An 'exact' two-group median test with an extension to censored data

In this note, we develop an 'exact' bootstrap test for comparing medians that is applicable for both censored and uncensored data. It is deemed 'exact' in the sense that an analytic solution is available such that no Monte-Carlo methods are necessary. The advantage of our analytic bootstrap hypothesis testing approach, as compared to standard parametric tests or permutation tests (oftentimes denoted randomization tests), is that the nonparametric bootstrap approach is completely nonparametric and asymptotically correct. In addition, we will illustrate that it has good finite sample behavior and is robust to departures from the classic exchangeability assumption that is a key component of permutation testing.