Statistical Science

New directions in adaptive designs

William F. Rosenberger

Full-text: Open access


In any sequential medical experiment on a cohort of human beings, there is an ethical imperative to provide the best possible medical care for the individual patient. This ethical imperative may be compromised if a randomization scheme involving 50-50 allocation is used as accruing evidence begins to favor (albeit not yet conclusively) one experimental therapy over another. Adaptive designs have long been proposed to remedy this situation. An adaptive design seeks to skew assignment probabilities to favor the treatment performing best thus far in the study, proportionately to the magnitude of the treatment effect.

Current researchers in adaptive designs are attempting to provide physicians with a wide choice of design options, and to address practical and ethical concerns within a rigorous mathematical framework. This paper focuses on several broad families of designs, including urn models, random walk rules and other rules. Numerous examples are given along with applications, dose-response studies, clinical trials for efficacy and combined toxicity-efficacy studies.

Article information

Statist. Sci., Volume 11, Number 2 (1996), 137-149.

First available in Project Euclid: 27 November 2002

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Clinical trials dose-response studies ethics quantile estimation random walks randomized play-the-winner rule urn models


Rosenberger, William F. New directions in adaptive designs. Statist. Sci. 11 (1996), no. 2, 137--149. doi:10.1214/ss/1038425657.

