Simultaneous confidence intervals for quantile differences of several heterogeneous normal populations: With application to vitamin D supplement treatment on colorectal cancer patients.

In many applications, comparing the q-quantiles of several normal populations are more advantageous than comparing their means. In this paper, we consider the problem of constructing simultaneous confidence intervals (SCIs) for quantile differences of several heterogeneous normal distributions. To the best of our knowledge, this problem remains unsolved. We propose a novel method for constructing a set of SCI. We propose two new sets of SCI by using the proposed technique and discuss two classic and two simulation-based SCIs. We show that the proposed classic SCIs are conservative for all population parameters configuration. We also show that the simulation-based SCIs have correct coverage probability asymptotically. We then compare these six sets of SCI in terms of average volume and coverage probability via an extensive simulation study. Results show that one of the proposed classic SCI can be recommended. Finally, the proposed methods are illustrated by a real example that is a vitamin D study on colorectal cancer patients.