Overview of multiple testing methodology and recent development in clinical trials

Multiplicity control is an important statistical issue in clinical trials where strong control of the type I error rate is required. Many multiple testing methods have been proposed and applied to address multiplicity issues in clinical trials. This paper provides an application oriented and comprehensive overview of commonly used multiple testing procedures and recent developments in statistical methodology in multiple testing in clinical trials. Commonly used multiple testing procedures are applied to test non-hierarchical hypotheses and gatekeeping procedures can be used to test hierarchically ordered hypotheses while controlling the overall type I error rate. The recently developed graphical approach has the flexibility to integrate hierarchical and non-hierarchical procedures into one framework. A graphical multiple testing procedure with "no-dead-end" provides an opportunity to fully recycle α across hypothesis families. Two hypothetical clinical trial examples are used to illustrate applications of these procedures. The advantages and disadvantages of the different procedures are briefly discussed.