Novel empirical likelihood method for the cumulative hazard ratio under stratified Cox models

Evaluating the treatment effect is a crucial topic in clinical studies. Nowadays, the ratio of cumulative hazards is often applied to accomplish this task, especially when those hazards may be nonproportional. The stratified Cox proportional hazards model, as an important extension of the classical Cox model, has the ability to flexibly handle nonproportional hazards. In this article, we propose a novel empirical likelihood method to construct the confidence interval for cumulative hazard ratio under the stratified Cox model. The large sample properties of the proposed profile empirical likelihood ratio statistic are investigated, and the finite sample properties of the empirical likelihood-based estimators under some different situations are explored in simulation studies. The proposed method was finally applied to perform statistical analysis on a real world dataset on the survival experience of patients with heart failure.