  We propose a new class of weighted logrank tests (WLRT) that control the risk
of concluding that a new drug is more efficacious than standard of care, when,
in fact, it is uniformly inferior. Perhaps surprisingly, this risk is not
controlled for WLRT in general. Tests from this new class can be constructed to
have high power under a delayed-onset treatment effect scenario, as well as
being almost as efficient as the standard logrank test under proportional
hazards.
