Interval-Censored Survival Analysis: A Comparative Monte Carlo Study of Weibull AFT and Cox Proportional Hazards Models

This study investigates the comparative performance of the Weibull accelerated failure time (AFT) model and the Cox proportional hazards (PH) model for interval-censored Weibull data. The study emphasizes baseline survival function precision and confidence interval coverage at key quantile-based time points across the survival curve. Through Monte Carlo simulation experiments and applications to the Breast Cosmesis and Diabetic Retinopathy datasets, we compare model performance using bias, empirical variance, estimated variance, and 95% coverage probability. We also evaluate two bootstrap confidence interval methods, the bias-corrected and accelerated (BCa) bootstrap and the Wald bootstrap, across the survival, log-survival, and complementary log–log scales. Results show that while both models provide reasonable regression coefficient inference, the Weibull AFT model consistently yields lower empirical variance for baseline survival estimation when the Weibull assumption holds. The complementary log–log scale provides the most stable coverage overall. These findings support the Weibull AFT model when its distributional assumption is plausible.