# Methods for Lowering the Type I Error (a), the Group Sequential Method with Adaptive Designs

So far decisions were limited to stopping or continuing a trial. Other decisions may be useful as well, e.g., change in sample size, in primary outcome parameter, in population, in treatments, in allocation rules. As long as blinding is maintained, many changes are allowed (using protocol-amendments), either without spending alphas or with, although such amendments may impact the power of the trial. We are talking of adaptive designs, if data are unblinded for the purpose. This subject is also discussed and reviewed in the Chap. 3. It should always be in the protocol, and never applied on an ad-hoc basis. Examples of adaptive designs are the

- seamless phase II/phase III trials.

They are combined-phase studies, that, instead of a single phase II and a single phase III study, consist of both of them with an interim analysis in between. For statistical analysis separate p-values are combined, using some sort of combination test, e.g., Fisher’s combination test which look a bit like a chi-square test 2k degrees of freedom (Fisher, Statistical methods for research workers, Oliver & Boyd, Edinburgh UK, 1932):

where X^{2} has two degrees of freedom, and p_{i} is the p-value for the ith hypothesis test.

The above trial recently published by the Ceftriaxone Study Investigators (Cudkowicz et al., Lancet Neurol 2014; 13: 1083-91) is an example of a seamless phase II/phase III trial. A Fisher’s combination test was performed, and the combined analysis was, virtually, statistically significant with a p-value of 0.055, while one of the separate phase studies was not statistically significant:

- - phase II: p-value=0.0416
- - phase III: p-value=0.2370
- - X
^{2}= -2*(log (0.0416) + log (0.2370)) = 9.2387, where * is sign of multiplication with degrees of freedom 2 k=2*2=4, the combined p-value=0.0554.