Statistica Sinica

Zhengqing Li and David L. DeMets

Abstract:Group sequential tests have been widely used to control the type I error rate at a prespecified level in comparative clinical trials. It is well known that due to the optional sampling effect, conventional maximum likelihood estimates will exaggerate the treatment difference, and hence a bias is introduced. We consider a group sequentially monitored Brownian motion process. An analytical expression of the bias of the maximum likelihood estimate for the Brownian motion drift is derived based on the alpha spending method of Lan and DeMets (1983). Through this formula, the bias can be evaluated exactly by numerical integration. We study how the Brownian motion drift and various alpha spending functions and interim analysis patterns affect the bias. A bias adjusted estimator is described and its properties are investigated. The behavior of this estimator is studied for differing situations.

Key words and phrases:Alpha spending function, interim analysis, maximum likelihood, robustness, stopping time.