A comparative study on nonparametric estimation procedures for survival quantiles

In survival or reliability data analysis, it is often useful to estimate the quantiles of the lifetime distribution, such as the median time to failure. Different nonparametric methods can construct confidence intervals for the quantiles of the lifetime distributions, some of which are implemented in commonly used statistical software packages. We here investigate the performance of different interval estimation procedures under a variety of settings with different censoring schemes. Our main objectives in this paper are to (i) evaluate the performance of confidence intervals based on the transformation approach commonly used in statistical software, (ii) introduce a new density-estimation-based approach to obtain confidence intervals for survival quantiles, and (iii) compare it with the transformation approach. We provide a comprehensive comparative study and offer some useful practical recommendations based on our results. Some numerical examples are presented to illustrate the methodologies developed.