Under-smoothed kernel confidence intervals for the hazard ratio based on censored data

In cancer clinical trials, it is often of interest in estimating the ratios of hazard rates at some specific time points during the study from two independent populations. In this paper, we consider nonparametric confidence interval procedures for the hazard ratio based on kernel estimates for the hazard rates with under-smoothing bandwidths. Two methods are used to derive the confidence intervals: one based on the asymptotic normality of the ratio of the kernel estimates for the hazard rates in two populations and another through Fieller's Theorem. The performances of the proposed confidence intervals are evaluated through Monte-Carlo simulations and applied to the analysis of data from a clinical trial on early breast cancer.