Asymptotically Efficient Sequential Tests of Multiple Hypotheses

• Activity Number: 132
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Shyamal Krishna De*+ and Michael Baron
• Companies: The University of Texas at Dallas and The University of Texas at Dallas
• Keywords: multiple comparisons ; stopping rule ; asymptotic optimality ; Pitman alternative ; sequential probability ratio test ; familywise error rate

Abstract

A number of sequential experiments include multiple statistical inferences such as testing multiple hypotheses, constructing simultaneous confidence sets, or making other decisions involving multiple parameters or multiple measurements. Examples include sequential clinical trials for testing both safety and efficacy of a treatment, quality control charts monitoring a number of measures, acceptance sampling requiring several criteria, and so on. In each application, it is essential to get a result of each individual inference instead of combining results into one procedure giving one global answer. A sequential procedure for testing multiple hypotheses is presented that achieves the asymptotically optimal rate of the expected sample size under the strong control for Type I and Type II familywise error rates. Stopping rules for the sequential testing are proposed, and the form of asymptotically optimal stopping boundaries is derived under Pitman alternatives. Stopping rules are compared; the resulting cost saving and reduction of error rates are analyzed.