My problem: parallel group randomized trial having a very right-skewed distribution of the primary outcome. I do not want to assume normality and use normal-based 95% CIs (i.e. using 1.96 X SE).
I am comfortable expressing the measure of central tendency as the median, but my question is then how to construct a 95% CI of the difference in medians between the two groups.
The first thing that comes to mind is bootstrapping (resample with replacement, determine median in each the two groups and subtract one from the other, repeat 1000 times, and use the Bias-corrected 95% CI). Is this the correct approach? Any other suggestions?