Export citation


  • Andersen, J., Faries, D. and Tamura, R. (1994). A randomized play-the-winner design for multi-arm clinical trials. Comm. Statist. A-Theory Methods 23 309-323.
  • Anderson, T. W., McCarthy, P. J. and Tukey, J. W. (1946). "Staircase" method of sensitivity testing. Naval Ordinance Report 65-46, Statistical Research Group, Princeton.
  • Anscombe, F. (1963). Sequential medical trials. J. Amer. Statist. Assoc. 58 365-384.
  • Athrey a, K. B. and Karlin, S. (1967). Limit theorems for the split times of branching processes. Journal of Mathematics and Mechanics 17 257-277.
  • Athrey a, K. B. and Karlin, S. (1968). Embedding of urn schemes into continuous time Markov branching processes and related limit theorems. Ann. Math. Statist. 39 1801- 1817. Bartlett, R. H., Roloff, D. W., Cornell, R. G., Andrews, A. F.,
  • Dillon, P. W. and Zwischenberger, J. B. (1985). Extracorporeal circulation in neonatal respiratory failure: a prospective randomized study. Pediatrics 76 479-487.
  • Begg, C. B. (1990). On inferences from Wei's biased coin design for clinical trials, with discussion. Biometrika 77 467-484. By ar, D. P., Simon, R. M., Friedewald, W. T., Schlesselman, J. J., DeMets, D. L., Ellenberg, J. H., Gail, M. H. and
  • Ware, J. H. (1976). Randomized clinical trials-perspectives on some recent ideas. New England Journal of Medicine 295 74-80.
  • Chevret, S. (1993). The continual reassessment method in cancer phase I clinical trials: a simulation study. Statistics in Medicine 12 1093-1108.
  • Coad, D. S. (1991). Sequential tests for an unstable response variable. Biometrika 78 113-121.
  • Coad, D. S. (1992). A comparative study of some data-dependent allocation rules for Bernoulli data. J. Statist. Comput. Simulation 40 219-231.
  • Colton, T. (1963). A model for selecting one of two medical treatments. J. Amer. Statist. Assoc. 58 388-401. Connor, E. M., Sperling, R. S., Gelber, R., Kiselev, P., Scott, G., O'Sullivan, M. J., VanDy ke, R., Bey, M., Shearer, W., Jacobson, R. L., Jiminez, E., O'Neill, E., Bazin, B., Delfraissy, J., Culnane, M., Coombs, R., Elkins, M., Moy e, J.,
  • Stratton, P. and Balsley, J. (1994). Reduction of maternalinfant transmission of human immunodeficiency virus ty pe 1 with zidovudine treatment. New England Journal of Medicine 331 1173-1180. (Report written for the Pediatric AIDS Clinical Trials Group Protocol 076 Study Group.)
  • Cornfield, J., Halperin, M. and Greenhouse, S. W. (1969). An adaptive procedure for sequential clinical trials. J. Amer. Statist. Assoc. 64 759-770.
  • Derman, C. (1957). Nonparametric up and down experimentation. Ann. Math. Statist. 28 795-798.
  • Dixon, W. J. and Mood, A. M. (1948). A method for obtaining and analyzing sensitivity data. J. Amer. Statist. Assoc. 43 109-126.
  • Durham, S. D. and Flournoy, N. (1994). Random walks for quantile estimation. In Statistical Decision Theory and Related Topics V (S. S. Gupta and J. O. Berger, eds.) 467-476. Springer, New York. Durham, S. D., Flournoy, N. and Montazer-Haghighi, A. A.
  • (1993). Up-and-down designs. In Computer Science and Statistics: Interface (M. E. Tarter and M. D. Lock, eds.) 25 375-384. Interface Foundation of North America, Berkeley.
  • Durham, S. D., Flournoy, N. and Rosenberger, W. F. (1996). A random walk rule for phase I clinical trials. Biometrics. To appear.
  • Farewell, V. T., Viveros, R. and Sprott, D. A. (1993). Statistical consequences of an adaptive treatment allocation in a clinical trial. Canad. J. Statist. 21 21-27.
  • Flehinger, B. J. and Louis, T. A. (1971). Sequential treatment allocation in clinical trials. Biometrika 58 419-426.
  • Flournoy, N. (1993). A clinical experiment in bone marrow transplantation: estimating a percentage point of a quantal response curve. In Case Studies in Bayesian Statistics (C. Gastonis, J. S. Hodges, R. E. Kass and N. D. Singpurwalla, eds.) 324-336. Springer, New York.
  • Flournoy, N., Durham, S. D. and Rosenberger, W. F. (1995). Toxicity in sequential dose-response studies. Sequential Analy sis 14 217-227.
  • Flournoy, N. and Rosenberger, W. F., eds. (1995). Adaptive Designs. IMS, Hay ward, CA.
  • Gantmacher, F. R. (1959). Matrix Theory 2. Chelsea, New York.
  • Gastonis, C. and Greenhouse, J. B. (1992). Bayesian methods for phase I clinical trials. Statistics in Medicine 11 1377- 1389. Gooley, T. A., Martin, P. J., Fisher, L. D. and Pettinger, M.
  • (1994). Simulation as a design tool for phase I/II clinical trials: an example from bone marrow transplantation. Controlled Clinical Trials 15 450-462.
