  Two-sample tests with censored outcomes are a classical topic in statistics
with wide use even in cutting edge applications. There are at least two modes
of inference used to justify two-sample tests. One is usual superpopulation
inference assuming that units are independent and identically distributed
(i.i.d.) samples from some superpopulation; the other is finite population
inference that relies on the random assignments of units into different groups.
When randomization is actually implemented, the latter has the advantage of
avoiding distributional assumptions on the outcomes. In this paper, we focus on
finite population inference for censored outcomes, which has been less explored
in the literature. Moreover, we allow the censoring time to depend on treatment
assignment, under which exact permutation inference is unachievable. We find
that, surprisingly, the usual logrank test can also be justified by
randomization. Specifically, under a Bernoulli randomized experiment with
non-informative i.i.d. censoring, the logrank test is asymptotically valid for
testing Fisher's null hypothesis of no treatment effect on any unit. The
asymptotic validity of the logrank test does not require any distributional
assumption on the potential event times. We further extend the theory to the
stratified logrank test, which is useful for randomized block designs and when
censoring mechanisms vary across strata. In sum, the developed theory for the
logrank test from finite population inference supplements its classical theory
from usual superpopulation inference, and helps provide a broader justification
for the logrank test.
