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This work presents novel and powerful tests for comparing non-proportionalhazard functions, based on sample-space partitions. Right censoring introducestwo major difficulties which make the existing sample-space partition tests foruncensored data non-applicable: (i) the actual event times of censoredobservations are unknown; and (ii) the standard permutation procedure isinvalid in case the censoring distributions of the groups are unequal. Weovercome these two obstacles, introduce invariant tests, and prove theirconsistency. Extensive simulations reveal that under non-proportionalalternatives, the proposed tests are often of higher power compared withexisting popular tests for non-proportional hazards. Efficient implementationof our tests is available in the R package KONPsurv, which can be freelydownloaded from {https://github.com/matan-schles/KONPsurv

$K$-sample omnibus non-proportional hazards tests based on right-censored data