  Drawing causal inferences from observational studies (OS) requires
unverifiable validity assumptions; however, one can falsify those assumptions
by benchmarking the OS with experimental data from a randomized controlled
trial (RCT). A major limitation of existing procedures is not accounting for
censoring, despite the abundance of RCTs and OSes that report right-censored
time-to-event outcomes. We consider two cases where censoring time (1) is
independent of time-to-event and (2) depends on time-to-event the same way in
OS and RCT. For the former, we adopt a censoring-doubly-robust signal for the
conditional average treatment effect (CATE) to facilitate an equivalence test
of CATEs in OS and RCT, which serves as a proxy for testing if the validity
assumptions hold. For the latter, we show that the same test can still be used
even though unbiased CATE estimation may not be possible. We verify the
effectiveness of our censoring-aware tests via semi-synthetic experiments and
analyze RCT and OS data from the Women's Health Initiative study.
