Bayesian Hierarchical Modeling and Clustering for Malignant Cancer Diagnosis

Late-stage cancer diagnosis remains a major barrier to improving survival rates, yet the relative contributions of tumor, patient, and region-level factors have not been well quantified. In this study, we develop a 3-layer Bayesian hierarchical logistic regression model to investigate late-stage cancer diagnosis. The model includes fixed effects for tumor characteristics and random effects for patients and regions. Model parameters are estimated using the No-U-Turn Sampler, and posterior samples are evaluated with effective sample sizes and convergence diagnostics. From intra-class correlation estimates, we find that patient-level variation has a substantially stronger influence on late-stage diagnosis than region-level variation. Lastly, we utilize a Gaussian Mixture Model to cluster posterior patient-level random effects, identifying nine distinct clusters characterized by age, sex, and tumor features. Our findings suggest that individualized, patient-focused strategies may be more effective than geographically targeted approaches for promoting earlier cancer detection.