Estimating the Dose-Response Pattern by the Maximal Contrast Type Test Approach

Abstract

In a phase II clinical trial it is simultaneously required to prove a drug is truly effective by showing a monotone dose-response relationship and also to obtain information on the recommended dose for the ordinary clinical treatments. Then the multiple comparisons of the interested dose-response patterns are more preferable than an overall testing of the null hypothesis or a fitting of a particular parametric model. In this article the maximal accumulated t statistic (max acc. t-test) proposed for the monotone hypothesis testing is compared with other maximal contrast type tests and shown to be useful also for estimating the dose-response pattern. It is even remarkable that the effect of adding other monotone contrasts to the basic contrasts of max acc. t is so small. The simultaneous lower bounds obtained by the inversion of max acc. t is also shown to be useful for this purpose and has some advantage in giving the lower confidence bound for the mean difference of the estimated optimal dose against the basic dose level. In particular a new formula is obtained in this article for extending the basic lower bounds of max acc. t to all the monotone contrasts by the unique and positive linear combination.

Keywords: :

• Closed test
• Max acc. t test
• Monotone contrast
• Optimal dose
• Simultaneous lower bounds
• Stepwise procedure