Estimating and reducing bias in group sequential designs with Gaussian independent increment structure

A concern in the use of sequential testing procedures is the bias associated with the estimates of treatment differences. Clinical trials that stop early because of evidence of therapeutic benefit are prone to exaggerate the magnitude of the treatment effect. We consider methods for estimating and reducing the bias of treatment differences estimators in group sequential designs with Gaussian independent increment structure. We derive an analytical expression for the bias and give an easy-to-calculate approximate bound for its variation. A simulation estimate of the bias, based on a Gaussian independent increment structure, is also described and a related bias reduced estimator is considered.