Umbrella tests for right-censored survival data

This paper considers the problem of testing for umbrella alternatives in th e one-way layout when survival data are subject to random right censorship. Testing procedures based on two-sample weighted logrank statistics are sug gested for both cases when the peak of the umbrella is known or unknown. Th e Pitman efficacy of the peak-known umbrella test is derived. A class of Le hmann and scale alternatives for which the peak-known umbrella test is opti mal in the sense of Pitman efficacy is then obtained under the assumption o f equal censorship. Moreover, the results of a Monte Carlo study to investi gate the level and power performances of the proposed umbrella tests are pr esented. Finally, application of the proposed procedures to an appropriate data set is illustrated.