Biometrical Journal, January 2014, Vol.56(1), pp.86-106
Adaptive designs were originally developed for independent and uniformly distributed ‐values. There are trial settings where independence is not satisfied or where it may not be possible to check whether it is satisfied. In these cases, the test statistics and ‐values of each stage may be dependent. Since the probability of a type I error for a fixed adaptive design depends on the true dependence structure between the ‐values of the stages, control of the type I error rate might be endangered if the dependence structure is not taken into account adequately. In this paper, we address the problem of controlling the type I error rate in two‐stage adaptive designs if any dependence structure between the test statistics of the stages is admitted (worst case scenario). For this purpose, we pursue a copula approach to adaptive designs. For two‐stage adaptive designs without futility stop, we derive the probability of a type I error in the worst case, that is for the most adverse dependence structure between the ‐values of the stages. Explicit analytical considerations are performed for the class of inverse normal designs. A comparison with the significance level for independent and uniformly distributed ‐values is performed. For inverse normal designs without futility stop and equally weighted stages, it turns out that correcting for the worst case is too conservative as compared to a simple Bonferroni design.
Adaptive Designs ; Copulas ; Dependent Test Statistics ; Inflation Of Type I Error Rate ; Inverse Normal Method
John Wiley & Sons, Inc.