Bringing a treatment to market is a long and expensive process. One key element of this is the length of late phase clinical trials. As a result, there is growing interest in platform trials that allow for the addition of new treatment arms as the trial progresses, as well as being able to stop treatments part way through the trial. The interest in platform trial designs has been further magnified by their use during the COVID-19 pandemic which also revealed how few specialised statistical tools have been developed for the design of platform trials. This work aims to study how to design and analyse platform trials.

This thesis focuses on three main topics. The first topic is how to allow for additional arms in a multi-arm multi-stage platform trial. This topic introduces two methods for designing a multi-arm multi-stage platform trial that allows for the addition of preplanned treatments. The first approach focuses on the addition of treatments at interim analyses and stopping the trial when the first effective treatment is found. The second focuses on the addition of treatments at any point within the trial and stopping the trial only when the conclusion is reached on all treatment arms. For both approaches stopping boundaries are found at the interim stages to control the type I error across the entire trial.The methods are then studied for a motivating example and compared to alternative approaches.

The thesis goes on to consider the effects of changing the control treatment when a superior treatment is found within a platform trial. We will show analytically and numerically that retaining the old information can be detrimental to the power of the study if the same boundaries are used. We further extend this to prove when there is guaranteed to be no benefit in keeping the old data for a multi-arm multi-stage trial with no later arms added.

Finally, we study how to design multi-arm multi-stage platform trials where no control treatment exists. The focus of the design being on controlling the type I error and power of the entire study for all pair-wise comparisons. In a motivating trial in sepsis, the design of the proposed approach is evaluated against alternative approaches. For this example it is shown that the proposed method results in the lowest required maximum and expected sample size when controlling the errors at the desired level compared to the alternative approaches. We finish this thesis by summarising the main contributions of the work along with proposing future directions to explore.