Journal of Advances in Mathematics and Computer Science

Background: Prostate cancer is a leading cause of cancer-related morbidity and mortality among Ghanaian men, with a predominance of advanced-stage presentations attributable to limited screening and delayed diagnosis. Traditional Cox proportional hazards models commonly presuppose linear relationships and may inadequately capture intricate biological patterns. This study employed a Cox proportional hazards framework augmented with restricted cubic splines (RCSs) and SHAPs (SHapley Additive exPlanations) to elucidate nonlinear and individualized determinants of prostate cancer survival.

Method: A retrospective cohort of 300 men with histologically confirmed prostate cancer treated at Korle Bu Teaching Hospital between 2015 and 2020 was analyzed. The candidate predictor variables included age, tumor size, prostate-specific antigen (PSA) level, Gleason score, clinical stage, lymph node involvement, and treatment modality. Nonlinear relationships for age and tumor size were modeled via flexible spline terms. Model adequacy and fit were assessed through the Akaike information criterion (AIC), Harrell’s concordance index (C-index), and diagnostics for proportional hazards assumptions. Shapley additive explanations (SHAPs) were employed to quantify both global and individual (patient-level) contributions to mortality risk. No assumptions are made about the real multicenter data. These are the standard, accepted scientific steps for multicenter external validation of an RCS–SHAP Cox model.

Results: The spline-augmented Cox model demonstrated significant nonlinear associations with tumor size (hazard ratio [HR] = 0.41, 95% CI: 0.17-0.99, p = 0.048) and a pronounced effect on the Gleason score (HR = 0.85, 95% CI: 0.74-0.99, p = 0.036). SHAP analysis identified tumor size (absolute SHAP value = 0.2015) and Gleason score (absolute SHAP value = 0.1591) as the leading predictors, followed by chemotherapy and prostate-specific antigen (PSA) levels. Beeswarm and partial-effect plots corroborated a nonlinear increase in survival risk with greater tumor burden and higher histologic grade, whereas moderate PSA levels and receipt of treatment exerted a protective effect. The combined spline-SHAP model demonstrated strong predictive performance (C-index = 0.84) with improved parsimony over the linear Cox baseline (ΔAIC = −13), confirming the dominance of tumor size and Gleason score as the most influential contributors to survival risk.

Conclusion: The integration of restricted cubic splines (RCSs) with SHAP-based explainability enhanced model flexibility, transparency, and clinical interpretability. The results underscore tumor size and Gleason score as the most influential determinants of mortality, highlighting the imperative for early detection, histopathological risk stratification, and individualized therapeutic strategies. This study is limited by its single-center design and the inherent constraints of retrospective clinical data. The SHAP-augmented RCS Cox framework provides a replicable approach for precision oncology and evidence-based management of prostate cancer in settings with limited resources, including Ghana. The incorporation of SHAP-based explainability enhances model transparency by allowing individualized interpretation of survival risk, thereby supporting clinically actionable decision-making in prostate cancer management. An incorporation of multicenter cohorts and longitudinal biomarker trajectories such as PSA kinetics to enhance external validity and predictive precision are recommended.