A Machine Learning Framework for Cancer Prognostics: Integrating Temporal and Immune Gene Dynamics via ARIMA-CNN

<b>Background:</b> Hepatocellular carcinoma remains a global health challenge with high mortality rates. The tumor immune microenvironment significantly impacts disease progression and survival. However, traditional analyses predominantly focus on single immune genes, overlooking the critical interplay among multiple immune gene signatures. Our study explores the prognostic significance of chemokine (C-C motif) ligand 5 (CCL5) expression and associated immune genes through an innovative combination of Autoregressive Integrated Moving Average (ARIMA) and Convolutional Neural Network (CNN) models. <b>Methods:</b> A time series dataset of CCL5 expression, comprising 230 liver cancer patients, was analyzed using an ARIMA model to capture its temporal dynamics. The residuals from the ARIMA model, combined with immune gene expression data, were utilized as input features for a CNN to predict survival outcomes. Survival analyses were conducted using the Cox proportional hazards model and Kaplan-Meier curves. Furthermore, the ARIMA-CNN framework's results were systematically compared with traditional median-based stratification methods, establishing a benchmark for evaluating model efficacy and highlighting the enhanced predictive power of the proposed integrative approach. <b>Results:</b> CNN-extracted features demonstrated superior prognostic capability compared to traditional median-split analyses of single-gene datasets. Features derived from CD8⁺ T cells and effector T cells achieved a hazard ratio (HR) of 0.7324 (<i>p</i> = 0.0008) with a statistically significant log-rank <i>p</i>-value (0.0131), highlighting their critical role in anti-tumor immunity. Hierarchical clustering of immune genes further identified distinct survival associations. Notably, a cluster comprising B cells, Th2 cells, T cells, and NK cells demonstrated a moderate protective effect (HR: 0.8714, <i>p</i> = 0.1093) with a significant log-rank <i>p</i>-value (0.0233). Conversely, granulocytes, Tregs, macrophages, and myeloid-derived suppressor cells showed no significant survival association, emphasizing the complex regulatory landscape within the tumor immune microenvironment. <b>Conclusions:</b> Our study provides the first ARIMA-CNN framework for modeling gene expression and survival analysis, marking a significant innovation in integrating temporal dynamics and machine learning for biological data interpretation. This model offers deeper insights into the tumor immune microenvironment and underscores the potential for advancing precision immunotherapy strategies and identifying novel biomarkers, contributing significantly to innovative cancer management solutions.