100051057). All participating hospitals/institutions were informed and agreed the study. The requirement for informed consent was waived due to the retrospective nature of the study.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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