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Original Articles

An Adaptive Optimal Design for the Emax Model and Its Application in Clinical Trials

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Pages 360-385 | Received 05 Mar 2008, Accepted 25 Jul 2008, Published online: 12 Feb 2009

REFERENCES

  • Atkinson , A. C. , Donev , A. ( 1992 ). Optimum Experimental Design . Oxford : Clarendon Press .
  • Atkinson , A. C. , Cook , R. D. ( 1995 ). D-optimum designs for heteroscedastic linear models . JASA 90 : 204 – 212 .
  • Bauer , P. , Brannath , W. ( 2004 ). The advantages and disadvantages of adaptive designs in clinical trials . Drug Discov. Today 9 : 351 – 357 .
  • Beal , S. L. , Sheiner , L. B. ( 1988 ). Heteroscedastic nonlinear regression . Technometrics 30 ( 3 ): 327 – 338 .
  • Box , G. E. P. , Hunter , W. G. ( 1965 ). Sequential design of experiments for nonlinear models . In: Korth , J. J. , ed. Proceedings of IBM Scientific Computing Symposium , White Plains : IBM , pp. 113 – 137 .
  • Chaloner , K. , Verdinelli , I. ( 1995 ). Bayesian experimental design: a review . Statistical Science 10 : 273 – 304 .
  • Chernoff , H. ( 1953 ). Locally optimal designs for estimating parameters . Ann. Math. Stat. 24 : 586 – 602 .
  • Downing , D. J. , Fedorov , V. V. , Leonov , S. L. (2001). Extracting information from the variance function: optimal design. In: Atkinson , A. C. , Hackl , P. , Müller , W. G. , eds. MODA6 – Advances in Model-Oriented Design and Analysis . Heidelberg : Physica-Verlag, pp. 45–52.
  • Dragalin , V. , Fedorov , V. V. ( 2006 ). Adaptive designs for dose-finding based on efficacy-toxicity response . J. Stat. Plann. Inf. 136 : 1800 – 1823 .
  • Dragalin , V. , Hsuan , F. , Padmanabhan , S. K. ( 2007 ). Adaptive designs for dose-finding studies based on sigmoid E max model . J. Biopharm. Statist. 18 : 1051 – 1070 .
  • Fan , S. K. , Chaloner , K. ( 2001 ). Optimal design for a continuation-ratio model . In: Atkinson , A. C. , Hackl , P. , Müller , W. G. , eds. MODA6 – Advances in Model-Oriented Design and Analysis . Heidelberg : Physica-Verlag , pp. 77 – 85 .
  • Fedorov , V. V. ( 1972 ). Theory of Optimal Experiment . New York : Academic Press .
  • Fedorov , V. V. , Hackl , P. ( 1997 ). Model-Oriented Design of Experiments . New York : Springer .
  • Fedorov , V. V. , Leonov , S. L. ( 2004 ). Parameter estimation for models with unknown parameters in variance . Comm. Stat. Theory and Methods 33 ( 11 ): 2627 – 2657 .
  • Fedorov , V. V. , Leonov , S. L. ( 2005 ). Response driven designs in drug development . In: Wong , W. K. , Berger , M. P. F. , eds. Applied Optimal Designs . Chichester : Wiley , pp. 103 – 136 .
  • Fedorov , V. V. , Gagnon , R. C. , Leonov , S. L. ( 2002 ). Design of experiments with unknown parameters in variance . Appl. Stoch. Mod. Bus. Ind. 18 : 207 – 218 .
  • Fedorov , V. V. , Gagnon , R. , Leonov , S. , Wu , Y. ( 2007 ). Optimal design of experiments in pharmaceutical applications . In: Dmitrienko , A. , Chuang-Stein , C. , D'Agostino , R. , eds. Pharmaceutical Statistics Using SAS: A Practical Guide . Cary : SAS Press , pp. 151 – 195 .
  • Flournoy , N. , Rosenberger , W. F. , Wong , W. K. (eds.) ( 1998 ). New Developments and Applications in Experimental Design . Hayward : Institute of Mathematical Statistics , Lecture Notes, v. 34 .
  • Gallo , P. , Chuang-Stein , C. , Dragalin , V. , Gaydos , B. , Krams , M. , Pinheiro , J. ( 2006 ). Adaptive designs in clinical drug development – an executive summary of the PhRMA Working Group . J. Biopharm. Stat. 16 ( 3 ): 275 – 283 .
  • Haines , L. M. , Perevozskaya , I. , Rosenberger , W. F. ( 2003 ). Bayesian optimal designs for phase I clinical trials . Biometrics 59 : 561 – 570 .
  • Hill , P. D. H. ( 1980 ). D-optimal designs for partially nonlinear regression models . Technometrics 22 : 275 – 276 .
  • Huet , S. , Bouvier , A. , Poursat , M.-A. , Jolivet , E. ( 2004 ). Statistical Tools for Nonlinear Regression. A Practical Guide with S-PLUS and R examples . New York : Springer .
  • Jennison , C. , Turnbull , B. W. ( 2000 ). Group Sequential Methods with Applications to Clinical Trials . Boca Raton : Chapman & Hall .
  • Kiefer , J. , Wolfowitz , J. ( 1960 ). The equivalence of two extremum problems . Canad. J. Math. 12 : 363 – 366 .
  • Magnus , J. R. , Neudecker , H. ( 1988 ). Matrix Differential Calculus with Applications in Statistics and Econometrics . New York : Wiley .
  • Miller , F. , Guilbaud , O. , Dette , H. ( 2007 ). Optimal designs for estimating the interesting part of a dose-effect curve . J. Biopharm. Statist. 17 : 1097 – 1115 .
  • O'Quigley , J. ( 2001 ). Dose-finding designs using continual reassessment method . In: Crowley , J. , ed. Handbook of Statistics in Clinical Oncology . New York : Marcel Dekker , pp. 35 – 72 .
  • Proschan , M. A. , Lan , K. K. G. , Wittes , J. T. ( 2006 ). Statistical Monitoring of Clinical Trials. A Unified Approach . New York : Springer .
  • Rao , C. R. ( 1973 ). Linear Statistical Inference and Its Applications. , 2nd ed. , New York : Wiley .
  • Ratkowsky , D. A. (1990). Handbook of Nonlinear Regression Models . New York : Marcel Dekker.
  • Ratkowsky , D. A. , Reedy , T. J. ( 1986 ). Choosing non-linear parameters in the four-parameter logistic model for radioligand and related assays . Biometrics 42 : 575 – 582 .
  • Rosenberger , W. F. , Hughes-Oliver , J. M. ( 1999 ). Inference from a sequential design: proof of conjecture by Ford and Silvey . Stat. Prob. Lett. 44 : 177 – 180 .
  • Rosenberger , W. F. , Haines , L. M. ( 2002 ). Competing designs for phase I clinical trials: a review . Statist. Med. 21 : 2757 – 2770 .
  • Whitehead , J. , Zhou , Y. , Mander , A. , Ritchie , S. , Sabin , A. , Wright , A. ( 2006 ). An evaluation of Bayesian designs for dose-escalation studies in healthy volunteers . Statist. Med. 25 : 433 – 445 .

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