On improving the accuracy of prediction in Cox models for failure times using copulas

The conventional Cox proportional hazards model is designed to measure the influence of factors on the timing of an event and focuses more on relative risk rather than absolute risk. In the presence of multiple time-to-event variables, this study introduces a copula-based extension of the standard Cox model, which facilitates the dependence structure between variables. We employ vine copulas to effectively model the potentially non-linear relationships between failure times. Through conducting simulation studies, we show that our new algorithm greatly improves the accuracy of predicting failure times compared to other existing methodologies. Our findings are applied to predict mortality timing in real medical data.