| Drop-the-Losers designs, as proposed in this dissertation, are special statistical experiments which have two stages separated by a data based decision. In the early part of the experiment, called Stage A, an investigator would administer k treatments and collect response data for each treatment. Then during a brief transition period, the investigator would use this data to select a subset of the k treatments for continuation into the second phase, called Stage B. In many instances, only one treatment would be selected for continuation into Stage B. At the end of the experiment, interest on estimation and inference would focus on the selected treatments. The purpose of the design is to provide one strategy for combining Phase II and Phase III clinical trials. This dissertation focuses on three specific settings. In Chapters 2 and 3, we look at inference for the parameter associated with a treatment that yielded the maximum response in Stage A Chapter 2 deals with normally distributed random variables. Chapter 3 deals with binomial responses. Both chapters look at inference for the selected treatment and comparisons between the selected treatment and a control treatment. Chapter 4 deals with the use of correlated variables that have a bivariate normal distribution for each treatment. The "surrogate" variables are used to make a selection (the treatment associated with the maximum surrogate response is selected) but interest focuses on the other variable, called the primary response, at the end of the trial. Chapter 4 looks at unbiased estimation. Combining Stage A data with Stage B data poses many challenges to inferential analysis and estimation. Traditional estimates can be seriously biased. Traditional inferential techniques often yield tests that have higher than advertised levels of significance and confidence intervals that have lower than advertised levels of confidence. However, carefully combining Stage A data could yields results that are more precise and accurate than could be obtained from analysis of Stage B data alone. The dissertation provides corrective methods with these goals in mind. |
