Survival modeling and assessing prognostic factors of colorectal cancer in Ethiopia: Addressing violation of statistical assumptions
Tuem Gebre Abraha, Mulu Reda Terefe, Zeytu Gashaw AsfawBackground
Colorectal cancer (CRC) remains a major global health challenge, with rapidly rising incidence in low- and middle-income countries, including Ethiopia. Survival outcomes are compromised by late-stage presentation, limited therapeutic capacity, and weak post-treatment follow-up. Although survival analysis is critical for characterizing CRC prognosis, insufficient attention has been given to the performance and validity of commonly applied survival models in Ethiopian populations, particularly when statistical assumptions are violated.
Objective
To identify key clinical and treatment-related prognostic factors influencing overall survival among Ethiopian CRC patients and to assess the robustness and interpretability of Cox proportional hazard model (Cox PH model), stratified Cox proportional hazard model, frailty model, and Accelerated Failure Time (AFT) models, focusing on model adequacy under assumption violations.
Methods
We conducted a retrospective cohort analysis of 161 colorectal cancer patients diagnosed between 2012 and 2016. Survival probabilities were estimated using Kaplan–Meier analysis, with group comparisons via log-rank tests. Multivariable modeling employed Cox proportional hazards, stratified Cox proportional hazard model, frailty, and accelerated failure time models. Model adequacy was evaluated through Akaike Information Criterion, concordance indices, and the Global Schoenfeld test for proportional hazards assessment.
Results
The Cox proportional hazard model violated the proportional hazards assumption (global p = 0.043), primarily due to histological subtype effects, indicating that the standard Cox proportional hazard model was not appropriate for this dataset. Assumption violations were mitigated using the stratified Cox proportional hazard model (global p = 0.122). Among accelerated failure time models, the log-logistic distribution provided superior model fit (AIC = 649.88; concordance = 0.724). Time-ratio (TR) interpretation showed that surgery extended survival by approximately 2.4-fold, whereas elevated baseline carcinoembryonic antigen levels and metastatic disease reduced survival duration by nearly half. Elevated carcinoembryonic antigen, distant metastasis, vascular invasion, and squamous cell histology were consistently associated with poorer prognosis, while surgery and chemotherapy remained protective across models.
Conclusion
Rigorous model checking indicates that the conventional Cox proportional hazards model is inappropriate for this cohort due to proportional hazard assumption violations. Accelerated failure time modeling, particularly the log-logistic form, offered improved fit and clearer time-based interpretation of covariate effects. These findings underscore the importance of model validation in CRC survival research and highlight the need for improved early detection, surgical access, and targeted management of aggressive tumor subtypes to enhance patient outcomes in Ethiopia.