Bayesian robust symmetric regression for medical data with heavy-tailed errors and censoring

Bayesian symmetric regression offers a principled framework for modeling data characterized by heavy-tailed errors and censoring, both of which are frequently encountered in medical research. Classical regression methods often yield unreliable results in the presence of outliers or incomplete observations, as commonly seen in clinical and survival data. To address these limitations, we develop a robust Bayesian regression model that incorporates symmetric error distributions such as the Student-t and Cauchy, providing improved resistance to extreme values. The model also explicitly accounts for both right and left censoring through its likelihood structure. Inference is performed using Markov Chain Monte Carlo (MCMC), allowing for accurate estimation of uncertainty. The proposed approach is validated through simulation studies and two real-world medical applications: lung cancer survival analysis and hospital stay duration modeling. Results indicate that the model consistently outperforms traditional methods when dealing with noisy, censored, and non-Gaussian data, highlighting its potential for broad use in medical statistics and health outcome research.