Repeated Significance Tests controlling the False Discovery Rate

Genetic research such as microarray experiments or gene association studies lead to extremely high dimensional data and results in large scale multiple testing problems. Suitable methods to adjust for multiplicity have to be applied that control an overall error criterion as the family-wise Type I error rate (FWER) or the less stringent false discovery rate (FDR). In this research project we will investigate new approaches to group-sequential repeated significance tests in this context. It has been shown that a sequential approach to large scale multiple testing procedures may lead to a pronounced increase in efficiency and flexibility compared to fixed sample tests. The focus of this research project will be on the recently proposed group sequential tests with simultaneous stopping of sampling (SISS) where sampling is stopped for all hypotheses at the same interim analysis. This is in contrast to the more classical group sequential testing with individual stopping of sampling (ISS) where for each hypothesis sampling of observations is stopped at an interim analysis as soon as its test statistic crosses a stopping boundary. The research project will consist of two steps: First, a thorough investigation of SISS designs controlling the FDR is planned. We will propose several new stopping rules and will study the performance of the procedure under a wide range of scenarios. While the asymptotic control of the FDR of the SISS procedure follows by analytical arguments, we will investigate the operating characteristics in the finite case by simulations. In this part of the project we plan to examine settings with correlated test statistics, different effect size distributions for the alternative hypotheses, and different types of test statistics. In a second step we will consider several extensions of the SISS procedure. Especially, we want to investigate the impact of data dependent sample size reassessment, such that the sample size of future stages is determined based on the data observed so far. Additionally, we will study a procedure that combines aspects of the ISS and the SISS design. These are a variant of the ISS designs, where in addition to the individual stopping of sampling the whole trial can be stopped early at any interim analysis (as soon as a certain number of hypotheses can be rejected). We will work on formal proofs that, asymptotically and under suitable conditions, one needs to adjust only for the actual number of performed interim analyses in order to control the FDR. Again we will use simulations to explore the operation characteristics of such a procedure. Based on data sets from microarray and proteomics experiments we will evaluate the applicability of the procedures in actual research settings.