A note on median regression for complex surveys

There is a great need for statistical methods for analyzing skewed responses in complex sample surveys. Quantile regression is a logical option in addressing this problem but is often accompanied by incorrect variance estimation. We show how the variance can be estimated correctly by including the survey design in the variance estimation process. In a simulation study, we illustrate that the variance of the median regression estimator has a very small relative bias with appropriate coverage probability. The motivation for our work stems from the National Health and Nutrition Examination Survey where we demonstrate the impact of our results on iodine deficiency in females compared with males adjusting for other covariates.