Sequential procedures for comparing several normal means

Abstract

A sequential clinical trial model is considered in which K≥3 treatments with normally distributed responses and unknown means are compared. For the case of equal variances, four sequential elimination procedures are studied—two based on the between treatments sum-of-squares statistic and two on the range statistic. Simulation indicates that the procedures based on the former statistic are slightly more efficient at determining the treatment with the highest mean. Approximations are also given for the bias of the sample mean vector following the designs and their accuracy is assessed using simu-lation. A generalisation of the procedures based on the between treatments sum-of-squares statistic to the unequal variances case is then considered. Some possible extensions to the work are briefly discussed.

Keywords:

• Between treatments sum-of-squares statistic
• Bias of sample mean vector
• Error probabi-lities
• Expected sample size
• Range statistic
• Unequal variances

Acknowledgements

Part of this work was carried out while the second author was a distance-learning M.Phil. student at the University of Sussex. The authors also wish to thank the referee for his comments and suggestions.