The main objective of this dissertation is to introduce a framework for two-stage adaptive procedures in which the blind is broken at the end of Stage I. Using our framework, it is possible to control many aspects of an experiment including the Type I error rate, power and maximum total sample size. Our framework also enables us to compare different procedures under the same formulation. We conduct an ANOVA type study to learn the effects of different components of the design specification on the performance characteristics of the resulting design. In addition, we consider conditions for the monotonicity of the power function of a two-stage adaptive procedure.
To foster the practicality of our framework, two extensions are considered. The first one is an application of our framework to the settings with unequal sample sizes. We show how to design a two-stage adaptive procedure having unequal sample sizes for the treatment and control groups. Also we illustrate how to modify an ongoing two-stage adaptive trial when some observations are missing in Stage I and/or in Stage II. Second, we extend the framework to unknown population variance. Our framework can construct a design that incorporates updating the variance estimate at the end of Stage I and modifies the design of Stage II accordingly. All the procedures we present protect the Type I error rate and allow specification of the power and the maximum sample size.
We also consider the problem of switching design objectives between testing noninferiority and testing superiority. Our framework can be used to design a two-stage adaptive procedure that simultaneously tests both noninferiority and superiority hypotheses with controlled error probabilities. The sample size for Stage I is chosen for the main study objective, but that objective may be switched for Stage II based on the unblinded observations from Stage I. Our framework offers a technique to specify certain design criteria such as the various Type I error rates, power and maximum sample sizes.
