Asymptotic Behavior of a Randomization Test for a Response-Adaptive Design

REFERENCES

• Atkinson , A. and Biswas , A. ( 2014 ). Randomised Response-Adaptive Designs in Clinical Trials , Boca-Raton : CRC .
   Google Scholar
• Balakrishnan , N. and Koutras , M. V. ( 2011 ). Runs and Scans with Applications , New York : Wiley .
   Google Scholar
• Begg , C. B. ( 1990 ). On Inferences from Wei's Biased Coin Design for Clinical Trials , Biometrika 77 : 467 – 484 .
   Web of Science ®Google Scholar
• Bélisle , C. and Melfi , V. ( 2007 ). Independence after Adaptive Allocation , Statistics and Probability Letters 78 : 214 – 224 .
   Web of Science ®Google Scholar
• Billingsley , P. ( 1986 ). Probability and Measure , New York : Wiley .
   Google Scholar
• Edgington , E. S. ( 1987 ). Randomization Tests , New York : Dekker .
   Google Scholar
• Flournoy , N. , Galbete , A. , Moler , J. A. , and Plo , F. ( 2013 ). Randomization Based Inference for the Drop-the-Loser Rule , in MODA10—Advances in Model-Oriented Design and Analysis , D. Uciński , A. C. Atkinson and P. Maciej , eds., pp. 81 – 90 , Heidelberg : Springer .
   Google Scholar
• Flournoy , N. , Haines , L. M. , and Rosenberger , W. F. ( 2013 ). A Graphical Comparison of Response-Adaptive Randomization Procedures , Statistics in Biopharmaceutical Research 5 : 126 – 141 .
   Web of Science ®Google Scholar
• Galbete , A. , Moler , J. A. , and Plo , F. ( 2014 ). A Response-Driven Adaptive Design Based on the Klein Urn , Methodology and Computing in Applied Probability 16 : 731 – 746 .
   Web of Science ®Google Scholar
• Hall , P. and Heyde , C. C. ( 1981 ). Martingale Limit Theory and Its Application , New York : Academic Press .
   Google Scholar
• Hollander , M. and Peña , E. ( 1988 ). Non Parametric Tests under Restricted Treatment-Assignment Rules , Journal of American Statistical Association 83 : 1144 – 1151 .
   Web of Science ®Google Scholar
• Hu , F. and Rosenberger , W. F. ( 2006 ). The Theory of Response-Adaptive Randomization in Clinical Trials , New York : Wiley .
   Google Scholar
• Hu , F. and Zhang , L. ( 2004 ). Asymptotic Properties of Doubly Adaptive Biased Coin Designs for Multitreatment Clinical Trials , Annals of Statistics 32 : 268 – 301 .
   Web of Science ®Google Scholar
• Isaacson , D. L. and Madsen , R. W. ( 1976 ). Markov Chains, Theory and Applications , New York : Wiley .
   Google Scholar
• Ivanova , A. ( 2003 ). A Play-the-Winner-Type Urn Design with Reduced Variability , Metrika 58 : 1 – 13 .
   Web of Science ®Google Scholar
• Knopp , K. ( 1990 ). Theory and Applications of Infinite Series , New York : Dover .
   Google Scholar
• Lehmann , E. L. ( 2006 ). Nonparametrics. Statistical Methods Based on Ranks , New York : Springer .
   Google Scholar
• Liu , G. and Liu , W. ( 1994 ). On the Strong Law of Large Numbers for Functionals of Countable Nonhomogeneous Markov Chains , Stochastic Processes and Their Applications 50 : 375 – 391 .
   Web of Science ®Google Scholar
• Mahmoud , H. M. (2009). Pólya Urn Models , Boca-Raton : CRC.
   Google Scholar
• Pesarin , F. and Salmaso , L. ( 2010 ). Permutation Tests for Complex Data, Theory, Applications and Software, Sussex : Wiley .
   Google Scholar
• Plamadeala , V. and Rosenberger , W. F. ( 2012 ). Sequential Monitoring with Conditional Randomization Tests , Annals of Statistics 40 : 30 – 44 .
   Web of Science ®Google Scholar
• Rosenberger , W. F. ( 1993 ). Asymptotic Inference with Response-Adaptive Treatment Allocation Designs , Annals of Statistics 21 : 2098 – 2107 .
   Web of Science ®Google Scholar
• Rosenberger , W. , Flournoy , N. , and Durham , S. D. ( 1997 ). Asymptotic Normality of Maximum Likelihood Estimators from Multiparameter Response-Driven Designs , Journal of Statistical Planning and Inference 60 : 69 – 76 .
   Web of Science ®Google Scholar
• Rosenberger , W. F. and Lachin , J. M. ( 2002 ). Randomization in Clinical Trials. Theory and Practice , New York : Wiley .
   Google Scholar
• Simon , R. and Simon , N. R. ( 2011 ). Using Randomization Tests to Preserve Type I Error with Response Adaptive and Covariate Adaptive Randomization , Statistics and Probability Letters 81 : 767 – 772 .
   PubMed Web of Science ®Google Scholar
• Smythe , R. T. and Wei , L. J. ( 1983 ). Significance Tests with Restricted Randomization Design , Biometrika 70 : 496 – 500 .
   Web of Science ®Google Scholar
• Zhang , L. , Hu , F. , Cheung , S. H. , and Chan , W. S. ( 2011 ). Immigrated Urn Models—Theoretical Properties and Applications , Annals of Statistics 39 : 643 – 671 .
   Web of Science ®Google Scholar
• Recommended by Nitis Mukhopadhyay
   Google Scholar