Ties between event times and jump times in the Cox model

Methods for dealing with tied event times in the Cox proportional hazards model are well developed. Also, the partial likelihood provides a natural way to handle covariates that change over time. However, ties between event times and the times that discrete time-varying covariates change have not been systematically studied in the literature. In this article, we discuss the default behavior of current software and propose some simple methods for dealing with such ties. A simulation study shows that the default behavior of current software can lead to biased estimates of the coefficient of a binary time-varying covariate and that two proposed methods (Random Jitter and Equally Weighted) reduce estimation bias. The proposed methods can be easily implemented with existing software. The methods are illustrated on the well-known Stanford heart transplant data and data from a study on intimate partner violence and smoking.