Institution: University of Bath
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Authors: C. Jennison and B. W. Turnbull
Title: Group sequential tests with data-dependent treatment allocation.
Abstract: Sequential procedures for selecting the best of k normal populations have been studied since the 1960s. Paulson?s (1964) elimination procedure based on two-population comparisons provides an effective, if slightly conservative, framework. Jennison, Johnstone and Turnbull (1982) extended this approach to accommodate data-dependent sampling.
Current practice favours group sequential, rather than continuous, monitoring. I shall describe the distribution theory needed for group sequential comparisons of k normal means. This theory underpins response-adaptive sampling in a two treatment comparison and leads to a very simple way to incorporate data-dependent treatment allocation in standard group sequential tests. Difficulties arise with more than two treatments and a multi-stage approach is needed to maintain the theoretical foundations.
References: C. Jennison and B. W. Turnbull (2000), Group Sequential Methods with Applications to Clinical Trials, Boca Raton: Chapman and Hall/CRC.
C. Jennison and B. W. Turnbull (2001), Group sequential tests with outcome-dependent treatment assignment, Sequential Analysis, 20, 209-234.
C. Jennison, I. M. Johnstone and B. W. Turnbull (1982), Asymptotically optimal procedures for sequential adaptive selection of the best of several normal means. In Statistical Decision Theory and Related Topics III, Vol. 2, (Eds S. S. Gupta and J. O. Berger), New York: Academic Press, 55-86.
E. Paulson (1964), A sequential procedure for selecting the population with the largest mean from k normal populations. Annals of Mathematical Statistics, 35, 174-180.