RANDOMIZED URN MODELS AND SEQUENTIAL DESIGN

REFERENCES

• Andersen , J. 1996 . Clinical Trials Designs–-Made to Order . Journal of Biopharmaceutical Statistics , 6 : 515 – 522 .
   PubMedGoogle Scholar
• Andersen , J. , Faries , D. and Tamura , R.N. 1994 . A Randomized Play-the-Winner Design for Multi-Arm Clinical Trials . Communications in Statistics–-Theory and Methods , 23 : 309 – 323 .
   Web of Science ®Google Scholar
• Artur , V.B. , Ermol’ev , Yu. M. and Kaniovskii , Yu. M. 1987 . Adaptive Growth Processes Modelled by Urn Schemes . Cybernetics , 23 : 49 – 57 .
   Google Scholar
• Athreya , K.B. 1967 . Limit Theorems for Multitype Continuous Time Markov Branching Processes and Some Classical Urn Schemes Stanford : Stanford University . Doctoral thesis
   Google Scholar
• Athreya , K.B. 1969a . Limit Theorems for Multitype Continuous Time Markov Branching Processes. I. The Case of an Eigenvector Linear Functional . Zeitschrift für. Wahrscheinlichkeitstheorie und verwandte Gebiete , 12 : 320 – 332 .
   Google Scholar
• Athreya , K.B. 1969b . Limit Theorems for Multitype Continuous Time Markov Branching Processes. II. The Case of an Arbitrary, Linear Functional . Zeitschrift für Wahrscheinlichkeitstheorie and verwandte Gebiete , 13 : 204 – 214 .
   Google Scholar
• Athreya , K.B. and Karlin , S. 1967 . Limit Theorems for the Split Times of Branching Processes . Journal of Mathematics and Mechanics , 17 : 257 – 277 .
   Google Scholar
• Athreya , K.B. and Karlin , S. 1968 . Embedding of Urn Schemes into Continuous Time Markov Branching Processes and Related Limit Theorems . Annals of Mathematical Statistics , 39 : 1801 – 1817 .
   Google Scholar
• Athreya , K.B. and Ney , P. 1972 . Branching Processes Berlin : Springer .
   Google Scholar
• Bai , Z.D. and Hu , F. 1999 . Asymptotic Theorems for Urn Models with Non-homogeneous Generating Matrices . Stochastic Processes and Their Applications , 80 : 87 – 101 .
   Web of Science ®Google Scholar
• Bai , Z.D. and Hu , F. 2001 . Asymptotics in Non-homogeneous Urn Models , Submitted
   Google Scholar
• Bai , Z.D. , Hu , F. and Rosenberger , W.F. 2002 . Asymptotic Properties of Adaptive Designs for Clinical Trials with Delayed Response . Annals of Statistics , 30 ( 1 ) in press
   Web of Science ®Google Scholar
• Bai , Z.D. , Hu , F. and Shen , L. 2002 . An Adaptive Design for Multi-Arm Clinical Trials . Journal of Multivariate Analysis , in press
   Web of Science ®Google Scholar
• Bandyopadhyay , U. and Biswas , A. 1996 . Delayed Response in Randomized Play-the-Winner Rule: A Decision Theoretic Outlook . Calcutta Statistical Association Bulletin , 46 : 69 – 88 .
   Google Scholar
• Bandyopadhyay , U. and Biswas , A. 1997 . Sequential Comparison of Two Treatments in Clinical Trials: A Decision Theoretic Approach Based on Randomized Play-the-winner Rule . Sequential Analysis , 16 : 65 – 91 .
   Google Scholar
• Bandyopadhyay , U. and Biswas , A. 1999a . Allocation by Randomized Play-the-Winner Rule in the Presence of Prognostic Factors . Sankhya B , 61 : 397 – 412 .