  • Hardwick, J. (1989). Comment: recent progress in clinical trial designs that adapt for ethical purposes. Statist. Sci. 4 327- 336.
  • Kalbfleisch, J. D. and Prentice, R. L. (1980). The Statistical Analy sis of Failure Time Data. Wiley, New York.
  • Karlin, S. and Tay lor, H. M. (1975). A First Course in Stochastic Processes. Academic Press, New York. Korn, E. L., Midthune, D., Chen, T. T., Rubinstein, L. V.,
  • Christian, M. C. and Simon, R. M. (1994). A comparison of two phase I trial designs. Statistics in Medicine 13 1799- 1806.
  • Li, W. (1995). Sequential designs for opposing failure functions. Ph.D. dissertation, College of Arts and Sciences, American Univ., Washington.
  • Mantel, N. (1966). Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemotherapy Reports 50 163-170.
  • O'Quigley, J. (1992). Estimating the probability of a toxicity at the recommended dose following a phase I clinical trial in cancer. Biometrics 48 853-862.
  • O'Quigley, J. and Chevret, S. (1991). Methods for dose finding studies in cancer clinical trials: a review and results of a Monte Carlo study. Statistics in Medicine 10 1647-1664.
  • O'Quigley, J., Pepe, M. and Fisher, L. (1990). Continual reassessment method: a practical design for phase I clinical trials in cancer. Biometrics 46 33-48.
  • Robbins, H. (1952). Some aspects of the sequential design of experiments. Bull. Amer. Math. Soc. 58 527-535.
  • Robbins, H. and Monro, S. (1951). A stochastic approximation method. Ann. Math. Statist. 29 400-407.
  • Rosenberger, W. F. (1992). Asy mptotic inference problems arising from clinical trials using response-adaptive treatment allocation. Ph.D. dissertation, Graduate School of Arts and Sciences, George Washington Univ.
  • Rosenberger, W. F. (1993). Asy mptotic inference with responseadaptive treatment allocation designs. Ann. Statist. 21 2098-2107.
  • Rosenberger, W. F., Flournoy, N. and Durham, S. D. (1996). Asy mptotic normality of maximum likelihood estimators from multiparameter response-driven designs. J. Statist. Plann. Inference. 55.
  • Rosenberger, W. F. and Grill, S. (1996). A randomized sequential design for threshold experiments. Revised for Statistics in Medicine.
  • Rosenberger, W. F. and Lachin, J. M. (1993). The use of response-adaptive designs in clinical trials. Controlled Clinical Trials 14 471-484.
  • Rosenberger, W. F. and Sriram, T. N. (1996). Estimation for an adaptive allocation design. J. Statist. Plann. Inference. 55.
  • Roy all, R. M. (1991). Ethics and statistics in randomized clinical trials (with discussion). Statist. Sci. 6 52-62.
  • Russek-Cohen, E. and Simon, R. M. (1994). Selecting the best dose when a monotonic dose-response relation exists. Statistics in Medicine 13 87-95.
  • Schmoor, C. and Schumacher, M. (1992). Adaptive statistical procedures for the analysis of nonmonotone dose-response relationships. Biometrie und Informatik in Medizin und Biologie 23 113-126.
  • Smy the, R. T. (1996). Central limit theorems for urn models. Stochastic Process. Appl. To appear.
  • Storer, B. E. (1989). Design and analysis of phase I clinical trials. Biometrics 45 925-937.
  • stein, J. H. (1994). A case study of an adaptive clinical trial in the treatment of out-patients with depressive disorder. J. Amer. Statist. Assoc. 89 768-776.
  • Temple, R. (1981). Government viewpoint of clinical trials. Drug Information Journal 16 10-17.
  • Tsutakawa, R. K. (1980). Selection of dose levels for estimating a percent point of a quantal response curve. J. Roy. Statist. Soc. Ser. C 29 25-33.
  • Wei, L. J. (1979). The generalized P´oly a urn design for sequential medical trials. Ann. Statist. 7 291-296.
  • Wei, L. J. (1988). Exact two-sample permutation tests based on the randomized play-the-winner rule. Biometrika 75 603- 606.
  • Wei, L. J. and Durham, S. (1978). The randomized play-thewinner rule in medical trials. J. Amer. Statist. Assoc. 73 840- 843.
  • Wei, L. J., Smy the, R. T., Lin, D. Y. and Park, T. S. (1990). Statistical inference with data-dependent treatment allocation rules. J. Amer. Statist. Assoc. 85 156-162.
  • Wu, C. F. J. (1985). Efficient sequential designs with binary data. J. Amer. Statist. Assoc. 80 974-984.
  • Yao, Q. and Wei, L. J. (1996). Play the winner for phase II/III clinical trials. Statistics in Medicine. To appear.
  • Zelen, M. (1969). Play the winner rule and the controlled clinical trial. J. Amer. Statist. Assoc. 64 131-146.
  • Zelen, M. and Wei, L. J. (1995). Foreword. In Adaptive Designs (N. Flournoy and W. F. Rosenberger, eds.). IMS, Hay ward, CA.