We wish to extend our sincere gratitude to Zhanna Zhang and Gongqiang Wu for their valuable suggestions and thoughtful insights regarding our recent work [1]. We are pleased to engage in further discussion on our methodology and findings [2].

First, Zhang et al. raised an important concern regarding multicollinearity, particularly with the inclusion of composite variables such as serum biomarker scores, including the albumin-bilirubin (ALBI) score, lymphocyte-to-monocyte ratio (LMR), and prognostic nutritional index (PNI). We fully acknowledge and share this concern, which is central to our study’s context: employing machine learning-based methods to enhance model performance and address issues like overfitting and multicollinearity. LASSO-Cox regression has been widely demonstrated as an effective method for variable selection, with the capacity to reduce overfitting and mitigate multicollinearity [3,4]. Consequently, we employed LASSO-Cox regression, and our CATS-INF score showed slightly improved performance compared to models developed using conventional methods. Based on these findings, we are confident that multicollinearity posed minimal concern in our study.

Second, Zhang et al. raised concerns about the potential limitations related to the follow-up duration, particularly given the favorable prognosis of early-stage hepatocellular carcinoma (HCC). While it is true that follow-up duration could be considered a limiting factor, our cohort had a median follow-up period of 38.0 months, which aligns with the methods and durations used in other well-regarded studies [5-7]. Additionally, we conducted further analyses involving HCC patients across all stages in a subsequent study, which yielded consistent results [8]. Therefore, we believe that the follow-up duration and stage-specific limitations are unlikely to have significantly affected our findings. Nonetheless, we agree that future research with longer follow-up periods would be beneficial.

We sincerely appreciate the comments from Zhang et al. and hope our response addresses their concerns effectively. Machine learning has significantly advanced survival analysis for patients with various diseases [9]. Additionally, it has been applied in evaluating non-fatal outcomes, such as the failure of direct-acting antivirals in hepatitis C virus patients [10]. We hope our responses illustrate our commitment to advancing the evaluation of HCC prognosis and contributing to personalized patient care.