   Google Scholar
• Bandyopadhyay , U. and Biswas , A. 1999b . Sequential Nonparametric Tests Based on Randomized Play-the-Winner Rule for Restricted Bivariate Alternatives . Journal of Statistical Planning and Inference , 79 : 45 – 57 .
   Web of Science ®Google Scholar
• Bandyopadhyay , U. and Biswas , A. 2000a . A Class of Adaptive Designs . Sequential Analysis , 19 : 45 – 62 .
   Google Scholar
• Bandyopadhyay , U. and Biswas , A. 2000b . Comparison of Two Treatments with Heterogeneous Experimental Units . Journal of Statistical Planning and Inference , 83 : 441 – 448 .
   Web of Science ®Google Scholar
• 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 .
   PubMed Web of Science ®Google Scholar
• Begg , C. 1990 . On Inferences from Wei's Biased Coin Design for Clinical Trials . Biometrika , 77 : 467 – 484 .
   Web of Science ®Google Scholar
• Biswas , A. 1996 . Some Sequential-type Monparametrics in Clinical Trials Calcutta : University of Calcutta . Doctoral thesis
   Google Scholar
• Biswas , A. 1999 . Delayed Response in Randomized Play-the-Winner Rule Revisited . Communications in Statistics–-Theory and Methods , 28 : 715 – 731 .
   Google Scholar
• Coad , D.S. and Govindarajulu , Z. 2000 . Corrected Confidence Intervals Following a Sequential Adaptive Clinical Trial with Binary Responses . Journal of Statistical Planning and Inference , 91 : 53 – 64 .
   Web of Science ®Google Scholar
• Coad , D.S. and Ivanova , A. 2001 . Bias Calculations for Adaptive Urn Designs . Sequential Analysis , 20 : 91 – 116 .
   Google Scholar
• Coad , D.S. and Rosenberger , W.F. 1999 . A Comparison of the Randomised Play-the-Winner Rule and the Triangular Test for Clinical Trials with Binary Response . Statistics in Medicine , 18 : 761 – 769 .
   PubMed Web of Science ®Google Scholar
• Cornell , R.G. , Landenberger , B.D. and Bartlett , R.H. 1986 . Randomized Play the Winner Clinical Trials . Communications in Statistics–-Theory and Methods , 15 : 159 – 178 .
   Web of Science ®Google Scholar
• Durham , S.D. and Flournoy , N. 1993 . Convergence Results for an Adaptive Ordinal Urn Design . Theory of Probability and Its Applications , 37 : 14 – 17 .
   Web of Science ®Google Scholar
• Durham , S.D. and Flournoy , N. 1994 . “ Random Walks for Quantile Estimation ” . In Statistical Decision Theory and Related Topics V Edited by: Gupta , S.S. and Berger , J.O. 467 – 476 . New York : Springer .
   Google Scholar
• Durham , S.D. , Flournoy , N. and Li , W. 1998 . Sequential Designs for Maximizing the Probability of a Favorable Response . Canadian Journal of Statistics , 3 : 479 – 495 .
   Web of Science ®Google Scholar
• Durham , S.D. and Yu , C.F. 1990 . Randomized Play-the-Leader Rules for Sequential Sampling from Two Populations . Probability in the Engineering and Informational Sciences , 4 : 355 – 367 .
   Google Scholar
• Eggenberger , F. and Pólya , G. 1923 . Über die Statistik Verketteter Vorgänge . Zeitschrift für Angewandte Mathematik and Mechanik , 3 : 279 – 289 .
   Google Scholar
• Freedman , D.A. 1965 . Bernard Friedman's Urn . Annals of Mathematical Statistics , 36 : 956 – 970 .
   Google Scholar
• Friedman , B. 1949 . A Simple Urn Model . Communications in Pure and Applied Mathematics , 2 : 59 – 70 .
   Web of Science ®Google Scholar
• Grill , S.E. , Rosenberger , W.F. , Boyle , K. , Cannon , M. and Hallett , M. 1998 . Perception of Timing of Kinesthetic Stimuli . Neuro Report , 9 : 4001 – 4005 .
