article · Journal of Cancer and Tumor International
A retrospective cohort study analysed data from 200 prostate cancer patients at a Ghanaian tertiary referral hospital to evaluate survival modelling methods. Standard Cox proportional hazards regression often assumes constant risk ratios over time, which may fail in complex clinical settings. A three-test sequential protocol combining Schoenfeld residual tests, complementary log-log graphical diagnostics, and a boundary-corrected likelihood ratio test for gamma frailty variance was applied. The analysis showed that the proportional hazards assumption failed, with age, rural residence, cancer stage, and hormonal therapy displaying time-varying effects. Furthermore, residual unobserved heterogeneity was detected. An extended Cox model incorporating both time-varying coefficients and gamma frailty achieved the strongest predictive performance. Applying this sequential diagnostic protocol ensures clinicians and researchers avoid obscuring important time-dependent prognostic factors.
Conventional survival models can misrepresent how clinical and demographic characteristics influence cancer progression over time. By systematically checking for non-proportional hazards and hidden patient variability before selecting a model, biomedical researchers can prevent biased prognostic conclusions. This ensures that prognostic tools reflect true disease trajectories in settings where patients frequently present at advanced stages with complex care needs.
The sequential diagnostic protocol represents an analytical framework ready for application in clinical research, epidemiological software pipelines, and biostatistical analysis of oncology datasets. Potential users include academic biostatisticians, clinical trial analysts, and medical data science teams evaluating patient survival. It is an applied statistical methodology tested on retrospective clinical data, making it directly adoptable by researchers conducting survival analyses across oncology and other biomedical fields.
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Background: Prostate cancer remains a leading cause of cancer mortality among men in Ghana and across sub-Saharan Africa, with many patients presenting at advanced disease stages where survival outcomes are influenced by disease progression, treatment failure, comorbidities, and sociodemographic factors. Aim: To develop and empirically apply a three-test sequential protocol for diagnosing non-proportional hazards and latent heterogeneity before Cox model application, and to evaluate its impact on hazard-ratio interpretation in a Ghanaian prostate cancer cohort. Study Design: Retrospective cohort study was undertaken. Place and Duration of Study: The oncology unit of a Ghanaian tertiary referral hospital; the cohort comprised patients with a confirmed prostate cancer diagnosis and a minimum of three months’ post-diagnosis follow-up. Methodology: Data from 200 patients with prostate cancer (161 prostate cancer deaths) were analysed. The three-test protocol integrated Schoenfeld residual tests, complementary log–log graphical diagnostics, and a boundary-corrected likelihood ratio test for gamma frailty variance. Four models were compared: the standard Cox model, the extended Cox model with time-varying coefficients, the Cox model with gamma frailty, and the extended Cox model with gamma frailty. Competing risks were assessed using the Aalen–Johansen cumulative incidence function. Model performance was evaluated using AIC, BIC, and 10-fold cross-validated concordance indices. Results: The global Schoenfeld test rejected the PH assumption (χ²(15) = 33.67, p = 0.004), with age, rural residence, cancer stage, and hormonal therapy exhibiting significant time-varying effects. Graphical diagnostics confirmed stage-related non-proportionality, and a significant gamma frailty variance indicated residual unobserved heterogeneity. The extended Cox model with gamma frailty provided the best overall performance (AIC = 1421.89; cross-validated C-index = 0.701), outperforming the standard Cox model (AIC = 1438.63; C-index = 0.671). Competing risks had a negligible influence on the survival estimates. Conclusion: The proposed sequential diagnostic protocol offers a systematic and reproducible approach to identifying non-proportional hazards and latent heterogeneity before final Cox model selection. Its application showed that conventional Cox regression may obscure clinically important time-dependent prognostic relationships in this cohort. The framework supports more appropriate model selection and may improve the validity and interpretability of survival analyses in prostate cancer and other biomedical applications.
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DOI: 10.9734/jcti/2026/v16i3369
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