Discussiones Mathematicae Probability and Statistics 24(1) (2004) 85-108


Anthony C. Atkinson

Department of Statistics
London School of Economics, London WC2A 2AE, UK


Adaptive designs are used in phase III clinical trials for skewing the allocation pattern towards the better treatments. We use optimum design theory to provide a skewed biased-coin procedure for sequential designs with continuous responses. The skewed designs are used to provide adaptive designs, the performance of which is studied numerically for designs with three treatments. Important properties are loss and the proportion of allocation to inferior treatments. Regularisation to provide consistent parameter estimates greatly improves both these properties.

Keywords: c-optimal design; limiting allocation proportion; minimization; randomization; regularisation.

2000 Mathematics Subject Classification: 62K05, 62P10.


[1] A.B. Antognini and A. Giovagnoli, On the large sample optimality of sequential designs for comparing two treatments, Journal of the Royal Statistical Society, Series A 167 (2004) (in press).
[2] A.C. Atkinson, Optimum biased coin designs for sequential clinical trials with prognostic factors, Biometrika 69 (1982), 61-67.
[3] A.C. Atkinson, Optimum biased-coin designs for sequential treatment allocation with covariate information, Statistics in Medicine 18 (1999), 1741-1752.
[4] A.C. Atkinson,The comparison of designs for sequential clinical trials with covariate information, Journal of the Royal Statistical Society, Series A 165, (2002), 349-373.
[5]A.C. Atkinson, The distribution of loss in two-treatment biased-coin designs, Biostatistics 4 (2003), 179-193.
[6]A.C. Atkinson and A. Biswas Bayesian adaptive biased-coin designs for clinical trials with normal responses, (2004) (Submitted).
[7] A.C. Atkinson and A. Biswas, Optimum design theory and adaptive-biased coin designs for skewing the allocation proportion in clinical trials, (2004) (Submitted).
[8]F.G. Ball, A.F.M. Smith and I. Verdinelli, Biased coin designs with a Bayesian bias, Journal of Statistical Planning and Inference 34 (1993),403-421.
[9] U. Bandyopadhyay and A. Biswas, Adaptive designs for normal responses with prognostic factors, Biometrika 88 (2001), 409-419.
[10]C.-F. Burman, On Sequential Treatment Allocations in Clinical Trials, Göteborg: Department of Mathematics (1996).
[11]D.R. Cox, A note on design when response has an exponential family distribution, Biometrika 75 (1988), 161-164.
[12]B. Efron, Forcing a sequential experiment to be balanced, Biometrika 58 (1971), 403-417.
[13] J.N. Matthews, An Introduction to Randomized Controlled Clinical Tials, London: Edward Arnold (2000).
[14]W.F. Rosenberger and J.L. Lachin, Randomization in Clinical Trials: Theory and Practice, New York: Wiley (2002).
[15]W.F. Rosenberger, N. Stallard, A. Ivanova, C.N. Harper and M.L. Ricks, Optimal adaptive designs for binary response trials, Biometrics 57 (2002), 909-913.

Received 12 October 2003