A modified logrank test for censored survival data under order restrictions

We previously proposed a class of ordered weighted logrank tests for analyzing censored survival data under order restrictions. However the power of these tests is asymmetrical with respect to possible alternative configurations and could be inferior to the non-ordered logrank test in extreme cases. A modified ordered logrank test is proposed to remedy this situation. The test is shown to be asymptotically locally equivalent to the generalized Jonckheere's test but computationally simpler.