Three excellent reviewers felt that this was a very good contribution, and while the fourth was slightly negative, I read the paper myself and concur that testing for quasi-independence (independence in the presence of a known ordering effect) is an interesting problem, and handling right-censored data is critical in clinical trials. The kernel methodology is solid, and this will have several applications. One drawback is the lack of an interesting (nontrivial) power analysis, but that is common to most papers in the kernel testing literature. Overall I congratulate the authors on a job well done.