Repeated Confidence Intervals Under Fractional Brownian Motion in Long-Term Clinical Trials

References

• Beran , J. ( 1994 ). Statistics for Long-Memory Processes . New York : Chapman and Hall .
   Google Scholar
• Beran , J. , Ocker , D. ( 2000 ). Temporal aggregation of stationary and nonstationary FARIMA(p, d, 0) models. CoFE Discussion Paper, University of Konstanz, Konstanz, Germany .
   Google Scholar
• Beran , J. , Schutzner , M. , Ghosh , S. (2010). From short to long memory: Aggregation and estimation. Computational Statistics and Data Analysis 54:2432–2442.
   Web of Science ®Google Scholar
• Coe , P. R. , Tamhane , A. C. ( 1993 ). Exact repeated confidence intervals for Bernoulli parameters in a group sequential clinical trial . Controlled Clinical Trials 14 : 19 – 29 .
   PubMedGoogle Scholar
• Cook , R. J. ( 1994 ). Interim monitoring of bivariate responses using repeated confidence intervals . Controlled Clinical Trials 15 ( 3 ): 187 – 200 .
   PubMedGoogle Scholar
• Cook , R. , Lawless , J. F. ( 1996 ). Interim monitoring of longitudinal comparative studies with recurrent event responses . Biometrics 52 : 1311 – 1323 .
   PubMed Web of Science ®Google Scholar
• Cumberland , W. G. , Sykes , Z. M. ( 1982 ). Weak convergence of an autoregressive process used in modeling population growth . Journal of Applied Probability 19 ( 2 ): 450 – 455 .
   Web of Science ®Google Scholar
• Daviesm , R. B. , Harte , D. S. ( 1987 ). Tests for Hurst effect . Biometrika 74 : 95 – 101 .
   Web of Science ®Google Scholar
• DeMets , D. L. , Hardy , R. , Friedman , L. F. , Lan , K. K. G. ( 1984 ). Statistical aspect of early termination in the Beta–Blocker heart attack trial . Controlled Clinical Trials 5 : 362 – 372 .
   PubMedGoogle Scholar
• Gassmann , H. I. , Deák , I. , Szántai , T. ( 2002 ). Computing multivariate normal probabilities: a new look . Journal of Computational and Graphical Statistics 11 : 920 – 949 .
   Web of Science ®Google Scholar
• Genz , A. ( 1992 ). Numerical computation of multivariate normal probabilities . Journal of Computational and Graphical Statistics 1 : 141 – 150 .
   Google Scholar
• Genz , A. ( 1993 ). Comparison of methods for the computation of multivariate normal probabilities . Computing Science and Statistics 25 : 400 – 405 .
   Google Scholar
• Giantonio , B. J. , Catalano , P. J. , Meropol , N. J. , O'Dwyer , P. J. , Mitchell , E. P. , Alberts , S. R. , Schwartz , W. A. , Benson , A. B. ( 2007 ). Bevacizumab in combination with oxaliplatin, fluorouracil, and leucovorin (FOLFOX4) for previously treated metastatic colorectal cancer: results from the Eastern Cooperative Oncology Group Study E3200 . Journal of Clinical Oncology 25 : 1539 – 44 .
   PubMed Web of Science ®Google Scholar
• Granger , C. W. J. ( 1980 ). Long memory relationships and the aggregation of dynamic models . Journal of Econometrics 14 : 227 – 238 .
   Web of Science ®Google Scholar
• Jennison , C. , Turnbull , B. W. ( 1984 ). Repeated confidence intervals for group sequential clinical trials . Controlled Clinical Trials 5 : 33 – 45 .
   PubMedGoogle Scholar
• Jennison , C. , Turnbull , B. W. ( 1989 ). Interim analyses: The repeated confidence interval approach . Journal of the Royal Statistical Society. Series B (Methodological) 51 ( 3 ): 305 – 361 .
   Web of Science ®Google Scholar
• Jennison , C. , Turnbull , B. W. ( 1991 ). Exact calculation for sequential t, x 2, F tests . Biometrika 78 : 133 – 141 .
   Web of Science ®Google Scholar
• Jennison , C. , Turnbull , B. W. ( 1993 ). Sequential equivalence testing and repeated confidence intervals with applications to normal and binary responses . Biometrics 49 : 31 – 43 .
   PubMed Web of Science ®Google Scholar
• Jennison , C. , Turnbull , B. W. ( 1997 ). Group sequential analysis incorporating covariate information . Journal of the American Statistical Association 92 : 1330 – 1341 .