   PubMed Web of Science ®Google Scholar
• Hall , P. and Heyde , C.C. 1980 . Martingale Limit Theory and Its Application London : Academic Press .
   Google Scholar
• Hardwick , J. and Stout , Q.F. 1998 . “ Flexible Algorithms for Creating and Analyzing Adaptive Sampling Procedures ” . In New Developments and Applications in Experimental Design Edited by: Flournoy , N. , Rosenberger , W. F. and Wong , W.K. 91 – 105 . Hayward : Institute of Mathematical Statistics .
   Google Scholar
• Hu , F. and Rosenberger , W.F. 2000 . Analysis of Time Trends in Adaptive Designs with Application to a Neurophysiology Experiment . Statistics in Medicine , 19 : 2067 – 2075 .
   PubMed Web of Science ®Google Scholar
• Hu , F. , Rosenberger , W.F. and Zidek , J.V. 2000 . Relevance Weighted Likelihood for Dependent Data . Metrika , 51 : 223 – 243 .
   Web of Science ®Google Scholar
• Ivanova , A. and Durham , S.D. 2000 . “ Drop the Loser Rule ” . In Technical Report #TR-00-01 Chapel Hill : University of North Carolina .
   Google Scholar
• Ivanova , A. and Flournoy , N. 2001 . “ A Birth and Death Urn for Ternary Outcomes: Stochastic Processes Applied to Urn Models ” . In Probability and Statistical Models with Applications Edited by: Charalambides , C.A. , Koutras , M.V. and Balakrishnan , N. 583 – 600 . Boca Raton : Chapman and Hall .
   Google Scholar
• Ivanova , A. and Rosenberger , W.F. 2000 . A Comparison of Urn Designs for Randomized Clinical Trials of K>2 Treatments . Journal of Biopharmaceutical Statistics , 10 : 93 – 107 .
   PubMedGoogle Scholar
• Ivanova , A. and Rosenberger , W.F. 2001 . Adaptive Designs for Highly Successful Treatments . Drug Information Journal , 35 : 1087 – 1093 .
   Google Scholar
• Ivanova , A. , Rosenberger , W.F. , Durham , S.D. and Flournoy , N. 2000 . A Birth and Death Urn for Randomized Clinical Trials: Asymptotic Methods . Sankhya B , 62 : 104 – 118 .
   Google Scholar
• Johnson , N.L. and Kotz , S. 1977 . Urn Models and Their Applications New York : John Wiley .
   Google Scholar
• Matthews , P.C. and Rosenberger , W.F. 1997 . Variance in Randomized Play-the-Winner Clinical Trials . Statistics and Probability Letters , 35 : 233 – 240 .
   Web of Science ®Google Scholar
• Posch , M. 1997 . Cycling in a Stochastic Learning Algorithm for Normal Form Games . Evolutionary Economics , 7 : 193 – 207 .
   Web of Science ®Google Scholar
• Robbins , H. 1952 . Some Aspects of the Sequential Design of Experiments . Bulletin of the American Mathematics Society , 58 : 527 – 535 .
   Web of Science ®Google Scholar
• Rosenberger , W.F. 1992 . Asymptotic Inference Problems Arising from Clinical Trials Using Response-Adaptive Treatment Allocation Washington : George Washington University . Doctoral thesis
   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.F. 1996 . New Directions in Adaptive Designs . Statistical Science , 11 : 137 – 149 .
   Web of Science ®Google Scholar
• Rosenberger , W.F. 1999 . Randomized Play-the-Winner Clinical Trials: Review and Recommendations . Controlled Clinical Trials , 20 : 328 – 342 .
   PubMedGoogle Scholar
• Rosenberger , W.F. , Flournoy , N. and Durham , S.D. 1997 . Asymptotic Normality of Maximum Likelihood Estimators from Multiparameter Response- driven Designs . Journal of Statistical Inference and Planning , 60 : 69 – 76 .
