Abstract: This paper considers the problem of testing for umbrella alternatives in the one-way layout when survival data are subject to random right censorship. Testing procedures based on two-sample weighted logrank statistics are suggested for both cases when the peak of the umbrella is known or unknown. The Pitman efficacy of the peak-known umbrella test is derived. A class of Lehmann and scale alternatives for which the peak-known umbrella test is optimal in the sense of Pitman efficacy is then obtained under the assumption of equal censorship. Moreover, the results of a Monte Carlo study to investigate the level and power performances of the proposed umbrella tests are presented. Finally, application of the proposed procedures to an appropriate data set is illustrated.
Key words and phrases: Monte Carlo study, one-way layout, Pitman efficacy, right-censored data, umbrella alternatives.