The researchers began with Kaplan–Meier estimates of survival probabilities and log-rank tests to compare patient groups, then fitted a family of multivariable models: the standard Cox proportional hazards model, a stratified version of that model, frailty models, and accelerated failure time models. Model adequacy was judged with the Akaike Information Criterion, concordance indices, and the Global Schoenfeld test for assessing the proportional hazards assumption.

That test returned a p-value of 0.043, indicating a violation of the proportional hazards assumption, driven primarily by histological subtype effects. In other words, the standard Cox model was not appropriate for this cohort. The stratified Cox model restored adequacy with a global p-value of 0.122, offering one route around the violation.

Among the accelerated failure time models, which operate on the scale of survival duration rather than hazard, the log-logistic distribution fit best, with an Akaike Information Criterion of 649.88 and a concordance index of 0.724. The time-ratio interpretation this framework affords is strikingly intuitive: surgery extended survival approximately 2.4-fold, while elevated baseline carcinoembryonic antigen levels and metastatic disease each cut survival duration nearly in half. Rather than expressing effects as instantaneous risks, these time ratios state directly how much longer or shorter patients lived under given conditions.

Across models, a consistent picture of prognosis emerged. Elevated carcinoembryonic antigen, distant metastasis, vascular invasion, and squamous cell histology were all associated with poorer survival, while surgery and chemotherapy remained protective. The consistency of these signals despite the shift between modeling frameworks strengthens confidence that they reflect genuine clinical relationships rather than artifacts of a single statistical approach.

The study’s broader message concerns statistical practice. Survival analyses of cancer prognosis are published constantly, yet the performance and validity of commonly applied models in Ethiopian populations had received little attention, particularly when assumptions are violated. By demonstrating that the conventional Cox model was inadequate for this dataset and that accelerated failure time modeling, especially in its log-logistic form, offered improved fit and clearer time-based interpretation, the authors make a case for rigorous model checking as a routine step in colorectal cancer survival research rather than an optional refinement.

The clinical implications are equally direct. The findings underscore the need for improved early detection, expanded surgical access, and targeted management of aggressive tumor subtypes to improve outcomes in Ethiopia. They also caution researchers in similar settings: before reporting hazard ratios, test the assumptions behind them, because the model that is easiest to fit may not be the model that tells the truth about how long patients live.

Subject of Research: Survival modeling and prognostic factors for colorectal cancer in Ethiopia, addressing violations of statistical assumptions

Article Title: Survival modeling and assessing prognostic factors of colorectal cancer in Ethiopia: Addressing violation of statistical assumptions

Article References: Abraha, T. G., Terefe, M. R., & Asfaw, Z. G. (2026). Survival modeling and assessing prognostic factors of colorectal cancer in Ethiopia: Addressing violation of statistical assumptions. PLOS One, 21(10), e0361233. https://doi.org/10.1371/journal.pone.0361233

Image Credits: AI Generated

DOI: 10.1371/journal.pone.0361233

Keywords: colorectal cancer, survival analysis, Cox proportional hazards model, accelerated failure time, Ethiopia, prognostic factors, statistical assumptions, log-logistic model, retrospective cohort, Survival, modeling, assessing