×

Sequential monitoring of response-adaptive randomized clinical trials. (English) Zbl 1194.62095

Summary: Clinical trials are complex and usually involve multiple objectives such as controlling the type I error rate, increasing power to detect treatment difference, assigning more patients to better treatment, and more. In the literature, both response-adaptive randomization (RAR) procedures (by changing randomization procedure sequentially) and sequential monitoring (by changing analysis procedure sequentially) have been proposed to achieve these objectives to some degree. We propose to sequentially monitor response-adaptive randomized clinical trials and study their properties. We prove that the sequential test statistics of the new procedure converge to a Brownian motion in distribution. Further, we show that the sequential test statistics asymptotically satisfy the canonical joint distribution defined by C. Jennison and B. W. Turnbull [Group sequential methods with applications to clinical trials. FL.: Chapman and Hall (2000; Zbl 0934.62078)]. Therefore, type I errors and other objectives can be achieved theoretically by selecting appropriate boundaries. These results open a door to sequentially monitor response-adaptive randomized clinical trials in practice. We can also observe from the simulation studies that the proposed procedure brings together the advantages of both techniques, in dealing with power, total sample size and total failure numbers, while keeping the type I error. In addition, we illustrate the characteristics of the proposed procedure by redesigning a well-known clinical trial of maternal-infant HIV transmission.

MSC:

62L05 Sequential statistical design
60F05 Central limit and other weak theorems
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C50 Medical applications (general)
62L10 Sequential statistical analysis

Citations:

Zbl 0934.62078
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] Andersen, J. (1996). Clinical trials designs-made to order. J. Biopharm. Statist. 6 515-522.
[2] Andersen, K. M. (2007). Optimal spending functions for asymmetric group sequential designs. Biom. J. 49 337-345.
[3] Armitage, P. (1957). Restricted sequential procedures. Biometrika 44 9-26. JSTOR: · Zbl 0082.35005
[4] Armitage, P. (1975). Sequential Medical Trials . Blackwell, Oxford.
[5] Athreya, 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. · Zbl 0185.46103
[6] Bai, Z. D. and Hu, F. (2005). Asymptotics in randomized urn models. Ann. Appl. Probab. 15 914-940. · Zbl 1059.62111
[7] Berry, D. A. (2005). Introduction to Bayesian methods III: Use and interpretation of Bayesian tools in design and analysis. Clinical Trials 2 295-300.
[8] Coad, D. S. and Rosenberger, W. F. (1999). A comparison of the randomized play-the-winner rule and the triangular test for clinical trials with binary responses. Stat. Med. 18 761-769.
[9] Cheng, Y. and Shen, Y. (2005). Bayesian adaptive designs for clinical trials. Biometrika 92 633-646. · Zbl 1152.62387
[10] Connor, E. M., Sperling, R. S., Gelber, R., Kiselev, P., Scott, G., O’Sullivan, M. J., VanDyke, R., Bey, M., Shearer, W., Jacobson, R. L., Jimenez, E., O’Neill, E., Bazin, B., Delfraissy, J. F., Culname, M., Coombs, R., Elkins, M., Moye, J., Stratton, P. and Balsley, J. (1994). Reduction of maternal-infant transmission of human immunodeficiency virus type I with zidovudine treatment. The New England Journal of Medicine 331 1173-1180.
[11] DeMets, D. L. (2006). Futility approaches to interim monitoirng by data monitoring committees. Clinical Trials 3 522-529.
[12] Eisele, J. and Woodroofe, M. (1995). Central limit theorems for doubly adaptive biased coin designs. Ann. Statist. 23 234-254. · Zbl 0835.62068
[13] Ethier, S. N. and Kurts, T. G. (1986). Markov Processes: Characterization and Convergence . Wiley, New York. · Zbl 0592.60049
[14] Gwise, T. E., Hu, J. and Hu, F. (2008). Optimal biased coins for two-arm clinical trials. Stat. Interface 1 125-135. · Zbl 1230.62097
[15] Hayre, L. S. (1979). Two-population sequential tests with three hypotheses. Biometrika 66 465-474. JSTOR: · Zbl 0418.62062
[16] Hall, P. and Heyde, C. C. (1980). Martingale Limit Theory and Its Application . Academic Press, New York. · Zbl 0462.60045
[17] Hu, F. and Rosenberger, W. F. (2003). Optimality, variability, power: Evaluating response-adaptive randomization procedures for treatment comparisons. J. Amer. Statist. Assoc. 98 671-678. · Zbl 1040.62102
[18] Hu, F. and Rosenberger, W. F. (2006). The Theory of Response-Adaptive Randomization in Clinical Trials . Wiley, New York. · Zbl 1111.62107
[19] Hu, F., Rosenberger, W. F. and Zhang, L. (2006). Asymptotically best response-adaptive randomization procedures. J. Statist. Plann. Inference 136 1911-1922. · Zbl 1113.62089
[20] Hu, F. and Zhang, L. X. (2004). Asymptotic properties of doubly adaptive biased coin designs for multi-treatment clinical trials. Ann. Statist. 32 268-301. · Zbl 1105.62381
[21] Hu, F., Zhang, L. X. and He, X. (2009). Efficient randomized adaptive designs. Ann. Statist. 37 2543-2560. · Zbl 1171.62043
[22] Ivanova, A. V. (2003). A play-the-winner type urn model with reduced variability. Metrika 58 1-13. · Zbl 1019.62076
[23] Jennison, C. and Turnbull, B. W. (2000). Group Sequential Methods With Applications to Clinical Trials . Chapman and Hall, Boca Raton, FL.. · Zbl 0934.62078
[24] Lan, K. and DeMets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70 659-663. JSTOR: · Zbl 0543.62059
[25] Lewis, R. J., Lipsky, A. M. and Berry, D. A. (2007). Bayesian decision-theoretic group sequential clinical trial design based on a quadratic loss function: A frequentist evaluation. Clinical Trials 4 5-14. · Zbl 0825.62863
[26] O’Brien, P. C. and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35 549-556.
[27] Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64 191-199.
[28] Pocock, S. J. (1982). Interim analyses for randomized clinical trials: The group sequential approach. Biometrics 38 153-162.
[29] Proschan, M. A., Lan, K. and Wittes, J. T. (2006). Statistical Monitoring of Clinical Trials, A Unified Approach . Springer, New York. · Zbl 1121.62098
[30] Robbins, H. (1952). Some aspects of the sequential design of experiments. Bull. Amer. Math. Soc. 58 527-535. · Zbl 0049.37009
[31] Rosenberger, W. F. and Hu, F. (2004). Maximizing power and minimizing treatment failures in clinical trials. Clinical Trials 1 141-147.
[32] Rosenberger, W. F. and Lachin, J. M. (2002). Randomization in Clinical Trials: Theory and Practice . Wiley, New York. · Zbl 1007.62091
[33] Rosenberger, W. F., Stallard, N., Ivanova, A., Harper, C. N. and Ricks, M. L. (2001). Optimal adaptive designs for binary response trials. Biometrics 57 909-913. JSTOR: · Zbl 1209.62181
[34] Rout, C. C., Rocke, D. A., Levin, L., Gouws, E. and Reddy, D. (1993). A reevaluation of the role of crystalloid preload in the prevention of hypotension associated with apinal anesthesia for elective cesarean section. Anesthesiology 79 262-269.
[35] 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. J. Amer. Statist. Assoc. 89 768-776.
[36] Thompson, W. R. (1933). On the likelihood that one unknown probability exceeds another in the review of the evidence of the two samples. Biometrika 25 275-294. · JFM 59.1159.03
[37] Tymofyeyev, Y., Rosenberger, W. F. and Hu, F. (2007). Implementing optimal allocation in sequential binary response experiments. J. Amer. Statist. Assoc. 102 224-234. · Zbl 1284.62496
[38] Wald, A. (1947). Sequential Analysis . Wiley, New York. · Zbl 0029.15805
[39] Wathen, J. K. and Thall, P. F. (2008). Bayesian adaptive model selection for optimizing group sequential clinical trials. Statistics in Medicine 27 5586-5604.
[40] Wei, L. J. and Durham, S. (1978). The randomized play-the-winner rule in medical trials. J. Amer. Statist. Assoc. 73 840-843. · Zbl 0391.62076
[41] Zelen, M. (1969). Play the winner and the controlled clinical trial. J. Amer. Statist. Assoc. 64 131-146. JSTOR:
[42] Zhang, L. and Rosenberger, W. F. (2006). Response-adaptive randomization for clinical trials with continuous outcomes. Biometrics 62 562-569. · Zbl 1097.62139
[43] Zhang, L. X., Hu, F. and Cheung, S. H. (2006). Asymptotic theorems of sequential estimation-adjusted urn models. Ann. Appl. Probab. 16 340-369. · Zbl 1090.62084
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.