   Web of Science ®Google Scholar
• Jennison , C. , Turnbull , B. W. ( 2000 ). Group Sequential Methods with Applications to Clinical Trials . London : Chapman and Hall .
   Google Scholar
• Jiang , W. ( 1999 ). Group sequential procedures for repeated events data with frailty . Journal of Biopharmaceutical Statistics 9 ( 3 ): 379 – 399 .
   PubMedGoogle Scholar
• Lai , T. L. ( 1984 ). Incorporating scientific, ethical and economic considerations into the design of clinical trials in the pharmaceutical industry: a sequential approach . Communications in Statistics, Theory and Methods A 13 : 2355 – 2368 .
   Web of Science ®Google Scholar
• Lai , D. J. ( 2004 ). Estimating the Hurst effect and its applications in clinical trials . Computational Statistics and Data Analysis 45 : 549 – 562 .
   Web of Science ®Google Scholar
• Lai , D. J. ( 2010 ). Group sequential tests under factional Brownian motion in monitoring clinical trials . Statistical Methods and Applications 19 : 277 – 286 .
   Web of Science ®Google Scholar
• Lai , D. J. , Davis , B. R. , Hardy , R. J. ( 2000 ). Fractional Brownian motion and clinical trials . Journal of Applied Statistics 27 : 103 – 108 .
   Web of Science ®Google Scholar
• Lai , D. J. , Moye , L. A. , Davis , B. R. , Brown , L. E. , Sacks , F. M. ( 2001 ). Brownian motion and long-term clinical trial recruitment . Journal of Statistical Planning and Inference 93 : 2239 – 246 .
   Web of Science ®Google Scholar
• Lan , K. K. G. , DeMets , D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70(3):659–63.
   Web of Science ®Google Scholar
• Lan , K. K. G. , Wittes , J. ( 1988 ). The B-value: a tool for monitoring data . Biometrics 44 : 579 – 585 .
   PubMed Web of Science ®Google Scholar
• Lan , K. K. G. , Zucker , D. M. ( 1993 ). Sequential monitoring of clinical trials: The role of information and Brownian motion . Statistics in Medicine 12 : 753 – 765 .
   PubMed Web of Science ®Google Scholar
• Lin , D. Y. , Wei , L. J. ( 1991 ). Repeated confidence intervals for a scale change in a sequential survival study . Biometrics 47 : 289 – 294 .
   PubMed Web of Science ®Google Scholar
• Lin , D. Y. , Yao , Q. , Ying , Z. L. ( 1999 ). A general theory on stochastic curtailment for censored survival data . Journal of the American Statistical Association 94 ( 446 ): 510 – 521 .
   Web of Science ®Google Scholar
• Mendelbrot , B. B. , Van Ness , J. W. ( 1968 ). Fractional Brownian motions, fractional noise and applications . SIAM Review 10 : 422 – 437 .
   Web of Science ®Google Scholar
• Mendelbrot , B. B. , Wallis , J. R. ( 1969 ). Robustness of the rescaled range R/S in the measurements of non-cyclic long-run statistical dependence . Water Resources Research 5 : 967 – 988 .
   Web of Science ®Google Scholar
• Mesa , O. J. , Poveda , G. ( 1993 ). The Hurst effect: The scale of fluctuation approach . Water Resources Research 29 : 3995 – 4002 .
   Web of Science ®Google Scholar
• Miller , K. , Wang , M. , Gralow , J. , Dickler , M. , Cobleigh , M. , Perez , E. A. , Shenkier , T. , Cella , D. , Davidson , N. E. ( 2007 ). Paclitaxel plus bevacizumab versus paclitaxel alone for metastatic breast cancer . New England Journal of Medicine 357 : 2666 – 2676 .
   PubMed Web of Science ®Google Scholar
• Molz , F. J. , Boman , G. K. ( 1993 ). A fractal-based stochastic interpolation scheme in subsurface hydrology . Water Resources Research 20 : 3769 – 3774 .
   Google Scholar
• Murray , S. ( 2000 ). Nonparametric rank based methods for group sequential monitoring of paired censored survival data . Biometrics 56 : 984 – 990 .
   PubMed Web of Science ®Google Scholar
• Murray , S. ( 2002 ). Group sequential monitoring of years of life saved with paired censored survival data . Statistics in Medicine 21 : 177 – 189 .
   PubMed Web of Science ®Google Scholar
• O'Brien P. C. , Fleming , T. R. ( 1979 ). A multiple testing procedure for clinical trials . Biometrics 35 : 459 – 56 .
   Web of Science ®Google Scholar
• Oppenheim , G. , Viano , M. C. ( 2004 ). Aggregation of random parameters Ornstein-Uhlenbeck or AR processes: some convergence results . Journal of Time Series Analysis 25 ( 3 ): 335 – 350 .
