Empirical Likelihood Inference on Survival Functions under Proportional Hazards Model

Abstract

Under the framework of the Cox model, it is often of interest to assess a subject’s survival prospect through the individualized predicted survival function, and the corresponding pointwise or simultaneous confidence bands as well. The standard approach to the confidence bands relies on the weak convergence of the estimated survival function to a Gaussian process. Such normal approximation based confidence band may have poor small sample coverage accuracy and generally requires an appropriate transformation to improve its performance. In this paper, we propose an empirical likelihood ratio based pointwise and simultaneous confidence bands that are transformation preserving and therefore eliminate the need of any transformations. The effectiveness of the proposed method is illustrated by a simulation study and an application to the Mayo Clinical primary biliary cirrhosis dataset.