Confidence bands for hazard rate function based on a debiased estimation

Abstract

The hazard rate function plays an important role in survival analysis. Extensive work has been carried out for building the point estimation of hazard rate function but limited work has been done for constructing its confidence bands, which is a fundamental issue in statistical inference. To fill in this gap, we focus on investigating this problem for right censored survival data in this paper. We first propose a debiased estimation for hazard rate function, based on which, we further construct the pointwise and simultaneous confidence bands for hazard rate function. We establish some theoretical properties of the proposed method, including the convergence rate and asymptotic distributions. The finite-sample performance of the proposed procedure is evaluated via both simulation studies and an application to a real data from the breast cancer study.

Keywords:

• Confidence bands
• debiased estimation
• hazard rate function
• Kernel smoothing
• survival data

Additional information

Funding

This work is partly supported by the National Natural Science Foundation of China grants (No.11901581); the Fundamental Research Funds for the Central Universities (No.CCNU18XJ040); the Fundamental Research Funds for the Central Universities, Zhongnan University of Economics and Law (No.2722020JCG064).