   Web of Science ®Google Scholar
• Pocock , S. J. ( 1977 ). Group sequential methods in the design and analysis of clinical trials . Biometrika 64 ( 2 ): 191 – 199 .
   Web of Science ®Google Scholar
• Posch , M. , Wassmer , G. , Brannath , W. ( 2008 ). A note on repeated p-values for group sequential designs . Biometrika 95 ( 1 ): 253 – 256 .
   Web of Science ®Google Scholar
• Proschan , M. A. , Lan , K. K. G. , Wittes , J. ( 2006 ). Statistical Monitoring of Clinical Trials: A Unified Approach . New York : Springer .
   Google Scholar
• Regine , W. , Winter , K. , Abrams , R. , Safran , H. , Hoffman , J. , Konski , A. , Benson , A. , Macdonald , J. , Kudrimoti , M. , Fromm , M. , Haddock , M. , Schaefer , P. , Willett , C. , Rich , T. ( 2008 ). Fluorouracil vs. gemcitabine chemotherapy before and after fluorouracil-based chemotherapy following resection of pancreatic adenocarcinoma: a randomized controlled trial . JAMA 299 ( 9 ): 1019 – 1026 .
   PubMed Web of Science ®Google Scholar
• Sandler , A. , Gray , R. , Perry , M. C. , Brahmer , J. , Schiller , J. H. , Dowlati , A. , Lilenbaum , R. , Johnson , D. H. ( 2006 ). Paclitaxel-carboplatin alone or with bevacizumab for non-small-cell lung cancer . New England Journal of Medicine 355 : 2542 – 2550 .
   PubMed Web of Science ®Google Scholar
• Scharfstein , D. O. , Tsiatis , A. A. , Robins , J. M. ( 1997 ). Semiparametric efficiency and its implication on the design and analysis of group sequential studies . Journal of the American Statistical Association 92 : 1342 – 1350 .
   Web of Science ®Google Scholar
• Shoben , A. , Rudser , K. , Emerson , S. S. ( 2010 ). Estimates of information growth in longitudinal clinical trials. University of Washington Biostatistics working paper series, University of Washington, Seattle, Washington, p. 358 .
   Google Scholar
• Slud , E. , Wei , L. J. ( 1982 ). Two-sample repeated significance tests based on the modified Wilcoxon statistic . Journal of the American Statistical Association 77 : 862 – 868 .
   Web of Science ®Google Scholar
• Stadtmauern , E. A. , O'Neill , A. , Goldstein , L. J. , Crilley , P. A. , Mangan , K. F. , Ingle , J. N. , Brodsky , I. , Martino , S. , Lazarus , H. M. , Erban , J. K. , Sickles , C. , Glick , J. H. (2000). Conventional-dose chemotherapy compared with high-dose chemotherapy plus autologous hematopoietic stem-cell transplantation for metastatic breast cancer. Philadelphia Bone Marrow Transplant Group. New England Journal of Medicine 342:1069–76.
   PubMed Web of Science ®Google Scholar
• Taylor , J. M. G. , Cumberland , W. G. , Sy , J. P. ( 1994 ). A stochastic model for analysis of longitudinal AIDS data . Journal of the American Statistical Association 89 : 727 – 736 .
   Web of Science ®Google Scholar
• Tsai , H. , Chan , K. S. ( 2005 ). Temporal aggregation of stationary and nonstationary continuous time processes . Scandinavian Journal of Statistics 32 : 583 – 597 .
   Web of Science ®Google Scholar
• Tsiatis , A. A. ( 1982 ). Repeated significance testing for a general class of statistics used in censored survival analysis . Journal of the American Statistical Association 77 : 855 – 861 .
   Web of Science ®Google Scholar
• van Houwelingen , H. C. , van de Velde , C. J. H. , Stijnen , T. ( 2005 ). Interim analysis on survival data: Its potential bias and how to repair it . Statistics in Medicine 24 ( 18 ): 2823 – 2835 .
   PubMed Web of Science ®Google Scholar
• Zhang , Q. , Lai , D. J. ( 2010 ). Operating characteristics of group sequential trials monitored under fractional Brownian motion . Communications in Statistics, Simulations and Computations 39 ( 4 ): 705 – 712 .
   Web of Science ®Google Scholar
• Zhang , Q. , Lai , D. J. ( 2011 ). Fractional Brownian motion and long term clinical trial recruitment . Journal of Statistical Planning and Reference 141 ( 5 ): 1783 – 1788 .
   PubMed Web of Science ®Google Scholar