Design and analysis for survival data under order restrictions with a modified logrank test.

We previously proposed a class of ordered weighted logrank tests for analysing censored survival data under order restrictions. However, the power of these tests is asymmetrical with respect to possible alternative configurations. While it is superior in most cases, the power can be inferior to the non-ordered logrank test in extreme cases. We propose a modified ordered logrank test which performs uniformly better than the non-ordered test. The power of the modified test is equivalent to the generalized Jonckheere's test but its computation is much simpler. We give sample size requirements for sufficient power to reject the global null hypothesis at specified hazard ratios between the control group and the best group. Following Fisher's least significant difference (LSD) strategy for multiple comparisons, power investigations indicate that the nominal power for the global test carries over to the control versus best comparison during pairwise testing. The power for detecting intermediate survival differences is inadequate but the sample sizes required to detect such differences may be impractical in most applications.