The short-term and long-term hazard ratios model with interval-censored competing risks data

This study presents an extension of the short-term and long-term hazard ratios model to handle interval-censored competing risks data, where subjects may fail due to multiple causes, and the failure time is only known to lie in an interval. The proposed method uses sieve maximum likelihood estimation based on B-splines, offering a flexible and robust approach to estimate the cause-specific cumulative incidence function without strong parametric assumptions. We conducted extensive simulation studies to evaluate the performance of our model under various scenarios, including different parameter values and baseline cumulative hazard functions. The results demonstrate that our model performs well, with small bias and sample standard deviation in the estimates, outperforming traditional models like the Cox proportional hazards and proportional odds models, especially when their underlying assumptions are violated. We also applied our model to a real HIV data set, revealing significant associations between patient characteristics and the risks of death or loss to care. Our findings underscore the importance of gender, age, and CD4 count at antiretroviral treatment initiation on these risks. The study concludes that the proposed model is a valuable tool for analyzing complex survival data in settings with interval-censored competing risks, offering insights with potential implications for clinical decision-making and public health policy.