Trendtests with adaptive scoring

The concept of adaptive two-stage designs is applied to the problem of testing the equality of several normal means against an ordered (monotone) alternative. The likelihood-ratio-test proposed by Bartholomew is known to have favorable power properties when testing against a monotonic trend. Tests based on contrasts provide a flexible way to incorporate available information regarding the pattern of the unknown true means through appropriate specification of the scores. The basic idea of the presented concept is the combination of Bartholomew's test (first stage) with an “adaptive score test” (second stage) which utilizes the information resulting from isotonic regression estimation at the first stage. In a Monte Carlo simulation study the adaptive scoring procedure is compared to the non-adaptive two-stage procedure using the Bartholomew test at both stages. We found that adaptive scoring may improve the power of the two stage design, in particular if the sample size at the first stage is considerably larger than at the second stage.