Conditional and Unconditional Confidence Intervals Following a Group Sequential Test

• Activity Number: 86
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Xiaoyin Fan*+ and David L. DeMets
• Companies: Merck & Co., Inc. and University of Wisconsin, Madison
• Keywords: group sequential ; confidence interval ; conditional coverage ; stopping time

Abstract

The naïve confidence interval (CI) of the parameter following a group sequential study is biased in terms of the coverage probability. There are several available exact CI methods based on different ways of ordering the two-dimensional test statistics sample space. While those exact CI's maintain the overall coverage probability, the conditional coverage probability at any given stopping stage could be well below the target level. A conditional CI (CCI) method can provide correct conditional coverage using the conditional likelihood inference at the stopping stage. However, the pure CCI method has serious drawbacks such as an unreasonably wide interval and inconsistency with the main hypothesis testing result. A two-step restricted conditional CI (RCCI) is proposed which takes advantage of both the stopping time and the test value at that point. Compared with available methods, numerical results show that the RCCI not only improves the conditional coverage considerably from the exact CI's, but also avoids the major undesirable properties of the CCI. The repeated confidence interval (RCI) method is compared as well but also found less appealing than the RCCI.