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The pharmaceutical industry is currently facing an industry wide problem of high attrition rates for new compounds and rising development costs. As a result of this, there is an emphasis on making the development process more ecient. By learning more about new compounds in the early stages of development, the aim is to stop ineective compounds earlier and improve dose selection for compounds that progress to phase III. One approach to this is to use adaptive designs. The focus of this thesis is on response adaptive designs within phase IIb dose-finding studies. We explore adapting the subject allocations based on accrued data, with the intention of focusing the allocation on the interesting parts of the curve and/or the best dose for phase III. In this thesis we have used simulation studies to assess the operational characteristics of a number of response adaptive designs. We found that there were consistent gains to be made by adapting when we were relatively cautious in our method of adaptation. That is, the adaptive method has the opportunity to alter the subject allocation when there is a clear signal in the data, but maintains roughly equal allocation when there is a lot of variability in the data. When we used adaptive designs that were geared to randomising subjects to a few doses, the results were more varied. In some cases the adaptation led to gains in efficacy whilst in others it was detrimental. One of the key aims of a phase IIb dose-finding study is to identify a dose to take forward into phase III. In the final chapter, we show that the way in which we choose the dose for phase III affects the expected gain, and so begin to consider how we can optimise the decision making process.