Simultaneous confidence intervals for contrasts of quantiles

Skewed distributions and inferences concerning quantiles are common in the health and social science researches. And most standard simultaneous inference procedures require the normality assumption. For example, few methods exist for comparing the medians of independent samples or quantiles of several distributions in general. To our knowledge, there is no easy-to-use method for constructing simultaneous confidence intervals for multiple contrasts of quantiles in a one-way layout. In this paper, we develop an asymptotic method for constructing such intervals both for differences and ratios of quantiles and extend the idea to that of right-censored time-to-event data in survival analysis. Small-sample performance of the proposed method and a bootstrap method were assessed in terms of coverage probabilities and average widths of the simultaneous confidence intervals. Good coverage probabilities were observed for most of the distributions considered in our simulations. The proposed methods have been implemented in an R package and are used to analyze two motivating datasets.