   Web of Science ®Google Scholar
• Rosenberger , W.F. and Grill , S.E. 1997 . A Sequential Design for Psychophysical Experiments: An Application to Estimating Timing of Sensory Events . Statistics in Medicine , 16 : 2245 – 2260 .
   PubMed Web of Science ®Google Scholar
• Rosenberger , W.F. and Hu , F. 1999 . Bootstrap Methods for Adaptive Designs . Statistics in Medicine , 18 : 1757 – 1767 .
   PubMed Web of Science ®Google Scholar
• Rosenberger , W.F. and Sriram , T.N. 1997 . Estimation for an Adaptive Allocation Design . Journal of Statistical Planning and Inference , 59 : 309 – 319 .
   Web of Science ®Google Scholar
• Rosenberger , W.F. , Stallard , N. , Ivanova , A. , Harper , C. and Ricks , M. 2001 . Optimal Adaptive Designs for Binary Response Trials . Biometrics , 57 : 173 – 177 .
   Web of Science ®Google Scholar
• Rout , C.C. , Rocke , D.A. , Levin , J. , Gouw's , E. and Reddy , D. 1993 . A Reevaluation of the Role of Crystalloid Preload in the Prevention of Hypotension Associated with Spinal Anesthesia for Elective Cesarean Section . Anesthesiology , 79 : 262 – 269 .
   PubMed Web of Science ®Google Scholar
• Smythe , R.T. 1996 . Central Limit Theorems for Urn Models . Stochastic Processes and Their Applications , 65 : 115 – 137 .
   Web of Science ®Google Scholar
• Stallard , N. and Rosenberger , W.F. 2002 . Exact Group-Sequential Designs for Clinical Trials with Randomised Play-the-Winner Allocation . Statistics in Medicine, , 21 : 467 – 480 .
   PubMed Web of Science ®Google Scholar
• Tamura , R.N. , Faries , D.E. , Andersen , J.S. and Heiligenstein , J.H. 1994 . A Case Study of an Adaptive Clinical Trial in the Treatment of Out-Patients with Depressive Disorder . Journal of the American Statistical Association , 89 : 768 – 776 .
   Web of Science ®Google Scholar
• Wei , L.J. 1977 . A Class of Designs for Sequential Clinical Trials . Journal of the American Statistical Association , 72 : 382 – 386 .
   Web of Science ®Google Scholar
• Wei , L.J. 1978 . An Application of an Urn Model to the Design of Sequential Controlled Clinical Trials . Journal of the American Statistical Association , 73 : 559 – 563 .
   Web of Science ®Google Scholar
• Wei , L.J. 1979 . The Generalized Pólya's Urn Design for Sequential Medical Trials . Annals of Statistics , 7 : 291 – 296 .
   Web of Science ®Google Scholar
• Wei , L.J. 1988 . Exact Two-Sample Permutation Tests Based on the Randomized Play-the-winner Rule in Medical Trials . Biometrika , 75 : 603 – 606 .
   Web of Science ®Google Scholar
• Wei , L.J. and Durham , S. 1978 . The Randomized Play-the-Winner Rule in Medical Trials . Journal of the American Statistical Association , 73 : 840 – 843 .
   Web of Science ®Google Scholar
• Wei , L.J. , Smythe , R.T. , Lin , D.Y. and Park , T.S. 1990 . Statistical Inference with Data-Dependent Treatment Allocation Rules . Journal of the American Statistical Association , 85 : 156 – 162 .
   Web of Science ®Google Scholar
• Zelen , M. 1969 . Play the Winner Rule and the Controlled Clinical Trial . Journal of the American Statistical Association , 64 : 131 – 146 .
   Web of Science ®Google Scholar
• Zhu , W. and Wong , W.K. 2000 . Bayesian Optimal Designs for Estimating a Set of Symmetrical Quantiles . Statistics in Medicine , 20 : 123 – 137 .
   Web of Science ®Google Scholar