A Bayesian Perspective on Survival Prediction in Colorectal Cancer Using Accelerated Failure Time Models

Abstract

Accurate survival prediction in colorectal cancer (CRC) is essential for guiding prognosis
and optimizing treatment strategies. This study applies a Bayesian Accelerated Failure
Time (AFT) modeling framework using three parametric distributions namely Weibull,
log-normal and log-logistic to estimate survival times based on clinical characteristics.
The models were evaluated using the Widely Applicable Information Criterion (WAIC),
Deviance Information Criterion (DIC) and Log Pseudo Marginal Likelihood (LPML).
Among the three, the Bayesian log-normal AFT model achieved the best overall fit and
predictive performance. Clinical covariates including age, sex, tumor stage, nodal involvement,
metastasis status and tumor histology were incorporated to assess their effects on
survival time. The analysis confirmed a strong association between advanced nodal stage
(N2) and prolonged survival, while estimates for tumor stages, tumor type and sex showed
wider credible intervals, indicating greater uncertainty and highlighting the importance
of individualized survival modeling. Posterior trace plots confirmed MCMC convergence
and parameter stability, reinforcing the model’s reliability. Moreover, The survival probability
plots from the Bayesian lognormal AFT model illustrated how age, when combined
with key clinical factors impacts the survivability of the patients. This work demonstrates
the practical utility of Bayesian AFT models in handling non-proportional hazards and
offers a flexible, interpretable framework for individualized survival estimation in CRC.
The findings offer a foundation for future studies integrating more complex covariates and
advancing personalized oncology.