Testing the Proportional Hazards Assumption before Cox Model Application: A Three-test Sequential Protocol with Empirical Validation in a Ghanaian Prostate Cancer Cohort

Abstract

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.