We consider seamless Phase II/III clinical trials which compare K treatments with a common control in Phase II, then test the most promising treatment against control in Phase III. The final hypothesis test for the selected treatment can use data from both Phases, subject to controlling the familywise type I error rate. We show that the choice of method for conducting the final hypothesis test has a substantial impact on the power to demonstrate that an effective treatment is superior to control. To understand these differences in power we derive optimal
decision rules, maximising power for particular configurations of treatment effects. Rules with optimal frequentist properties are found as solutions to multivariate Bayes decision problems. Although the optimal rule depends on
the configuration of treatment means considered, we are able to identify two decision rules with robust efficiency: a rule using a weighted average of the Phase II and Phase III data on the selected treatment and control, and a closed testing procedure using an inverse normal combination rule and a Dunnett test for intersection hypotheses. For the first of these rules, we find the optimal division of a given total sample size between Phase II and Phase III.We also assess the value of using Phase II data in the final analysis and find that for many plausible scenarios, between 50% and 70% of the Phase II numbers on the selected treatment and control would need to be added to the Phase III sample size in order to achieve the same increase in power.